%%%!!%%!?%%!%?!%%%!!%%%%%%%%!?%!%%%!%!?!!?%!%%%%%%%%%!%?%!!%!!!%%%!%!?!!%!%!?%!%%!!%?%%%%!%?%!%!%%%!%%?%%!!?!%%%!!!!?%!!%%?%%%%!%%%!%%%??%%%?!!?%%?%%%!%%!%%!!%!!%?!%!%?%?!%%!%%%!%%%?!!!!%%%%%?%?%%!%?%?%%???!!?%%%%!!?%?!%!!%%?!!%%!%?%%?%%!!%%?%%!!%?%%!%?!%%%%!?%?!%%%!%!!%!%!?!%%%%!%!%%%!%%%%%!!%!%!!%%!?%?!%!%!!?%%%?!%!!!!?!!!?!%%%!!!!!!%?%!!?%?!!%!??%?%%?!!!!%%%!!%%%%!%?%%!%!%%!!???%%!%%%!%!%!%%!?%%!?%%%!%!!%?%!!%%%!%%!%?%?!!%%?%%%%!%!!%%%%?%%!!??%%%?%%?!%%!%%?!?!%%!!?%!%!!%!!%!!!!?!%%?!!?%%?%!%!?%!%%%!?%?%%%?%!%?%%!!%?%!!%??%%!%?%!!%?%%%!%%%%?%%%%?%%?%%%%%!%%%%!%?%!!%%!%!%%?%!%%%%!%%!%%?!%?%!!!!?!%?!!??!?%%%%!!%?!%!!?%!%%%!%%%!%??%%%%%%?%%%!%!%%%%%!%!%%%%%%!!%!!%%!!?%?!!%!!%?%!!?%!%!%%%%!%%?!%%%?!%!?!%??%%%!!%?%%%%!%%!!%!!%!?%%!?!%%?!!%?!%%?%%%%%!?!%%%%??!!!%%!!?!!%%%?%%%!%!%?%?%?%!%!%!!!%!!!%?%!%!!%%!!%%%%%%!!!??%!!%%!%%%!!%!!%!%%!%%?!%%%%%%?%%%%%%!%?%!?!%!?!%%!%!!!?%%!!%%%!%!%%!%?!?%%?!!%%%!?!!?!???%?%?%%%%?!%?!%%%%%!%%!!%?%%?!!!%%!!%%%?%%%!?!!%!%?%%%%!%?%!!?%%!%%??%!%%%%!%!%!%!?%%%%%!%!%%!%%%%%!%!%!!%!!%%!??!?!%!%%%??!!?!%%!?%%?!!%%%?!?%%?%%?%?%!%%%%!!?%%?!%!!%!%?%%%%?%%%!%%%%!!%!%!%%!%!%???!%%%!%?%%!!%%%?%%?%!!%!%%!%?%!%%?%%!?!?%!!%%%!%%%?!??%?%%!%%%!%%!?!?%!!%?%!%!%!!%?%%??!!%!%?%?%?%?!?%%!%%???%??%!!?!%!%%%%%%%%%!%!!!%%%%!?%%%?%!!!!!!!%%%%%%%!%!%%%!!!%??%!!%%!?%?%%%%?%%!!%%%!%%!?%%%!?%?!%%%!%!!%%%%?%%%!!!%%%%%!!%!%!%?%%%!%?%?!!!%%?!%%%?%!%%%%?!%%!%!!%!!%!?%!%%%%???!%!?%!?%%%%%%%!??!%!!!!???%%%%!!%?%?%%!!%%!%!!%%?!!%%?????!!?%!%!?!!!%%%%%%%?!%%%%%?!??%%?!%%%?%!!!%%!%!%?%!?%!!!%%!?%%%?%!%!%!!%%%%?%%?!%?!?!%%!!!!%%%%%%%!%%?%%?!%%%?%%!%%%%!%!?!%????!%%??%%%!!%!%%?!%?%%!!?!%%!%%%%!???%%%!%%%%%?%?!%%%!?!%!%!!%%%%%%%%%!?!%%!%%?!!%????!%%%!!%?%!!%!??!?!??%??!??%%!%%?%?%%!%?%!!!%%%%!%%%!%%!%%!?%!%!%!%!!%%!%%%%%%%%%!!%%%!%%???!!%%%%!!?!!!%!%?!!%%!!!?!%!%!%?!!%!%%?%%%%!%????!%!!%%%!?!%%%!!??%%!!??%%!!%!?%%%%?!!!%%%%%%!!?!!!%%%!%?%%%!%!!!?%%%?!%%?!%!%%%!%%%%!!!%?%%%!!!?%%%!?!?!%%%!?!?!%!?%!%?%%!%?!%%!!%!%??%?!%%%%!%?!??!??!%!%?%%??!%?%!!!!!%%!%%%%!%?%??%%??%%%%%%%%%?!!!%%%%!%??%!%!?%?!!%?%?%?%!!%?!?%!!%!?!?%%%%!%%??%%%!%%%!%???%%!?%?!%!?%!%%%%!!%!%??%!!!!!%!!!!%!?%?!%%%!??%?%?!!!!%%?%!%%!%!%%?!%%%%%!%??%%!%?%??!?!%!%%%%!%%!%!%%!%%?!%!!!%%??%!!?%%%%?%!!!%!!%!%!%!!!%!%!%!%?%%!%?%%?%%%!%!%!%%%!!%?!%%!%!?!!!%%!!%%%%?%%!?%%!!%!%%?!?!!!?!%%!!%??%%!!%%%%!!%%!%%%!?%!%%!!%%%%%!!?%!%!%%%%%%!%%!%%%%!!%%?%%!%!!!%!!%%%!?%!%%%!!%!%%%%!?!!%%%?!%%!?!!%?%!?%%???%%!%!%%%!!%%%%%?%%%%%%??!%%%!!!%%%%!%%%!%%?!!!%!!%?%!%?%%%?!%?%%?!!%%?%!!%??!%?%!!!!%?%%%%%?!%?%!%!?%?%!%?!%%!?%!!%%!!%!!%%%%?!?%!?!%!%%%%!%?%%!%!%%%?!%%%!?%!%?!%%%!%??%?%!%%%%%?!%!%%%!%!%%%??!!%?%!%?!!?!!!%?!%%?!%!???!!!!%%%?%%!%!%%%?!?%%%?!%??!%!?%!!!!!??%!!!%!?%%?!!%?!!%!%%?!%?!!!!%?!!%?%!%%!%!%%%%?%%!!!!!!%%?%%!!%%%!!%%!!!%!!%?%!!%!!%%%!!?%!?%!%!%%!%%%%%!%?%!%!!%!!!?!?!%%%%?%??!!!%!?!??!%!%!%!%!%!%!%!?%!?!!%%%%%%?!%%%??!!?%!?%!%%%%%%!%!%?!%%?%!%%%%%?!%!!%%%?%?%%!!?!%%?%%!%%!?!!!!!%!!?%!!%?%?%%?%!%!%%%%%%%%%!%!!%?%!%%%%%%!!%%!?!%?%?!!%%%!%%?!!!????%!?%?!%%!?!%!%%%%?%%%%%%!!%%%!!%%?%!?!%%!%?%!%!%?!%%!???%%?!%!%!?!!%%!%%!%%!%%!!%!!%%%!%!!?!%!!%!!!!%%%%%%!%!?!%!%%??!!%%%??%!??%%%?!!%!%!%!!%%%%!%%!%%%!?%%%%!%?!%%??!?!%%%!%%%%%!?%%?%%!!!!%%!!!!??!!%!?!?%?%%??!%%!%%!!%?%%?!?%!%!%%%%!%%???%%%%%%%?!%%!%!!!?%!%!??%?!?!%%%%!%%!!!%%?%%%%!!!%%%!%%!%%?%%%!!%?!%%?%!?!!%!%%%!!%%%%%%!%?!!%!%%??%%!?%?%%%%?%%%!%%%?%%%%?%!%%%!%!%%?%!%%!%!!%%%%%!!!!!%%?%!?%?%!%!!!%%%!%!%%?!%%!?%%%?%?%?%!%%%?%!%!?%%%!!!%%!%%?!%%!%%%%%!!?!%!!%!%?%!?%!!!%%%%!%!%!%%%??%%!!%%%%%%%!?%?!?%!%!%%%?%!%??%?%?%!%%!!%%%!!%!!%%%!?!?%%?%!!%!%!!?%%?!!%!%!!!!?!?%!?!!%%%!%!?!??!%%!?%%%%!%%%%%%%!??!%?%%%!%%!%%!%%!%%!?%?!%%!%?!!%!??!!!%!!?!!!%%!%!%%!%%%%%%%%!%%?%%%%!%!!!?!!!%?%%%%!%!%%%%?!?!!!!?%%%?!%!!!!!%??%!%%%!%!%%!!%%?%%%!%!%%%?%%%?%%%%%!%%%?!%%?%%%!!?%%%?!?%!%%!!%?%%?!?%?%?%%%%%!!%?!%%%%%%!?%%!%%%!%?%!!%%%?!%!%%!%%%?%?%?%%!%?%%!!%!%!!%%!%%%!%%%?%?%!%%!%!!%%!%%!!%%%%!%!%?%!!!%?%%%%%%%??%?%%%%%!!?%%!%%%!%%?!!!!%%%!!%!%!%%%?%%%!!?%%?!!!%%!%!?!!!!%%!!??%!?!?!!!%??%%?%?%?!%!!%%%%%?!%%?!!??%!!?!?%!?%%!???%!?%%%?%!!%%%%%%%!%%!%!!%?%%??%%%!%!%!%%?%!%!%%%??!!%%%%?%%%%!?!!??%%!%%!%!%%%!!%%!%!!%?%%?%%%%%!%!%%%%%!!%!?!!%%%%%%%%%!%%%%%%%%%!%%%%%%?!%!%!%!%%%?%%%!%!%%!?%??!?%%%?!?%??%%%%%%%%?!%%?!%%!%%!!%%!%%%!%!%!%!%!!?%%%%%!!?!%?%!!%?!!?!!%!!?!%%!!!%!?%%%!%%%%?!???%%%!?%%%%?%!%%!%!???%!%!%!!%%%%??!?%!%!!!!!%!%%!?%!!%%%!!%%!%%?!!%?%!!!!!?%%%%%%%!!%!%!?%!%!%%%%%%!!?!!%%!!???!%%?%%?%!%?!%!!%%%%%?!%!%%%!!%!?!!%%!%%?!%?%%%%%%!%?%!!%%%!!%%%!!!%%!%!%%%!!%%%%!!%!%%!?!?!!!?%?!%%%!!!!%!%!%%?%!%!?%!!!!!!%?!??%%%?%?!%?%%!?%?%!%!!%%%%!!?!!!!?%!%!!!%?!!?%%%!?%!?%?!%%%%%!%?!%%%?%%!!!??!%%!!?!!%?%%?%?!?!!%?%%?%%?!??%!%!!!!!!%%%%%%!!%%%%%!%!!!%?%?!!!!%!%%?!!?%%%%!%%!!%%%!!?!%!%?%%%!%%!!!!?%!%!%%%%!%!?%!%!!!!%%?%!%%%%!!%!%%?%!%%!%%%%!%!%%%%!%?%%%%!!%!?!!?!%?%%%%?%%%%?%%?!%?!!!!!%!?%!%%%?!!!?!%!%??%%%!!??!%%?!%!%!%?!%%?%%!?%%%!%%!%%%!?!%%!!%%%?%%%!!?%!%%%!!?!?%%%%%%%%!%%%%!!!%%%%%!%%?%?%%!?!%%?%?!?%%%!%%?%%%%?%%%%!!???!?%%?%%%!!!%%%%?%??!!!???!%%!%!%%%?%%!%!!!%%%!%?!%!!!%%%!!!??%%?%!!%?%%!%%%?!%%?%!%%?!!%%!!%%%%%%!?!%!!?%??%??%!%!%!??%!?!%%!!%?%!%%%?!!!!!!%%?!%!%%%?%%?%!!%!%!%%!%!??%%%%%%%%%!!%??%%%!!!?!%?!%?%!%?!%%!!%?%!?%%%!%%%!!!%?%%%!%!!!!!%%%!?!!?!%%??%%!%?!%?%%%%?%%!?!%%!!%%%?!%%?!!!!?!!!%!%?!!!%%%!!!?%?%!?!%%!%!!!%!%?%!%%!!!!?%?!!!%%%%!!%%!%!%%%?%!!%%!%!%%%??%%!?%%!?%%?!%!%!%%!?!!!?!%!%?!!!%%!%!%%%%!%??%!%?%%!%%!%%!%%!%!??!???%%%!!%%%%%%%?!!%!!%!!!%?%%%%!!%%%!?!?!%!!!%?%!?%?%%?%%!%%!%?!!??!%%%?%!!%?!%!!!!?%!%??%%!%%%%%%!%!%!?!%%%!%%%?!%!?%!%!?!!%%?%%%!%?%!%!?!%!!%?!%%?!%%%%%!!%!%%!!!%%!!%%%!%?!%!!?%!!!?%?%!%?%%!%!%!%!%!!!?%!%%%!%!!?%!!!%%%!%%%%?!?%!%%%%!%!?%!%!%%?%%%!%%%?!%%?%?%%!%?%!!!%%?!!%!%%?%%%!%?%%%!%!?%%%!!?%!?%!?%%!!%%!?%%!!?%!!%%%?!%!%!!%!!!%!%!!%!%!%%%!!?!%!%?%%!?!%!%!%%!%%?!?!!!%%??!!!%!%!!!?%!%%!%%!??%!!%%!%!????%!!%%%%?%?%!?!%?%%%?%!??%?%!!?%%!??!!!!!?%?!%!%!%?%!%%!!%!%!!!!%%!!%?%%%?%?!!!%?!!%%!%%?!%%%?!?%?!%!%?%?%%!!?%%%???%%%!%%%?%%%%!%?%?%%??!!!!!%!%%%%%%%%!!!!%%%%%?!!?!%!!!%!!%%%!!%%!!%%%?!!!%!!!!!!%!%!?%?!%!!?!???%%!!%%!%%??%%!%!%!%%%%!%%%!!?!%?!!%!%!%%%?!%%?!?%%%!!%!%%!!%%!!?!?%%!%!!!?!%%!?%%!%!!%!!!!!?%%%%%%%%%!%%%%%%%%?!%!!%%!!%!!!!%!%?%%%?!!%!%%%%!%!?!!!??!%!%%?%!%%%!%??!%%%%%!%%!!%!!??%%%%???%?!%%%%?%!!?!%!%%%%?%%!%%%%%%%%%%%?%%!!?%!?%!!!?%%%%%!!!?%%%!%?!%%%?%!?%!%??!??%%!%%?!%!%%!!%?!!!!!%%%?%%%?%%%?%!?%%%%!!!%?%%??!!?!?%%!??%!%%!!!%%!%!%%!??%%?%%!%!%!!%!%%%!%%%%%%!%%%%????%%%%!%!%%!%%!!%%%?!%?!!%%%%!%!%%!%?%%!!%%?!%!%?%!!!!%!%%??%%!??!!%%%?%?!%%%!!%%?%!%!!?%%?%!!%%!!!%%%!!%%%%!%%!%?!%?!?%%!%%%!!!!%!?%%%!%%%!%!!!!%?%!%!?!!%!??%?%%!%!!%%%%!%!!!%%%?????!!!%%%??%%!%%%%!%%!!%%%!%%?%%!%!!%%!%?%!!%!!%?%%%!!!%!?%%?!?!!!!%%%?%!!!?!%?!!%%!%%!%??!!%%%%%%??%%%%!!%%%!!!?%?!%!%%!!%%%%??%%!%%!%%%%!!%%%!!%%!?!%%!!?%%!!!%%%!%!%%%%??%!???%%%%%%%%?%%%%!%%?!!%!!%!?!%%%%%%?!%%%%?!%%%%!!!%?%?%!?%%%!%!?!%%%%%%%%%!%!!%!%!%%%%%!%!!%%%%%%!!!!?%%!%?%?!?%%!!?!%%??!%%%%%!!!?!!%%!%%%%?%?!%%%?!!%!!?%?%%!!%%!%%!!?!!%?%?%?%%?%!!%%%%?%%%!%%!!?%!!!!%????!!%%%!!%%%?!!%!%%?%???%?%!%!%%!!!%%?!!%!%!!%%?!%%%!!!!!%!%!%?!!%!!!%?!!%%!%%!?!%%?%%!%!%???!!!!%!%%%%%!!!%%%%?%%?!?%!!?!%!%%%!!!!%%!?!%%%%!%!!!%%%!%!!%?!!%!%%?!%%%??%%?%!%!%?%!!%?!?!?%%!%?!!??%%!!%%!%!?!!?!%%!!%?%%%!%%%%!!%?!%%%!!!!%??%!??%!%!!!!%!!%!%!%%%%%!%?!!%?!!%%%?!!?%!!!%!!%!!?%!!?%%%?!!%!!%%!%%!%?!!!%%%!!?%%!!%%%?%!??!!!%%%%%?%!%!%%%?%?!?%%%?!!!!!%!%%%?!!%%?%!!!?%!?%%%%%%!%!%!!!%??!%!%?!%%?%!%%%%%%%?!!%!%%%%%%%%!?%%?%?%!%?%!%!%%%!%%!!%!%?%!%%!%!%?%!%%%%%%??%%?!!!!%%?%%??!%?%!%!!??!!!?!?%%%?!?%?%%%%??!???%%?%%%%!%?%!%%!%%?!%?%!%!!!%!!%!%%!!!%%!%!%%!%%?!!%%%%%%?!!??%%%%!%!%%%?%!?%%%?%!!??%%!%?%%!%!!!%!%%?!%!?%%!??%!%!!%%!!??!%%%!%%%!%?%!%!!!%!%%!!%%%%?%%%%%!!??!!%%!%%!%!%%%!?%%!%%%?!%%%!?!?%!%%%%%!%%!!%!%??%%?!?!?%%!!%!!%%%!%!!%%%%%!%?%%!!!%%!?!%!%!?%%!%%!%!?%%%?%!%?%!?%!?!%?!!!!?!?%!%!%%%%%%?%?%?!!%%%%?%!%!%!!%%!%%!!%%!!?%%?!%!%%%!?%%%!!%!?%%!%%!%%%%%!%%!%!!!%!%%!!!?%%!%%!%?!?%?%?!?%%%%%%%!?!!%!%%%!!%!!?%!?%%%!%!!!!!!%%!?%!!%%!%?!%%!%%!%!!%!%!%%%??!%!%%%%??%!%?%!%%%!%%!%%%?%%%%?%%%?%%%!%?!!%%!!%!!%%%%%%%!%%%%%?%%%?!%!%!%?%!?%%%?%!%?%%%!!%%%%%?!!!%%!!%%!!!%%!%!%%!!!%!%%%!!!%%?%%?%%!%?%%%%%%!%%%%!%%%%%!!%%?!?!%%%!%%??%!!?%!%!?!!!%%!!%!!%%%%!!!?%%!%%%%!%%?!?%??!%!%?%%!!%!%%%!%!%?%!!%!!%%?!%!%!%!!?%?%!%%!%%%?%?%!%??%?!%!!%%%%!%!%%?%!?%%!%!!%!%%!%%%!%%%%%%!?!!!??%%?!!%!?%%%%%%?%%%?%%!!%!%%%%?%%%!%?!!%?!%!%?!%!%!%%!%???!!%!!%!!!%%%!%%?%%?!%!%%!%!%!%%!%%!%%!?!??!%!%%!%?%?!!%!!%%%%%!!???%?%%!%?%%!!!%!!!%%?!%%%!!%%!!%!%%%!!!!?!%?%!?%%!!%%??%?!%%?%%!%%!??!!%?%%%%%%?%!!?%??%%!??%!!!!?%%%%!%?%%?!%%%!!%%!%%%!%%!%%%!!%%!%?%%!%%%%%%%!%?%%%%%!%?%!%%%!%?%!!!%%%!%!%!!%%%%!!%!??%?%%!!%!??%?%%!!%!%%?!!!!!!!???%!%%?%%!!?%!?%!??!!!!!??!%?!!%??%%%!!%%%?!%!%%?%%%%%%!%%!%%%?%!%%?%!%%?%?%?!%%!%%%!%!?!!!%!%%%%%?%%?%?%!%%%%?%%%?%%%%?!%???%%%%?%%??%%%%%%!%!?!?%!!!%%%%%!%%%%!%!!%!!%!%!%%%%?!!%?%??!?%%%!?%!?%%%!%%!!%!!%%%%?!????%%%?%?%%%%%!?%%%%%%!?%%?%%!?%%%!!!!!!!%%!???!!%!!%!!%!!%!!?%!!%?%?%!!!?!%!!%!%?%%%%%?%!%%!%%%%?%?!!%!!%%%%?%%%?!%%%%%!%!!%?!%%%?!!!?%!%%%%%%%?%?%!%%?%%!!?!!?!%!???%?!!!%%%%%%%%%!!?%?%%%%?!%!%?!!!%?%%%%%!%%%%!%!%%?%%%%%%!!!??%!!%!?!%%%!!%%%%%%?%%%!!%%%%%%%%!%%!!%?%!!%%%%?%%!!%%!!%!?!??%!%%!%?!!?!?!?%?%!%?!%%%?%!%%%%%!!!!!?!%%%%!!%!%%%!%%%%%%?%%%%!%?%%!%!!%!%%%%%%%!?%!?!%%!!?!%%%!?%%?%%%%??%%!?%!%!%!?!%?!!%%%?%%%%%????%%!!%%%%?!??!%%!?%!!!!%%?%!?!!!!%%?!!??%%%%?%%%%%%!!!!%%%%!?%?%%%?%%!%?!!!!?%!!!!!!%%%!%!?%!!?!!%%%%%?!%!!%%?!!!!%%!!!!?%%%?!!!%%!?%!?!%?!!?%!%%?!!?%%?%%!!?%!%?!!%%!!?!%%?!?!%%%?%%!%!?%!???%%%!%?%!%!!%?%%%??%!!%%%%%???%!?%!%!%%!%?!?!%?%%%%!?!!!?%%!!?%%%!%!%%!?%%!!!%!!%%%!%%?%!?!%%!!!!%?!!!?%!!%!%!%%%!%%%%%%%!%%%!?%!%!%!%!%%!!!?!%!%%%!?%?%!%%!%%%%%%%%!?%%!%%!%%%%%?%%!%!%!%%%%!!!?%!????!%%%%?%?%%?%%!!?%%!%%%!?!%!%??!!%%%%!?!%?%%!!%%!%!%?!!%%?%%%%!!%!%!%!%%!%%%??%!%%?%%%%%%%!%%%!%%??%%?%?%!%!!%%%%!%%?!%%!%%%?!%%%%%%%??!!%!%!%???%!%%!?!%?!!!%!!??!%!%!??%%%%%!?!%%%%%%%%%!%!?%?%%!%??%??!%?%%%%%%?%%%!?!!%!%%%!%%%%%!%!%?%???!%!!?!%???%%!%!%!!!!!!%%!?%!%!%%?!!%!!!!?!%!!%?!%!%!!?!?!%%!%%%!%?!!?%%!!%%%%%%%%!%%?%%%%!?%%!%?!!%%?%!!!?!!%?!!!??%%%!%??!%%%!?%%??%?!!%!!!%!!%%%!!%!!?!%!%%%%?!%?!?%!!?%%%!!%%!%!%?%??!%%%!!%%??!!!?%%%%%%!%%%!%%%%?%!%?%??!%%%?!%%!%%%%%%%%%%!!%!%%%%?%%!!!%!!!!!%%%?%%!!%!!?%?%%!%%%!?%!?!!%!%%!!%%?!!%!%%!!!%!!!%?%!!%!%!!%%%%!?!!%?!%???%%!!%%!?%??!%%!!%%%?!%%%%%%%!!%%%%!%%!!%?%%?%?%?%!%%%?%?!%!%%%!%%!?%!%%!?%!%%%!%%%%%%%%%%%%?!%!%%%??!!!!!%%%!%!!%?%%!%%%?%%!??%?!%%%!%%!!!%!!%%%!%%!%!!?!%%%???!!%%%!%??%?!%?!!%%!?!!!!%!!%!?%%%!!?%%%!%%!%?%%?%%%!%!!%!%%%%%%!%%!?%%!%%%!%!%!?!?%!%!%%%!%%%?%%%%!?%?!!!%%?%%%!%!%?%!%!!??!%%%!%%%!?!%?!!!!%%!%%%%?%!?!?%!%!!?%%%!%%%?%!!%?%!!!!%!?%%%%%!!!??%!!?!!%?%%%!!!%!%???%!?!?%%%%?%!!%?%%%?%%%?!!%%%%!?%%!!?!?!?%%%?!!?%%%%!?%%%%!!%!!?%%%%%%?%%%%%?%%%!%!%!%!?%!%!!%?%!?%%??!!!%%%%!?%%!%?%%%%!%%!??%%!!%%%?%%%%!!?%%%!%%!%??!%!?%%!?%%!%%%!%!!!%%!%!!!!!%%%!?%!!%!%%%!!!!%??%!%%!%?!%?!%!%!%%?!?!!!!!?%%!%%%%%!%!!!%??%%%!?%!%%%?%%!%%?%%%!%!?!!%%%%%%??%?%%?!?!%?!?%%!%!%%!?!!%!!%%%%%!%!%%%%?!?%!?%!%!!%!!%%!%%%%%%??!%%!!%%?!%!!!%!!%!%?!%!!!!%?!%!%%%%%%!%%!!%%!!%%?!%!!?!?%%?!!!??%!%????%!%!%%%?!!%!!!%!??%!%%%%?%%%?%%!%!?%%!%!%!%%%%?%?%?%%!%%!%!!!%%%%%%%!?!%?%%%%%?%?!%%?%!!%%?!!?!?!%%!%%!%%%?%%%%%!%%?%!%!%!%%%%!%?!%%!%%%%%%!%!!%%?!!!?!%?%!?!?!%?%%!!%%!!?%%!%%%%%!%%!%%%!%!!%!??!!!%%%%%%?%%!?%%%!%%%!!%%%%!!%%!%%%%%%%%?%?%??!!%%!%?!%%%%%!!%?%%%%%!%%%?!?!!!?%%%%?%%?%%!!?!%!%%%%%?%!?%%%%!%%%%!%!%%%%??!!!%%%%%%%%?!!!!%!%%?!!?%!!!?!??%!%%%?%%!%????%%!?%%!%%!!%%!!?!!%?%?%%!!!!!?%%%%!%!!%%%%%?%%%%!!%!!!%%%!!%?%%%%%%%%!?%?%!%%%%!%!!%!%!%!!%%?%%%%%%!%%%!?%!!?%?%!%%%!!?!%!%%%%%%?%%%%%%%%%?%%?!?%%!?%%!%!??!?!?%!!!%!%%!%%%%%!%%%?%??!%!!%!!?%?%!%?%?%%?%%%%%%%%%%%!?!!%?!!!%%%%%%!!??%?%!!!!%?!!%?!%%%%?!%%?%%!%!%?!!!?!%%%?%%?!?%!%!!!%!%!!!%%%%!!!%?!%!!%%%%%%!%%!%!!!%%%%%%%??%!?%%%??!!?!!%?!?%!!!%!%!!%!%%%%!%!%%%!%%!%%?!%?%%?!%??%!%?%!%!?%%?!%%?%?%%!?%%?%%!!!%?%!?%?%?%!%%!%%!!%!%%%%!%%%%%?!!!%!%!?%%??!%%%%!!!?!%%%!!%!!!!%%!??!%%?!!%%%??!!!!%%?%%%%??!%%%?!%!??!!%%!?!!%%?%%%%%!?!!%!%%%!%!%!%?%!%%?%?%%%%%%%%%!%%!?%%!%?%!?!!?!%!%%!?%?!%!?%%!%%!?!%%%%%%%%%%%?!!!%%?%%!%%%%!!%%!!%%!%?%%!?!?%!?%??!!%!!!!?%!!%%??!!!%???%!?%?%%%%%%!?!!%%!%%%%!!%!%??%%%?%!!!%?%%?!!%!%%%%%!%!%%%!%!?%%%!?!????%%!%?%%%%?%!%!!?%?!%?%%?%%!?%%!%%?%!%?%%!!?%%%%%%!!%!%%%!!!!%%%?%!%%%%%?%%%%?!!%%!!%!%%%%?%%%%?!!!!!%!%%!%%!%%!%%!??!!!!!%%%%%!!?!%!?!%!!%%%%?%!%%%%%%!%!!%%?!%%?%?%%!%!!??%%%%%!%%!!!!%!!?!%?%%?!%?!%%%%%%!?%%!%!?!?!%%%?%%!!?%%%!%%!%%%%!%%!%%!?%%!!%!%?!%%%%?%?!??%!!%%%!%?!%%%%%%%?!%%?%%%%%??!?!%!%%%!!!!%?%%%!!%!!%!??!!!!%%%!!%%%%%%%!%!!!%!?%%?%!%!%!%%!!!%%?%%%?!%!?%%!%%?!%!%%!%!!!!!%?%?%!?%??%!%!!%%?!%%!%%%!!%!%?%%%!?%?!?%!%%%?!%%%%!!%!%!!!%!%%%%%!%%!%%?%%?%%%%!!?%%!?!!%!!!!!?%?%%!?!!!!%?%!?!%%!!%%%%?%%!!!!%%%!%%?!!?%!!??!%?%??%?!!!!!%%%?!%!%?%!%!%%!!%?!%??%%?!?!%%?%!!!%%??!%%!%%!!?%??%%%?%%!!!!?%%%!!!%%%!?%!!!%%!!%!%!%%%!%%!%?%%!!!!!!%%?!!?%!!??%%%%%?!%!!%%!!?%%%!%!%!%!%!%%%?%%?%?%!?%%!?!!%??!%!%!%!%%%!!%%%%%%!%%?%%%??%%%?%?!%%%!%%%%%%%%%?!%!%??%!?!%%%%!???!?%%%?!!?%%!%%%!!%?%%%%%???%%??!!%%!%!%%%%%%%??!%!%%!%%!%%?%!%!??%!%%?%!!!!!%!%!!?!%%!%%?!?!%%%!%%%!%!?%%?%%?!!!%%%%%!%!!%%!?%?!%!!%!%%%!%!%%%!?!%!%!%%%%!!%!!%!%?!!!%%%%%%%!%!?%%%?!%!??!!%!%?!!%%!%%!%%%%%?%!?%%%%%%%!?%?%%%%%%?!?%%!!?!!??!?%!%%!%??%!%!!%!???!%?%%!?!%%!%?!!%??%%!?%%!?%%%!%%!%?%%%!%%!%!!%!!?%%%%!!?%%?!?%!%%!%%!%%%%!!%%!?!!%?!?!!%!%!!!!%!!?!%!%!%%!!%%%!??!!!%%!!%%?%!?%?%%!%%?%??!%?!%%?!%%%%%%%%%%%%%?%!%?%!%%%%%%!%!!!!!%%!!!%%!!!%?%!!!%!%%%%!!?%%?%%?%%!!%%!!%%?!%%?%%?%%!!%?%%!!!%%%%%!?!?!?%%?%!%%??!?!!%%%!%!!%!%!%%%%%!%%%!!!%%!%%%??%!!!%%!%!!%!!!!!!?%%?%?%!!%?!%%%!?%?%%!!%?!!%!!!%!%%!%??!!!!%%%%!?%%!!!?!!%%%!%%%?%!!%??%!%%%!%%!!%%??%?!%!??!%%!!!!!!?!%%!?!%??%%?%!%%!!%%%%!?!%!%%?%%%%!!%%%!!%!!%?%!!%?%!!?%!%%?%%!?%?%!%!%%!%%%%??%%?%%?%?!!%%%%%??%?%!??%%!?%%!!!%%%%%%??!?%?%%%!%%!!%%%%%%??%%%%%%%!%!%%!%%!%!!??!%?!%!%!%%%%!!%%?%%?!%???!!!?%%%%!%?%%!?%%!?%!%%%%??%?!%!?%!!%%?%%%!%%%!?%!%!!?!!!!%?!%%!!?%!?!!!!!?!!%?%?%%!%!!%%?!%?%%%!%%%%?!%%%?!%!!?%%??!%%%%!!!%!%!%?%%%%!!%%!!%%!%%?%%%?%!%%%%%%!?%%!%%!%!%%!!!!?!%!%!?%%?!??!%!%%??!%%!?%%?%%%%!?!!!%%%%!%?%%!%%%!%!%%%!!!?%%?%!%!!%%!%%%%%%%%?%%!%%%%!%!%%!%!!%???%%!%!!%%!!%%?%!!?!%!%!%?!!%?!!%%?!?%?%!?!%%%!%!%???%%%!%!!%%%%!%!?!%%%?!??%!!?!?%!?!%!%!??%%!%%!!%%!?%%!!!%%!!%%%!%!!!!%!%%%?!%%%!%%!?!%??%!!%%!!!!%%%%%%%?%!%%!%!?%%%?!!%%%!%?!%!?!!%!%%%!%!!%%!%%%?!%%%%%!%%%%!!%?!%%%%!%%%!!%?%!%!!%%?%?%%%!%%!?%?%?%!%%%!?!%%!%?%!?!!%!?%!!!%!?!???%!%%?%!!!%!!%%%?%!%!?!%!%%!?%%%%!?%!??%%??%%!!%%!!!!!!%?!%?!?%%!!!!!!!%%!%%%!!!!?%%?!?!!%%%??!%%??!!?%!%!!!%!!%%!!%%?%??%%%?%!?%%%%!!?%%%%%!?!%!?%?%%%%!?%!%%%%%%%!!%!?%?%!?%!%%%!%%%%%?!!%%%%!%%?!%!%?%!%??%!%?%?%%%!!%%!??%?%%!?%%?!%%%!?%%%%%!%%!%?%!%!!%??%?!%%%%%%?!%%?%%?!%!??%%%%%?!%?!%%%%%%%%%!%%?%??!!!!!%%%%!%!?%!%%%%?%!%%!?!!!!%%!?%!???%%%!%!!%%!%?%%%!?%%?%%?%!!%!!%%!?%??!!!%!!?%%%%???%%%!%%%%%!%!%%%!!%??!!%?%%%!??!%%%!!%%%%%%%?!%?!!!!%%!%!%%%!%%%?%%%%!!??%%!?%?%%%!?%%!!%%!%!!!!!%%%%!%%%%!%%%%?%%!!%!!?%%%%!!!%%%!?%%!?!!%?!!%%??%%%!%%%!!!%?%!%?%?%!?!%!%!%?%!%!?!%%!!?!!?!%?!%!!?!%%!!%!%%%!%%?%!!!!?%?!!%%%!%%!!%!??%?!%%?%?!?!!!!?%!%%?!?!%%%%?%!%%%%%!%!?!%%%!!!%?!!%??!%%%!%?%!!%%?%%%!%!!?%!%%%%!%!!%?!%!!%%!%?%%?%%%?%?%!??!%%%!%%%%%??!%?%!%?%%?%!?%%!%?!!%!%%%!!%%%!%%%%!%!?%%%%%??%%%!??%%!%!%%!%?%!%%%%?%%!!%%%%%!%%?%?%!%!!!%%%?!%!%%!%%!%%!!%%!%%%!?!?%?!%?%!%%!!?%%??!%%?%%%%!!%%%%%!?%!%?!%%%?%!!!%%!%?%%!%%%%!??%!%%%!%%!!!%%!??%!%!!%%%%%%?%%!%%!%%%?%%!?!!%%%??%?%%!%!?%%?%%!?%%%%%%%!%%%%%!?%!!!%?!?%!%!%!!%%%%!%!!!%%!%?!??%!?%%%!%!%?%%%!%?%%%?%%?%?!!?!?!%?%?!%%?%!!%!!%%!!%!%!%%?!!!?!%%!%%%%!%%!!%%%%?%%!!%!??%%!!!!%%!?%!%%?!%!%%%%%!?%%!%%!!!?%%%!!%?%!%!!?%!!%%!%%?%%?!%%!!%%!%!%!%%!%?%%%%!?%?!!?%%!%!!!!!%%%%!%%!%%%%%!?!?%!!?!!%!%?%!!!!%%?%!%%%?%%%?!%!%%%%%%%!?!!!!%%%%!%%%??!!%?!!%%%?!%%!!%%!??%!!?%%!?!!%!!%%!!%!!%%?!!!%?!%!?%%%%!?!!!%%!%%?%!?!%!%%%%%!%?%%!%%%%%!!%%!%%?%%%?%%!%%%%!?%%!%!!!%%??%!%!!%%%%%%%%%!!?%!%!%??!!!%?%!?%%?%?%%%%%!%%%!%!!%!%!!!%%?%!!%!%?!??%!!!?!!!%!%!?!!!%%!%%%??!%%%!!???!!!%!%%%?%!%%%?%%?!?%?!%?!?!%%!%!%!?%%%!?!%%%?%?%!?!??!?%%!%%?%!%%!!%%%%!%%!%!%%?!!%!!?!%%%%%?%%!%%%!?%%?!%%%!%%?%!%!%!%?%!!%%%?%%%%%%!?%%%?!!%??%%?%%%%!?!%!%!%!!!?%!!%%!%%!??!!!?%%!?!!%%?%?!!?%%%%%%%?%%%%%%!%%%%%!!?!%!%!%%%%%!?!%%!??%!?!!%!?%!!%?!?%?!!!?%???%%??%%%%!!!!%%%%!%%!%%!%!!!!%!!!!%%!!%%!!%??%%%%%!%%%!?%?!!%%?%!!!%%%%%%!%%%%?!%??%%!!%%%%!?%!?!%%!!!%!!%!!!!%%%?%%!!!%??%%%?%?!?%?!%%!!%!%?%??%!%?%%!!%!%!!%%%!?!!%%!??!?%%%!?%!%!?!!!%!%%%?!!!%!%!%!%!%%%!%%?!?!%%!!?!!%%?!!!%%%?%!%%%?%%%%%!%%!!%%%%?!!!!!%%%%??%!!!%?%!??!?%%%!%!%!!!%%%!%%!%%%!!%!!%%%%!%!%%%!!!%!!%!?%!%!%%?%!!!%!!!%!%!!%????%%%!!%?!%%!!%%!?%%!?!%%%%%!%%?%!%??!%?!%!%!?!%%!?!??%!%!%!!??%%%%%!%%%%%!%%?!%!!!!%!???!!!!%?!??%!%%%??!?%%%%%?%?!%%?!?!%?!%!%%!%!!%%!!!%%%%%!!%!%!!%!%%%%!!?%%!%%?%%%%?!%%%!%!?!%%??%?!%?%!?%%!%?!?%!%%?!?!%!%!%!%%%!!%%%!!!%?!!%!%!%%!!!!!%?%%!%%!?%!%?%%!?%!!%%%!%?%!!?%%!!!!%?%%%?%!?!%%!!!%%!!!!%%%!!%%!%!%!%!?%!%!%!%%!!!%!!%!%!!!%!!!!%!%!%%%%%%!!!?%!!%!%!!!!!%%?%%!!%%!?!%%?%%!!??!!%?%%%?!%!%%?%%!!%%!%!!%!!%!%!%!!%!?!!?!%%!%%!%!!%%!!!%!%%%!%!!!%%%!!%%?%?%%?%!!!!%!%!!?!!%%%!?%!%!%??!?!%!%!!%%?!?!!!!!%%!%?!%%!!?%%%?%!!%?!?%!?%?!!%!%%%!%!%!!%!!!?!?!%%!?!?%!%%%%%?%%%%?%%!%%%%?!%%%%???!?%?%!!?%%?%!!!!%!??%!%%%%!??%??%!%%%%!!!!?%%?%%%%?%%%%?%!%!%%?%?%%?%!%!?%%?!?%%%!%%!%?%!%%?!!!?!!?%!?%?!!?!!%!?!??!!%?!%%!!!%%!%!%??%%%%%%%%?!%%%%%%?%%!!%!%%%%%!!%%!%?%%!%!!!%%??!?%!%%%!%!!%!!%!%%%%%!!%?!%!!%!%?%??%%!%%%!%?%!%!!%%!%%?!!%?!?%!%%!?%%%%!%?%!!%%?!!%!!!%!?%!%%%!!%?%!%??%?!?%!%?%%!!??%%%%?!!%%%!%?%%%!%!%%!!?!%!!%%%?!!!!%%%?%%!%%%%!%%!%?!%%!%?!%%%!!%?%!!%%?%!!%%%!%!%!%%%!%%%!%!%!!%?%!%!%??!!!%?!?%%!?%%!%?%%!!%?!!%%!!!%%!%??%!????%!?%%!!!%%!?!%%!!?%!?%%!!%!?%!%%!!!%%%?%!%?!!?%!!%!!%%%%%%%!!%%!%%%?%!%%!??!%%!%!!%%!!?%%?%!%%!!%!%!%%!%%!%%?%%%!!%%?!!!%%%?%!!%!%!??!!%%?!!%!!??%%!!?%%!!%!%%%!!%%%%%%%!!!?%?!%!!%%%%%!%%!%%%!?%%%!!?!!%??!!%!%!%%%%%%?%!!!%%?!%%%%%%%?!!%?%!%!!%%!%%%?!!!%!%%%%!!!!%%%!?%!%%?%%?%!%?%!??!%!%%%!%!%?%%%%%!%!%??%!!%%%%%!?%!!%??!!?%%!!!!%%%%%%?%%?%?%!???!%%!%!!!!!!%?%?%%!?!%%%%%%%!%%!?!%%?!%!?%?%%!%!%%!!%?%%%%!%%%??!%!?!!!??%%%!!%??!%%%!%%%?!!?!?!%!%!?%%!%%!!%!%?%%%%!?!%?!!!%%%%%!??%%%!%%%!%!!!!%!%?!!%%!%%?%%!%%%%%!%%!!?%!!%!??%!%!%!%%!%%!%%!!?%?%%???%!%%!%?%!%!%??%%?%!!%%%!%??%!!%%%%!!%!?!!!!!%?!!!!%%??%%!!!%%%%%%%???!!%!!!!%%%%%%!!!!!%%%%!!%!%%!?!!!!%!%%%%%%%!!!%!?%%?%!%%%!!!%!%?!!!%%%%%%?%%?!%!!!%?%?%%%?%%!!%%!%!%%%%%!??%!!??%%%!%%%!%%!%%%?%??%!?%?!?%%%!!%%%%!%!?%?!%!!%%!%%!?!%!!?!%%%!%!!?%!!%%%!!?!!!%!%?!%!%%!%!%?%!!%!%!?!%!?%!!!!%?!%%!%!%%!!%%!%%%?%%!%?%?%%!!!%%!%%?!%%!!?%%!!%?%%%%%%%!?!!%%%%%%%?!%!?!!%%%!%%%?!?%%%!!%?!%!%%!!%%%!?%?%%%%%!%!%!!?!%!%!!%!%!?!!%%%%%%%!%!!?%%!%?!%%?!%!%%%?!%!?%%%%?%%%%!%!%%!%?!!!%????%%?!!!!!!!%?!!?%!%%!%%%%!%!!!!%%%%%!!!%?%%!%!!?!??%?%%%%%?!%!%??%%!!%???%%%%%%?%!?!!%%%%!%%?%%!!%%%!!%%???%%%%%!?%%%!!!!%!!!!!?!%%%?!%%%%%!!%!%!??!?!%!%%?%??%%%%!%%%%%?%!%%!?!!!!!%?!!!!!%%%!%%%!?%!?!%?%%!!!!%!%!%?%%%???!!??%%!!%%%%!!??%!?%%!!%?%%%!!%%%%%!?!%?%%!!??%!%!?%!%%%!%%?!!?%!?%%?%!!!%%%!%%?%?%%!?%%?!!!?%!%!%!?!%%%%!%%!!!%!%!%%%!?%%!%!%!%!%!%%??%%%?%?%%?!%??%!%%%%!%?%%%%!%%%%%!%?!%!!%%?!%?!%!%?%!?%%!%!!!?%!%?!%!%!%%!%?%!!?%%%!!!%%%!!?%?%%%!%!!%%?%!%%%?%?!!!?!!%!%%%!%%!?%?%!?%?%?%%%%%%%!!?%!%%%?%!?%!!%%?%%!%?!%%%%!%%%%%!!!!%%%%!!!%%%!!%?%%%?%!%!??!!!!?%!%%%%!%!!%?!%?%!!%!?!%!!!%?%!%?%%%?%?!!?%%%?!!!!?%%?!%!%!%?!!%?%!?%%%?%!%!?%%%%?%%??%%%%%%?%%%!?%%%%%%%%%!%%%%!%%!!!%?!%%!%%%!!%!!%!%!?%!?!%%%!!%!??%%!!%%?!%%%%%%%%!%!!%?%%?!!%??%!%%!%%!%%%%?%%%%!%?%%%%%%!!!%!%!!%%%%%!!?!%?%!%%%?!%!!!%%%%!%!%?%?!?%!!!?%%?%%??%!%!!%!?!%%%%%!?!!%%?%%%?%?%%?%%?!??%%%!!%%%!%!%!%%%%!??%%%!%?%%?!!%!%%%%%!%!?!%!???%%!%%?!%%%%?%?%%!%?!%%!!!!?!%%%%%%!?!%%!!%%%!%%%?%%%%?%!%%!?%!?%%%!?%%!%%!%?%%!!!%%%%%!%?!!%%!!!?%?%%??%%%??%!!!??%!?%%!%%??%!!!%!%%%!!%!%!%%%%%!!!!%!%?!%?%!%%%%%!%?%%%%%%%%%%!?!!%?!!!!!%%%!%!%%!!%!%?!%!%%?!!%!%?!!!!!%%?%%?%!%%%?%%%%!%!%!%%%?%?%%!?!%%!!!!!%%%%!?!%!!%%%!%%%%!%%%%%%%%??!%%!!%%%%!%%!!%?!??%%!%!?%%%%%%?%!?!%!!%%!!%?%%?!%%??%!%%%!%%%!%??!!??%%!?%%?!!!!%!!?%%%%%%!%%%!%%!!%%%!%%%%!%!!%!%!%!%%!!%?%!%!!?!?%!!!?!!%?%!%%%!!!%??%!%?%!%%%%!!%%!%!%%?%%!!%%!%!%%!%?%!!!!%!%?%%%%%%%!?%!!%?!??!!!%?%!!?%!%!%%%%!%??%!!!?!%!%%%!!%%%!%!%%%??%?!!%%%?%??%!!?!!%?%!%%?!!%%!!%%%!!%?!%%??!%!%%?%!!!?%%!!%%!!!%!%%?!%?!!!%????%!%%%?!%??%%!%!!%!!%!?!%%!%%?%?%%?%!%!%%!%?!%!!!%%%!?%?%!%!%!?%%!%!!%!?%%!!%?!%%?!%%%%!%%%%!!%?%%%%!!%?%%%%%!%?%%%%!!%%?%%!?!%!!!%%%!%%%?!!?%%!%?!%??%%!!%!%%!%%%%%%%!!?%%%!%!?%%?!?%%%!!%%!?%!?%%!!%!!%%%!?!%%!%?%?!?%!!%%%!%?%%%%!%%%??%?%%%!%?%%%?!%!%!?%%?!?%!!!!%%?%%%!%!%?%%%!?%?!%%!?!!!!!!%%%?%%%%!%!%?!%%%%!%%?!%?%!%%%%%%%!%%!%!?!!!%???%??!!%%?!%%??%%%%%???%!%%?%!%%?%%?%%?%%?%%!?!!?%%%!?%!!%?!%%%%%!?%%%%%%!!%!!!!!!!!%!%!??%!!%%%%!%!?!%?!!!!%!?%%?%!%%!%!!!%%%%%%!!?%!%%%%%!?%!!%%?%?!%%!%!%!!!%!%%%?%!!%!%!%%%%?!?!!?%!!!!!??%!%?%%?!?!!!!%!????!%!!%%%%%%%?%!%%!?%%%?%!!%%?%?!%!?%!!%!?!!!?%%%!?%%%!%?%!!%?!!%!%%%!?%%%!?%!!!!!%%?%!%%!%!!%!!!%%!??%%!%!!%!%?!?!?%%%%%!%%!%%!%%%%%!%%!%%%%!%!!!%%%!!?!%!%%!%%%?!%?%%%%??!?%%%!%?!%?!!%?%%!%%%!!%?!%%%!??!!!%%%%!!!%%!%!?%%%%?%%%%?!!%%!%%?%%%%!!!?%%!?%!%%%!???!%!?%%!%%%%%%??!%?%%%!!%?!!%%%%%!!%??!!%?%!%?!!%%%!?!%!%!%?!!%!!!%%%%%%!%%%%!!%%!%%%!?%%?%%???!%?!?%%%?%%?!%%!%%%!??%?%!%%!%%??%!%?!%%%?!%??!%?%?%%%!?%%%!%!?%!!!!%%%?%!!%%!!%%!!%?%!%%%!!%%%!!!%%!%%%!!!%!?!%??%%!!!%%%%%%!!%!%!%?%!%!%%??%?%%%%?!!%?%%%!%%!??%%%!%%!!%!%%?%!%!%!%%%?!%%?%!%%%%!?%%!!%!??!%%!%%!%%!?!%!%!!!!%!?%%%%?!?!?!%?!!%!!!%!%!!?%%!%!!!?%?!%%??%%%!%?%!%?%%%%??!%!?%%%!%!%?%%%%!!%%%?%!%%%%?%%%%%!!%%!!%!!!%!%%%?%%!%%%%?!%%%%%?!%?%%%!%?!%%!%!%!%??%%!%?!!%%!?%?!%???!%!%!%?!?%!!%%%%%!%%%!%!!%%%%!%%!%%!!%%?!!!%!!%!?%!%%!%!?!%%%!%!%%?%!!%%!!%?!!!%%!!%?%%!???%%!?%%!%?%%%%%?!!!%!!%%%%%!?%!!!%%!??!?%!%%%!%%!?%!!%?!?!%%!%!!%?!!!%%%%%!%%!%%%!!??%!%!!!!!?!!?!%!?%%%?!!!%%!!!!%%!%%%??!%%?!%!!!!%!!!?!%%%?%!%!%??%?%!!%%%!%!%!%!!!%%!!!%!%%%%!%%%!%%??!%%%%%??%!?%%%!!!%%%%!%?%%?%!?!!%!?!%%%!!??!%!!%%?!!?%%!%!%?%%%!!?!!%!!!!!?!%%!!!!?%?!!!%!!%%?!%!%!!%%?!%?!?!%?%%!?!%?%%%!!%?%%%!!!!%%?!%%%?!!%!%%?%%!%?!%%%!%%!!?%%!!!%!%!%!?%?!?%%%??!?!%%%?!%%!%%%%!%%%!%!?%?!?!%?!!%%!%??!!!%%?%!%%%%%!!%%?!%%!!%%%%%!%!?!!!%??!!%%!!!%?%%?!?!!!%?%%%%?!%%??%!!%%%?%!%!%!%!%%%!!%!%%!!%%%%?%!%%!%!%%?%%%!%%%?!%?%!%!%%!%??!!%?!%%!%!%?!!%?%!%%!%%%!?%%??%!%!%%%%%%?!?!%?!?!!%%%%%!%%!!%!%?%%!!!%%!?%%%%%%%!!%!%?%%!??%%%!?%%%%!%%?%%?%?%%!!!!%%!%!%%?%!!%?%%!!%?%?%!?%%%%?%!%?%?!!?!%?%%!!!%!%!%%%%?%???%%%?%%!!%!!!%!%?!%!!?%!!%!!%%%!!?%!%!?%%%%%!%%%!!!!?%%!%%%%%%%?%%?%!!?%?!?!%%!!%!%%!%%%!!%%?%%?!%!?!!!%%?!?!!!%%?%%%%%?!!%!%!%!%?%?!!%%!%??!%%?%%%%%??%!!!%%%%%!%?!%%%%!?!!!?%!%!?!%%%!?!%%%!%!%%?%%%%%?%%!%?%!%%?!??!?!!%%!%!!%%%%%%%?!%%%%%%%!!%%!%%!%%%%?!%%%?%!!?%%%%%%!!%%?%%!%%%%%!!%%!!%%!!!!%!%!%!%%?%?!?%!!%%%%%?!%%%%%?!!%%%%?!!!%??!!!?!%%%%?!!%%!%!%!!?%%!%%!!!%%!%%!%%!%?%%?!%%%%!%!%!!!!%%%!!!%!!?%!%??%%%%!%!%!!%!?!%%%!%!%?!%%!%%%!!!?!%!%%!%!%%!?%%%%!%%%?%%!%%%%?%!%!%%%%?%!!%!%%!%!!!%!%%?%%%%?!%%?%!%?!?%%%%%%!%??%!%%%?!?!!%%??!%%!!!%!!?%?%!!%!!!%!%!%%%!%!?%%!!!?!!!??!?!!?%??!!%?%!!?%!%%!?%!?%!%%!%!%%%%%!%%%%%?!%!%!%!?%%!%%%%!%?!%%%%%%%%%%%%!?%!??%!%%%!%!!!%%?%%%%?%%!!!!?%%%?%%!%%??%!?%%%!%?%!!%!!??%%%%%!?!?%%%!%%%?%!%%%!%!%%%!?%%%%%%!!%%!!!%?!!!%!%%!%%!?%!?%%!%%%!!%!!%%!!!%%!?%???%%!!!%%%!!!%%%?%%%%%%%!!%%??!%%!!!%%%%?%??%!%!!%!%%%%%!%%!%%!!%?%?%?!?%%???%!%!%%?%?!!?!??%!%%?%%%%!%%!%!%??!??%!%!%!%!!!%!%%?!%%?%%!!!??%!%%!%%%%%!!?%%%?%!%%?!%%!%!%%?%?%%%!%!!%!?%!%?%!!!%%%!%%%%!%%%%%!%!!?!?%%!!!%!!%%%!??%!?%?!%!%%%!!%?!!!%?%!!%!%!%%!!!%!%?!%%!!!!%!!?%!%?%%%?%%%%?%!!!%%%?!%%%!?%!?%%?%%!%%%??%%!%???%?!%%%?%%!!!%%?%!!%%%%!%%%?%%%%?%%!!?!%%%%!%?%%!!!%%!??%%!!%!%%!%!%%!!%?%%%!!%%!?%!%!%%!!?!?%%%!%?%%%%%!%%!%?%!%?%!%!%%%?%%%?%!?%!!%%!?%!!!!%%%!!!!%%???!%%%%%%%%%%%!!!%%%%%?%%!?!?%?%?%?%%%%!%%%?%?!!!!%??%%%%%!%?%%!!?%?%!!!!%!?%%!!%%%%!%%%%!%!%%%!%!!!??%%!%%??!!!%?%!%!%%%%!%!!%%%%??%!%!%%!%%!%?!!!%!%%!!%%!?!%!!%?!%%!!?!%%?!?!?%!!%%!%!!?%%%!%%?%!%%!%%%?%!!!???%%!%%?!%%%%%!%%%!%%%%%%?%%%%%!%?%%!?%%%%!!%!%!%%%%%%!!!%!!%%!!!%!%!!%!%!?%!%%!%!%!%!%%%%%%%!%%!??%!!?!??!%%?!!%!!!?%!?%%?%%?%%!%%%!?%%??%??!%%%%%%%%%%?!!%?%%!!!%%%!%!?%!%!%?%?%%%%%!!!%??%%%!!!!???%%?%%!!!%%%?%?%!!!!??%%!?%%!??!%!%?%!%!%%?!%%!!%%%%%!%%?%!%!!%!!%!!?!%!%?%!!!%!%?%%%!%???%%?%%%?%?%%!%%%!!%%?!?%!%!%%%?%!??!%!!!?%!!!!%%%%!%!%!%%!?%!!?!%%%%!%%!%?%%!!?%%!%%!!%?%%%?%%%!!%%?!!%%!?!?%!!!%%%!!!%%!%%%?!!!%%%%!%?%!??%%%?%%!%!%%!%%!!?%%!%??%!!%%%??%?!!!?%!?!!!?%%%%!?%%?%%%??%%!%%?%??!!%!%%?%?%?%%%??%?%%?%%?!%!%?%%???!?%%!%%%%!%%%%?%?%%!!!%%?%!%%!%?!%!?!%%?%!?%%!%%!?!%%!%%%?!%%%!%???!?%!!?%%?!!%!!%%%%??%%%??!%%%!!%%%%!!%!!!!!%%%?%%!%?!%%%!%?!!%!%%!!!%!!!!!%%!?%??%%%!%%%%%%!!?%%!?%?!%%%%!??!?%!!%!!!%%%%?!!?!%?%%%?%?%%!!!!??!!%!!%?%!%%%!??%%?%!%!!!!%??!%%%!%??!?%!!?!?%%%!!?%%%?%!?!%%?!!!%?!?%!!%!%?%%!!%%%%?%!!!?!%!!!!!%%!%%??!%!%!!!%%%!%!%%!%!!%!%??%%%!?%!?!!%%%?!!!?%?!?%!%%%!%%%%?%!!%!!%%%?%%!%?%%?%%%!!?%!?%!?!?!!!!%?!!!%%%%%?!!%!%%?%%%%!!%?!%%???!?!?%%%!!!%%%%!!!!!%%??%!?%%%!!?%%?%?!%!!?!%%!!??%!?!%%%%!%!!%!%%!%%%%!%%!%!%%%!%!!!!!!!!%?!!%!%!%%!!%!?!%%?%??!%?!%%!%%!!%%%%!!!%!!!!%%!!%%%!??%%%?%%%!!%%%%!?%%!!?!%!%!!!%%?!%%?%!!!%!%?!%%?%!!%%!%!!%%%%!?%!%%%!!?%!!???%?%%?%!??!%%?!%%%!!%%%!%%?%%?!!!%%%%%!%%%%%%?%%%!?!?%!!!%%!?!%%?%!?%!!%?%%!%?!?%?!?!!%%%!?%!!%!%!%%%%!!!?%%%%!%%!!!!%!!%?!???!!%%%%%!%%%%!!%!?%%%!%%%!?%%??%!!?!%%!?!%%!?%%!%%?!??!%%%?%%?%?%%%!!!%!%%%!%?!!%!%!!!?%%%!!!%!%%!?%%%%%%%%?!?%?!?!%!!?!!!%!%%?%%!?%!!%%%%%%%%???!??%%%%%!?%!%??%?!?%?%!?!!!%%%!!%?%%%%?%?!%?%?!%%%%!%?%%%%%%!%%!?%!!%%%!%?%%?%?%!%%?%!%!%!?!%!!!!%%!%%%%%%?!%%!!%!???!%%?%?!%%%!!%!%%%%!!%%!%!??%!!!%!!?%?%%%!%%!%%!%%????%?%?%%?!%%%!!%!!!?!%%%!%!!?%%%%!%?%%!?!!%?%%%?!!%!%!%%%%!!!%%?%%%?%!%%!%!!!??%%%%!?!?!?!!%%%!%!%!%!%!??%%%!!!!!!!%!?!?%%%%!?%%%!%!!?!?!%%!!%%!%?!!%%?!%%??%%?%!??!%%!?%!?!%%!%%?%!!%%?%!!!!%%?!%!?%%?!!!%!?%%!%!%?%%?%%!!?!%%!%%%%!%!%%!!!%??%%%%!!%!!%%%!%%%?!%?!!!?%%!%%%%?%%%?!!%%%%?%%%%!%!%%%?!%%%%%!!%!%%?!!!?!%?!%!%%!%%%%!%%%!%%%!%??!!??%!%?%%%?!%?%%!%%%%!%%?%%%%!!%!?!%%%?%%%?%!%!%!!!!%%%!%%%!?%%%?!%!%%!%%?%%%%!?%!!!!%%%%%?!%%%%?!%%!!%%!?!%%!%%!?%%%%!!!!%???%?%%!%!%!%?%?%?!%!!?!!!!!%%%%%?!!%!%%!%%!%!%%!!!!!?%%!?%!?%!!!%??%%%%%?!?!%!!!?%?%!?!%!!?%!!!!?%%%!?!!??%!!?%%!%%?!!%%?%!!?!%%%!%%!%%!%%?%%%?!%!%!?%%?!?!%!%!!?!%%?!!!!%%%%!!%%%?%?!%?%!?!%%!!!%%!!%!?%!!?!%?%%%!!!%%%%!%!!!!?!%%%??%%%%?%!!?!%!%!%%!?!%%%%?!??%?%?!%?!?%!?%!%%%%?%!!?%!??%!!!?!?!%%!!%%!%?%?%%%%%!%!%!%!%!?%?%?%%%%?!%%!%!?%!%!?!!!!%!%%!!??%?%%%?%!!%!!!%!!%%!%%%!!%!??!%%!%!%!!!%%%%%?!%?!%?!%%?%%?!%%%%%?%%??!!%%%!!%%%%%!!!%??%%%%?!%%!!%?%%??%?%!%%!!!%!?!%%%%%%%%%!!%?%%!!%!!!!%%%%!%??%??!%%!!!!%%%%%%??%%!!!%%%%!%%!?!%?!!?!%%!!?!?%%%!!!!?%?!!?%%%!%%!%%%?!%?%?!%%%%?!!!%%!!!%%%!!%!%%!?%%!%!%%%%%?%%!?!%!!%%%?%%%!%!%?!?!%%!!??%%!%%?!%?%!!%%%?!%%%%?%%%%%!!%%?!%!%???%?%!%?%%!%%!%!?!??!%%%!%%!!?!!!!!!!!%?%%!!%%%!!%%%%?%%%%%!!!%!!!%%!%%%%?!???!%%%%%%?%!%?%%%%?%%%%!?%%%%%%?!!%%!%%!%?%%%!%%?%!%!!%!%!!!%%%?!?%??!?%?%??!%%?%!!!%%%!%!!!!!!?%%?!%!%!!%%!?%%%%%%%!%?!%!?%%%!!%?!%!!!?%!%?%%!?%!!??%%?!!??%!?%!%!%!%%%%!!%%%?%!%%%?%!!!%!%%%%%?%%%%!???!%%%!%?!?%%!%%%%%!?!%%!!%%?%!%!?%%!%?%?%!%%%%%!%%!?!%!%!???!!!!%?%%?%%?%!?%?!%!!%%?%%?%!!?%?!?!??!!!!%%%!%%%%!%%%!??!%??%!%%%!%%!!!%!%%%%%!%!!?%!%%!!%!%%!!%?!%?%%%!?!%%%%?!!%?!!%%?!%?!!%%!!%%?%%!%%!!%%?!!!%%%%!%!%!%%!%!!!%%%!%!!!%%?!%%??%%!%!%%%%%%%%!?%?%%%!!!!%%%%?!%!!%%%!!?%?!!%??%%?!%!%%!%!!!%%??!!!%%!%%!!!%%!!%?%%!%!!!!%%!?!%%!%!%%%?!?!%%%%%?%?!!%%??%%%!!?%%%%!%!!%!%!%!!!%%%!%?!!%?!!??%%%%%%?%??%%%%!%!%!%?%?%%%!%!??%%%%%!?!%!!%!%???%!?!!!?%!?!%!??%%%%!!%?!%!!???%%!!!%%%!?!!!%%?%%%!%!?!!?%!%!%%!%%!%%!?%!?!%!%?!?%%!%!!%%??%!!?%%!?%%%!%%??!%%%!%%?%!?%%%%!%%!!%%%%%!??%!%%%%?%%!%?%%!%!%%%%?%!%!??!!!?%!%!!!%?!%!%%%?!%?!%?%?%?%%!%!%%?%%!%!!!%%?%?%%?!?%!%!!%?%!%%!%!%%?!?%!?%!%!%!%!%%%%%!!!!%%%%%?%?%%!%!%!!%%!!!%!%%%!!%!%??%%!!%%!%%!?!?%?%!%!%?%%%%!?!!%%?%%?%!!!!%%%%%%!%%%!!!!%?!?%%?%!%%%%!!%?!?%!?%!%%%?!%%%?!?%!%!!%%%!!%%%%%!?!!!%?!%?%?%!?!%!%?!!%%%!!!%!!%!?%!!%%??!%%%%%%%%%?%??%!????%!%%%%%%%%%?%%!??%%!%?%?%%!%%%?%!?%%%?!%!%%!!!!!?%?!!%!%!!!!%!%?!%!%!%!?!?%!?%%?!??!!!!%%?!%%??!!%!!!?%!!%%!?%%%%?!??!%!%%!%%%!%?!?%%!%%%%%?!%%%%%?%%%%%!?%?%%%%%!?!%!!?%!?%%??%?!?!%%?!!%!%!%%%%%!%%!!%%%%%!!%!?!?!%%%!%%%%%!%%%!%%!?%%%%%%?%!!%%!?%??!?%!??!%!?%%?%%?!?%?%!?%%?%%%%%%%!%?%%!!!!%%%%%%%!%!%%!!%%!%!%!%?!!%%%%%!%%!%!%!?%!!%%!%%%!%!???%?!?!%?!!%?%%?%!%?!!%?%!%%!?!%!%!!?%%%%%%%%%%%!%?%%!!%%%%!?!%%!%%%%!!%!?%%%%?%%!%%%%!%!!%?!!%%%%?%%?!%%!!!%%%%?!%??%?%%?%%!?%%%%?%%?!??%?%%%?%!!?!!%!?%%%?%!%!!!??%!!?%%%%%%!!%%??%!%%?%%?%%%?!!!%%!!%!%!%%!?!???%!!%!!%%!?%%%%%%%%%!?%%%!?!%%%!!!%?%%%%%%%!!%!!%?%%%%!%%!!!%!%!!%%!?%!%!%?%!!%%%!%?!?!!%%!!!%!%?%%%?%!%%!%%!!%!%%?!%%!??%?%%!!%%!%?!?%!%!!%%!!?!?%%%?!%%%%????%%!?!%%%%!%%%%!%!!%%%%!%%?%!%?%!%!%!%%%%!!!!%!!!!!%%!%??%!!%%%%%!!%!%%!%?%!%%%%%%?%!%%%%!!?%%!%!!%%%%?%%%!%%!%!!?!%?!!?!%%%!!??%%%%%?%%!%?!%%!!%!!%?%!%%!??%?%!%%!!%%!%?%!%%%%%?!%!!%?!%!%!%!%!??%?!?%!??%%%?%?!%%%!%%%%%?%?!%%%!!%%??%%%!?!%%%!%?!??%?!!!!%!%?!%%!%%?%!!?!%!%?%?%%!!%?%%%?%%!%%%!?%%!%%%!%?%%%%%!!!?!%%%?!!%?!%?%?%%%?!!!%%%!%%%!%!!?!!!%?%!%%!%!%!%!%%?%?!%%%%!%!%!!%!?!!%?%!%!?!%%!!!!%%!!!!!%%%%!??%%%!?%%%%%%!%?%%%!?%!%??%%!%?%?%?%!!%!?%%?%%%%!%?%!%?%!%%%!!!!?%%%!%!!%?%%%%%%!%%%?!!?!%%%!%!?%%!%%!!!!%!!???%?!%%?%!!??!!%%!%?!%%!!!%!?!%%%%%?%?%!%!!%??%%%!!%%%%%!%%?%!%%%?%%!%?%%%%?%%%!%!!%!%%%?!!!?%?%!?!%!%?!%%%???%%?!%%%%!!!%?!!%%%%??!!??%!!%%%%?!%!%%%%%%?!%!%!!%%!%%?%!?%!%!?!%%!%%?!!%%%!%!%%%%%%?!!!%%%!?%?!?%!!%%%!!%%%%!?%!!!!!%!!%!%%%!%%%%%!?%%%%!!%?!!!?!%%!%!?%!!!!!!%!%%?%!%%!%!?%!%%%%?%%!%%?!%?%!!%?%%!%!!%%?%!%%%%?%%!!!%%%!!!?%%%!!%!!!%?%%%%!%?!!?%!%?!%?%%%!%!??!%%%%%!%%?%%!%!%%!!!!!%%%%%%!%?!?!??%!!!%%!?%%!??%!!!?%%%%?!!%%!?!%?%%?%!%!!!%%%!%!%!%%!!!!%!%%!!!%!%%!?%!%?%!%%%%%%!%!!!!%%%%!!!%!?!?!%%%%!%%%!?%!??!?%?!!?!!!?!%%%!%!%%!%%%%%!??%?%%%?%%?%%!%??!%%%?%%!%??%!???!%%??%!%!!?!?%??!!%!!!%%%%!%?!%!%%%?!%%?!%!%!%!!%?!!!!!!?%?%?!%%%%?!!!%!?%%!%!%%??%!?%!%%%%!!!!%?%%%%%%!!%%%!%%?!%?%%!!!%!!!?!?%%%!??%!%%%%?%%!%%%%?%%%!!?%%!%!%!%?!?!!%%!%%?!!%!%%%??%%%!%!!%%?%%!?!!%%%?%!%?!!!?%%%!%%%%%%%%!!!?!%%!%%?%%?%!%%%%!!%%%?%?%%%!!?!?!?%%!%!%%!%?!?%%%%!%%%%%%??!!??!%?%!!%%%%!!%!!?!?%?!!%!%%?%%!%%%%??!%%%%!%%%!%?!?!%%%!!%!!%%%!%?%%%%%!%?%%%?!!?!!%?!?%!!%?%%!%%!%?%%%%!%!!!!%%?%%%!%!%!%%%%!!%!%!%%!%!%?!!?!%?%%%%!!%%%!?!??%%%%%!%!!%%%%!!!?!!!!%?%!%?%?%%!%!%%%%%!%%!?%!%!!!!%%%!%!!%!!!%%?%%?%%%?%!%!%%%!?%!%??!%!?%?!??%!%!%!%%!?%!?!?%?!!%!%%%!!%%%!%!!%!%%%!%%%?%%!%!!!?!%!%%!%%%?!!!?!!!%?%%%!%?%%!%%!!%%%%!!!?%!%%%%%%%%??!!%!!!%!%%%?!!%!%%%%??!%!!!!!???%%!%!?%?!!%!%!!%%?%!??!%?!%%?!%%?%%%%?%?%%%%%%%??%%%%!!%%%%%%%%%!!!!%%???%%%%%%?%!?%!!%?!?!!?%%%!!!%!%!%%?%!%%?!%%%%%%%!!?%!%%!!?%%%%%%%%%!?%!!!%%!!%?%%!!%?%%??!!%?%?!?!%!%?!%%!%!%!%!%%?%?%%%%!%%?!%!?!%!%!%%!!!%%??!%%!%%%%%%%%!!!%!!%!%!%!%%?!!?%%%?%%%%!!!%???%%%%%%!!?%%%!%??!%!%%?%%%%?!!%!%!!?%!!?!!%?%%?!%%%%%%!!!%%!!%?%%!%!%!!!!?%%!%%%!%%%%?!%?%?!!?!%?%?%!?%%!%!!%%%!%!!%!%!!%%%%?%!?%%?!%%%!?!%!!!!%%!%!%%%%!%%?%%?!!!!?!!%??%%?%%!%%%??%%!?%%!%??!!%%%!?!!!%?%!%!%!!%%%!!%%!%?%%%!?%%%%!%!%!%!??%%%?%?!%!?!%!%%!!%!%!%?!%!?!%%%??%!%%%%?%!%?%%??%%%%?!?%%!!%!%%!!%?%!!%%%!%%%%?!!?%%%!!!%!!?!!!?%!%%%!%!!???!!%%%!%!!!%!!%%%%%%!?%!%%?%?%%%?%%%%!!%!%!?!!?%!%!!!%%%%?!%%%?%%?%%!%!%!?%%%?!?%%%!%?!%%%!%!%%%!!%!%!%%?!?%!?!%%?!?!%!%%?!!%%%%%%%%%!!?!%!%!%?!%?%%???%%%%!!!%%%!%%?%%!%!!?!?%!%%!!!%%!?%!%!%%?!%%%!!%?!%%?%%%%%!?!!?!%%!!!!?%??!!!!!???%?%!!!!?%%%%!%!!%%%!%!?%!%%!%%??%?!%%%%!!%!?%!%!%!?%!!?%!!%??%%?%!!%?!!!?%!!!!!!%%!!%%%!??!%!?%?!%%!!?%%!%?%%!%%?%!%%!%?%%%%%?%%!!!%?%?%!!??!?%?%!%%?!?%%?%!%%!%%!%?%?%?!%!%%!?%%%!??!!%%!!!%?!%%?%%??%%!%%%!?!!?%%?%!%%!?%?!%!!!!%%?%%%%?%%?%!!%%!%%%%?%%!%!%%?!!%!%%%!!%!??%??!!!!!%?%%!%%%%!%%%?!%?!%!%%??!!!!?%%%%%%%%%?!%%%??!!?!?!%%!!%%%%%!?%%!!%%!!!?%%%!!%%!!!%%%%%!%%!!%%!%%!!!?!%%??%?!%!!!??%!!%%!%!!??!%%!%%!%%!!%?!%???%%!!!%%!%!%%!%%!?!!!%!??%%%?!?%!%!%?!??%%%!%%%???!!!%!!?%!?%%?!%%%?%!!%?%%?%%%?!%%!%!?!%%!%!!!!!%%!%!!!%!?%%%!%!?%%?%%!!%%%?!!%!%!%!%%!%?%!!%%?%!%%!%?%?%!!%?%%!%!?%%%%!!?%%!%%?%%%%%????%%!%%!%!!!!%!%%%?%%!%%!%%?%%!!%%!!%%%%!!!%%%!!!%!%%%%!!!%%%%%%!!%?!?!%%!%?!%%%%%?!!?%%!!?!?!!%?!!%!%!%%?%%%%!?!?%%%!%?%%%%%?%%%%!??%!!!!%!??%%!!%!%%?!%%?!%%%%%?!!%%%!?!!!?%%!!!%%%%!!!%%%!%!?%%%%!!!!!!%%%?!?!%%!%?!?!!!%?!%%%!!?!%!%%!%!!!?%?!%??%%%%%%!%!%!%!%%%!%%%%?%?%!!??%%?%?%%!!!?%%!!!%?%?%!!?%%?!??!!!%?%?%??!!!%%%%%%%!%!!!%%!??!%%%%%?!%%%!%!%%%%!!?%?!%%%?%?!!%!%%%%%!%!?%%%!%?%%!!%%%%%%%??%?%!!%%%%%%?%!?!?%%%?%%%%%%%%%!!!!%?%!!!?%%%!!!!%%%!%?%%!%%%!%%??!%%?%!!!!!?%!!!%%%%?%!%%??%!??!%!%%%?!%%?!!%%%%%%%!!!%!%!%!%%%%!%%%!!?%!!%?!!!??%%!?%%?%%%!%!%!%%%%!?!!%?%!%!%!?%%%!%%!!!%!!%%%%%!!%%?!%!%%!!%%%!!%!%!%%??!%%!!!%%%!!%?%%%!%!%!??%!?!!%%%?!%!%!%!!%!%!%!%%?!%%!!?%!!!!!%%!%%%?%%%%%%!!!?%!%?%!%!%!?%%%%!??!%%!%??%!%%!!%!?%%%%%!!%%!?!%%%%%!%%%%%?%%!?%?!%%%?%!!?!!%%%!%%!%%%%%?%%%!?!%%%!?%?%!!%%?%?!%%?%%%%%%%!!%!?%%%%%%!!%%%?%!!!%!%%?%!!%!!%%!%%%?%??%%!?!%%%%%%!%!%%!!!!%%%%%!%!%?!!!!%!%%%!!??%%%!?%%%%%%?%%%!!!!!!?!%!%??!%%%!%!!%%!%%%%?%?!!%!!!??%%!?%%!%%%%%%!?%%%?!!%!!?%!%%!%!?%!?!!%?%%%%!%!!%??%%!!!!%%!%?!!!%!%!!%%%!%%%!!??!%!!!%%!%%?%?%!!%%%!!!%%%!%!!!%!!?%%%%%%%!!%!%!??%%!%?%!%?!!%%%!%?%%%%%!%%%%?%?%%%!!%%%!%!!%?%!?%!?!%!!!%?!?!???%!!?%%!%%!?!%!!?%%!%%%%%!%?!!?%%%%%!!%!!?!!%%!%%%?%%%!??%??%%%%!%!%%%?%%!!%%!%!!%!%!!?!%%%%?%!%!%%%%%?!%%!%%%!!?%%?%%%%?!%%!%%%%%!%?!%%%?%%%%%!%?%!!%!%%%%!!!%?%!%%%?%%?!!%?!%%!%%!?%%%%%%!?!?%%%%?%%!!!%!%!%?%%!!!%%!%%!?%?!%?!%!!%%%!%!!%%?!%!%?%%%!?%%%%!??%%!!%%?%?%!?!!?!!!%?!!?%!%%%%%%?%!%%%%%%!?%!?%?%!%%!!%?%!!?!%%!!!!!!!!%!?%%?%!!!!%?!?!!??%?%!%??%??%%%!!??!?%!%!%%!!%???%!!%%!!%%%!!!!%%!?!%??%%%!%???%!!%!%!%!%%!%%%%!%%%!!!!%!%?%?!%%?%%%!%!!%%?!!%%!!!!!%%!!!%%%%!!?!%?%?!!!?%!%%%%!!%!??%%%!??!!!!%%!?%!%%!%%!%!%?%%%?!!?%!!%%?%?!%%%%%%!!%!!%%!%!!?!!!?!%??!%!%%!%%%?%?!??!!%%%?%%!%%!%!%%?!?%!%!%%%!%%%?%%?!!%%?!?!!%!!!%%???!%!%?%!!!%!%%%%?%!%!%?%%%%%!%!!%%%!%%!%?!%%!%!%?!%%?!%!?%%!%%%!!!!!!!?!%%%%%%?!??!%%!?!!%%!%%!!!?%%%%!%?%%!%%!%%!%%!!%%%?%!?!%%%!%%?!!%!%!!%!%!?!!!%!!%?%??!%%!!!%!%!%!%%%!!%!!!%!%!%%%!?%!?%%!%!!?%%?!!%!%!%%!?%%!?!%!%!%%%%!%%%%%%!!?%%%%%?%!%!%!%%!!??%%%%%!%?%?%%!!!%%%%%?%!%%??%%!?%%%!%!?!!?!!%%%!%%!%!?!!%!!!%%?%%?%%!%?!??!%!?%%%?!%!%!%!!%%%!!%%%%%%!%??!%%%!%!%%!?%!!%%%?%%%??!%%!%?!!!!%!!?%%%%!!!?!%??%%!?%%?%%%!%%?!%%%!%%%?%?!%%!!?!?!!%%!%%%!%%?%%!%!?!?%!!%%!%%!?!%%%???!!%!%%%%!%!!%!%%!?%?!!?!%!%%%%?%?!%!%%%!%%%%%!%!?%!??!!%?%!%%%%%?%?!%%%!%?%!%!%?%%%!%%?%%!!!%%?%%?%!!%%!%%%!%%?!?%!!%!!%%%!%!%%?%!%!%!%%%%??%%%%!%%%?%!%!!!!%!%!!?!!!%%?!!!??%!?%%%!??%%%!??%%!!!?%%!?!!%!%!!%!%!%!%%%%!%!%!?%%%!!%!%!%%%!%%%!!!!%?%%%?%%%!%%%!%!?!%!?%%%%?%%%%!?!%%?%%??!!%%%%%%%%!%%%!%%!%!!%!!!!%%%?%!%%%?!?!%%%!%%%%!!!%%?!?%?%%!!!%!%%??!%!?!%!%%%%?!!!%%%%!%%%%%!!?%!%!?%%%??!!!!%?%??%%!%%?%%%?!!?%%%!?%!%%?%%%!?%%!?%!%%?%%!%%%?!%%!%??%%?!!%?%?%%%%!%%!!!!%%%%%%!?!%%%%%?!?%!!!%!?%?!?!%%!!!!%!?!!!%%!%%%??%!!%%!!!?!%!%!!%%%%!%%!!!!!??!?%!!%!?%%!%%??%??%!%!%%?%!!!%!?%%%?!!!%%?%??%??%!??%!%!%%?!%%?%%!?!!!!%%?%%%%%!%%?!%??!%%%!?!%!!!!!?!%?!!%%??%!?!!!%!%?!?!?!%%!!!%%%!%!%%%!%%%%?%%%!!%!%?%%%%%%%!%!?!%!%%!!!%!!!!%%!??!%!%%?%%!%%??%??!%%?%%?%!%?!?%!?%%%!?%%%%!%%!?%%?!!%!??!%!?%%%%!%?%%!%%?%%!!%%%%?%%%%%!%!%!???%!!%%%?%%%!?!%?%%%%%%%%!!!!%?%??!%%%!%%%%!%?%!!%%%%?%!!!%%?%%!%%%?%!!!!%?%%%%%!!%?%?%!?%!%%%!??%%%!%%?!%%!%%%%%%??!?%%??%%%%%%!%?%?%!%!%!!?%%!%?%!!?!!%%!%!!!%!?%!?%!!!!!%?!%%!%!!%!%%?%%!%%??%!%!%%!!%!!!%??%%%%!!!!%%%!%%%%!!%%?%!!!!%?!?!!?!%?!%%!%!%?%!%%%?!%%?%!%%!%%?!%?!%!%%%%%?%?%!%%%%!?%%%%?%%!!!!!!%!%!?%%!!!%!!!?%%%%%??%!%%%!?%!!%%!!%?!%%!!?%%%!%!!%?!%!%!?!%%?!%?!%%?%!?%!%!!%%!?!%!%?%?%%?!!???%!%%!?!%%?!%%%%%!!!%%%%!%%!%%!%!!!?!%%%%!!%!!%?!%!??!!%%%!%%!%%%!?%%?%%%%!%%%%!%%!%%%?!%%%%?%?%!!%%!!!%!%%%!!!%!%!?%!!?!!%%%!%!%!!%!%%%%%!%!!%!%%%!%%%%?!%!!!%?%%%!%??!!%%%?!!%!!!%%!??!%!!%!?!%!%!!!%!%!?%%%!!?%%%%!%!%!%%!%%!!%%!!%!%%?%?%%??%!%%%?%!%%%!!%??%?%!%??!!%!!%%!!!%%?!!%%!!??%?!!!?%%%%%?!%%%%%!%?%%%%!%!%?%%%!%%!!%%%!%%?%!%!?%!%%%!?%%%%%%%%%%?%%!%%%?%%!%?%?!%%%%!?!!?%%?!??!!??!%!!?!%?!??%%!!%!%!%?!%?%%%%%%%%%!?%?%!!!!!!!%%?%%!%%?!%%!%%?%%?%!??!%!!??%!!!%!!%%%%%%?%?!!%!!?%%%?%%%??!%?%%%%?%!?!!!????%!%!%%%%?!?%!!!%!%%%%%!%?%!!%%%!%?%?%!%%%!%%!??!%!%%%!%???!%%%%?%!!?!!%%!!%%??%!%?%%%%%!%?!?!%!%!!!?!%!?%%%%%!!%!%%?%%!!%%!!%!%%!%!%!?!%%%!?%%%%%?!%%!%%!%!!%%%!%!%!%%!!%%%!%%%!!?!%!!%!%!??%???%%?%!!!%??%%!%!%%%%?%!!%%??%%%!!!!??%%!!%!%!%%%%%!!?!%!!%%!!!!%!%%%!!?%%%!%!!%!?!%!%%%!%%?%??%!%!%!!%%?%%?%%!%!!%%%?%%%?%!%%%!%?%%!%!%?%%!%!%%!%!%?%%!!%!!?%%!%?%%%??!%!!!%!!!?!%%%?%%%?%%??%%%%??%!?!%?%%!!!!%%%?%??%?%?%%%!%%%%!%%%%??%!?!%!!%!%%%?%?!!%?%%%%%!!%%!!%?%!!%%?%%?%!%%%%?!?%%%!??%?%%%%?%%!??%%%%!!!%%%!!!%%?%%%%!%%!%!??%!!%%!%%%%%%%!%%!!%?%!!%??!!?%%?!!?%%?%%%%?!!!?!%%?%%%!?%!!!!%!!%!?!%!%!%!%%!%%%%??!?%%!%!%%%!%!%!!!%!%?!?%%!%%%%?!%?%%%!%%%!%%%!!?%!%%!%%%?!?%%?!!!!!%!%%%%%%%!%!!!!!%!?%!%%%%%%%?!%!!%!%?!%?%!!!%!!!!!%!!%%%!%!%?!%!%?%!%!%%!%%%%%%%%%%%!?%%!%%!?!%?%%?%?!?%!!!%!%%%?%%%!%???%!%%%??%?%%%!???%????!%!!?!?!!%?%!?!%!?!%%??!!%?!%%%%%!%%?!%!%%!%%%!%%!!!%%%%!!%?!%%!!!%!!!!!!%?!%%%%%%?%?%%!?%!!%!!!%??%?%%%!%%!%?%%!!?!?%!%%%%%%!%!!%%%?%!?%%%!!!!%%!%%%?!%!???%%!!%%!%%!%%%%%%?%!!!%%!%%?!%%%%!%??!!?!!%?%?%!!%!!!%%!%%!!?%%?!?!%%%!%%!??!!%%?%?!%%??%%!%%%%%%!%!!%%%%%%!%!%??!%!%?%!%!%!%%%?!?%%%%!?!%%!%?%?%%%!%?%%?%%!?%%%%??!!%!!!!?%%%%%%%!!!!%%!%?%!%?%!%%%%!!?%%%%%!%!?%%?%%!?%!!???!%%%%!%%!!%!?%!%?%?!%%!?%%!!%?%?!!!%!%%%%%%%??!!?%!???%%%?%!%%?%%%?%?!?%?%%?%%!%%!?!!%%?%?%!%%%%%!!?!!!!%%?%%!%%%!!%!!!!%!!?%?%!%!!%!%!%%%!!%%!%%!!!%%!?%!?%!%!!%%%!%%%??%%%??!%%%!%%!%%%%!?%?%!!%??%%!!%%%%!%%?!%!!!?!%!%%?!!%%!!?%!!%?%%!%!%%%!??%???!?%%%%?!!%!!%%!!?!%!%!?%!?!!%%??!%!?!%??%%%!%%?%%%!%!!!!??%!?%%!%!%!%%?%%!!??%!?!%!!?%%%?%%!%?!?%%?%%%%!!?%%!!%!%%!?%?%!%!%??!!%%?!%%%?%%?!!?%!%??%%!%%%%!%%%%%!%!??!%%%!?%%%!%%%?!%!!!!%%?%??!%%?%%%!%!!%%%%!!!%%?%%!%%%!%%!%?%%%%!!%%%!!!!%?%!%?%!!!!%%!%!!%!!%!!!?%?%%%!%!%!!!%%%%?!%%!%!!!%!%%?!%!%???%%%!%%!%%!%%???%%%!!?%!%?%!%%??%?%%!!!!?!%%%!%%%%!?!??%%%?!%%%%%!!%%%??%!%%%%%%%%%!%%%!%%!?!!!%%!?%!?%%%?!?!%?%%?!?!!?!?%%%%%%%%?%%!!??!%%%%!%!!!%!!?%?%!!!!!!!?!?!%%%?%!?%!%!!!?!?%!%!%%%!%%?%!%%!!%%!?%!!!?%%%%!%?!%!%!%%%!?!!!?%%?!!%%%??%%%!!%%!!!?%!?%%!%%%%?%!?%%?!?!?!!?%!%%%!%%?!?!!??%?!?%%%!%%%%%%!!!?!!??%?!%%%?%!%!%?%%%!%%!?!%!?%?%!%!?%%%%!%!!!%??!???%%%%%%%%%?%!?%%%%%!!!!%???%!%!!%%?%%%!%%%%%%!%%!!?%%%%?%%%%%??!?%%%!%!?!%%%!!!%!!??%%%%%!%%%!%?%%%?%%%!!%%?%%%?%!!%%?%?%!?%??%!%!!!%%%%!!%?%%%%%%!%!%?%!!%????!!%%!?%%!!!%%%!!%?%!%?%!%%%!????%!?%?%%?!?!?%%%?%%%%%%?!!%!?!%%?%?%?!!!!!!!%%%%%%%?%!%%?%!%!%%%%!!%%%!%%?!%%%!%!?!%%%!%%!!!%%?%%!!?%%%%%%!!%%!%%%%%!%!%%%%!!??%%?%%%%!?%!%%%?%?%!??%%%!%%%%?!?%%?%%%%%%%!!!!!%?!!%%?%!!!!%%?!%%!%?!!%%%?!??%!%!%%!!?%!?%!!%?!!!%%!!!%%%!!%%!!%!!%!%!%!!!??!%!%%?!%!?!%?%%%?%!%?!%!%!%%%?%!%%?!%?%%%%?%%%?!!!%?%%!%!%%%%%!%?%?%%%%%%%?%?%%%%!%!!%%!%%??%%%!!%%??%!!%!%%!%%!%%?%!!!?%!%%%!%%%!!!?!!%%?!%%%?%%%!%!!%%%%%!!!!??%%%%?%%%!%!!%??!%%%%%!%%?%%!!??%!%!%!!?%%%%%%?%!!?%?%%!%!%!!!?%%%%%!?!!!?%%%?%%%?!%%?%!!?%!%%!%%!!!!!%%!!?%%%!%?%!%%?!?%?%!%%%!%!!!!?%%?%%%%%!!%!!?!!%%%!%%?%%%!?%%?!%%!%%%%?%!!%?%%??!%%!%?%%!%!%%?!!%%!%??!%%??%%?!%?%?!%%!%%%!?%%%%%%!%!%!!%%!???%%%!?%%!?!%!%%?!%!!%??%!!%%?!!%!!%!%?%!!%!%%%!!%%%%?!%!%%%!!??%!%%%%!%!!%%?%!?!!!!%%%???????%!%%%!!!?%?%!!%!!%!%%!!%??!!!??!!??!?!%??!?%!!!!?%%%?%%!!%!%!%?%%!!!?!!!%!%%!!%%!?!?%!%!%?%%%%%!%%%???!?!!%%?%%%%%?%!???%%!%??%?!!%%%%!!!!%?!!%%!?!%!!%!%!%%%%%%??%%?!%%%%??%!!?!!?!!%%%!?!!!%!%!!%%?%%?!%%%%%%!%%%%!%%?%%%?%%%?!!%!!%!%%?!!!%%%%!!%?%%!%%???!?%!%%!!!%%%!!%%!%???!%!%%!%%%!!%!?!!%??%!!%!%%%!?%!%%!?%!?%%!%%!%!%?%!%!%!%%%?%%?%%%%%%%!%!%?%%%?!?!?%!%%!%%%%%!!%%%?!%?%!%!?!???%?%%%???%%!%!!%!%%?!!%!%?!%?%%%?!!%?!%%!%!?!%%!!%%!%!%?!%??%?!%%?%?!%%!!%!?%!!!%!%!%!%!%?!%%%?!%%%!!%%%%??%!!%%??%?%??%%!%?!%!!%!%?%!%%!?!!%%%%%!?!!%?%%%!!%?!?!%!?%%!%?!%?%%?%???%%%?!!?%%%!!!??%%%!%%!%%%%%!%!%%!!!!!%%!!%!?!!!?%!%?!%!!%!?%%!?%%%?!?%%!%!!?%?%?!%%%??%%!!?%!!%%??!%!??%??%%%!%!%!!!%!%%?%%%%%?%%%%%%%!%!%%?%!%%%%%?%%!!%?!!!?%!!!?%?%%!!!?%%%!?%!%%!%!!!%%?!?!!?!%?!!%!!!%!??%!%%?!%!!%!!%%%%%!%%%!!%!!?%?%%%%?%?%!%?!%%%%%!%%!%!?!?!!%%%%%%!!%?%%?%!%?%!!%!%?%%%?!%%?%!!!%!%!%!?%?!!%%!%%??%!?%!%?!?%!%%!%%%!%%%%%%%!%??!%%%?%%%%?!%?%!%?!!!%%%%%%%%!!??!%%!!?!?!?%!%!%?%%%!!?%??%%%!%?!??%%!%?%?!%%%%!!%???%!%%%?%%%!!?%%!!!!?%!?%%%!!%%!!??!%%?%?!!!%!%%%%%%!!?!%?%!%???%!%%!!%%!!%?%?%?!?!%!!!!%%?%%!%%!!!!?%?%!??%!?!%!?!!%!%!%%!?!%%%??!!??%%%%?!!%%!!?%!%%%%?%%%?%%?%!%%%!%%!%%%%?!%?!!!%%%%%?!%%!!!%!?%?%!!!%?%%%%%!%!%%%??%!%%%%!%%!%!!%?%!!%%%%?%!!%%?!%?%%%!%%%!?!!!!!?%%!%%%%??!%?%?%%!%%!%%???!!!?!%%!?%%!%?%??%%%!%%!??!%%??!?%!%%!??%%%!!%!!!!%%!?!?%%?!!!!!%!!!!%!%%?%%?%!%!%?%!%!%%?%!??!%??%%%%!!!?!!%!%%%!!!?!?!!%%%%%!?!%%%!%!%!%%?%%!!%%%%%!%!%%%!!%!!%!%?%%%!!%?!%%!!!%!%?!???!%%?!%%??%%?%!%%%??!!%?!%?%!%%!%%%%?%%!!%!%?!!%?!!%!?!%%?!%?!%%!!%!%!!%??%%?%%!!%%%%%%%%%%!!%?%!!!!?%!%!?%%%%%%?!?%!%!!%%!?%??%!%!%%!?%%!?%%!%%%%%%?!!%%!%%!%%!!!?%%%%%%?!!!!%%%%%%%!!!!%!%?!%%%%%!?%!%!!!!%!%??%!?!!?%%?%!%?!!!%%!%!!%%!!%%!%%!?%!!!!!%%!!%%!!%%%%!%%!!%!%%%!!%?%%!%%?!!%!!%!!?%%!!?%%%!!%!%%%!?%!?!!!!!%!%%!%!??!?!%%%%!!?!?%%!%%%!%!!!!%!!!%%%%?!!%!!%!!%%!?%%%!%!!%?!%%%?!%!%%?%%!%!!%!?!!%!!%!%%%%?%!!%?%?%!%??%?%%%%?!%%!!%!!%!%%%%%!!!%!%%%%!%%%?!%!!%??%!!?!%!!%%!%!!?%??%!%!!%!%!??!!%!%?!!%?%%!%%%!%!?!%%!!?!!!!%%%%!%!%%?!??%!!!?%%!!%?!%%!%%?%%!%%%%%%!%!%?!?!!!%!%%!?!%%%??%!?%%%?!%%?!!%%!!%%?%?%%??%%!!!!%%!%%%%!%%!?!?!?!!%!%%%!%%%%!!?!!%%%!?!%%%%?%%%!!!!%!!!%%%!!%%!!%%%%%%%%%?%%!?%!?!%?!!%%%!!%!!%%%%!%%%%%!?!%%%!!%%?%!%%?%!%!??!%%?%%!?%%%!!!%%%?!!%%?!%!!%??%!%%!!!!%?%!%%!%!%!%!!%!?%??%%?%%%!%%!!!!%%%%!?!!%??!?%%%%%%%%%%%%!%?%%!??%?%!!!!!%%%%%%%%!%?%%%%!!%%?%!!?%%%!!?!%!!?!!!%%%?%!?!%%!%%!?%%%!!!!!!%%?%!%!!!!!?%!%%%!%%%%%??%?!%?!%%%?!!%!%!%%%%%?%!?%?!!!?%!%%!%%%!!??%!%!!!???%!!%%%%!%!%%!!%%?!!!!%%!%!!%%%%!?%%%!%!%%!%%%%!%%??%?%%!!%??%?!%%!?!%%!!!!?%%!%!!!%!%%!!%!!?%%!%%!%!%!!!%??!%??%?!%%%!%%%%%!!!!!%?%?%%%%%!%%%?%%!!%%%%%!%!%%%!%%!!!%?!%%%!%!%!%%?%%!!!%!%!%%!%!%%%!%?%%%!%!?%%%!%%!!!?!%%!%%!%%%??%%%%%%?%!?%?!!%%?%%%%%%%??!!!!%!%%!%!%?%!%!%!?%%%!%!%%?%!%%!?!?%%!%%?!!?%???%?%%?%%!!!!?%%?%%%!%%?%%%!!!!%!?!%!%?%!!?!?!%%!%%!!!!%!!!?%%%%%%%%!!!%%?!%!%%!?!?%%%!%!%%?%!%%!?%!%!!?!%%%??!%!%!%%!%!%%?!!!?%!%?%??%%!%!%!?!%?%%!!%%%!!%%%!%!!!%!%%%?!!!%%%?!%%%%%!?!?%??%%!%!%?%%!%?%%?%!%!%%%%%!?%%%%!?%%%%%%?%%!!%%!!!?!%%%%%!%!!!%%!%!%%!?%?!!%?%%?!%!%%?%?%%!!%%%%%??!!%!?%?%%%%!?%%%!%%%%!%%!%%%!?%?%!!%!?%%!%%?%%!%!%!?!%!%?!!%!?!!!%%?!%?%!%%%!%!%%%%!!%!!%!!!%%!%%%??%?!!%!%!%%!%!%!!!%!?%%!!!!!%%%?%!%%?%??!%?%%%?%%%%!?!%?!!%%%%?!!%!%%?%%!%%!?%!!%?!%?%!%%!%%!%!!!%%%?%!!%!%%!%%%%!%%!%%%%%%%!%%%!?%%!?!%!%!!!%!!!%%%%!%%%%?%%!!?!%%%!%!%!?%%!%???!?!%!!??%!%!%!?%!!!!%%%?%!!%%%%!%?%!%!??!!!!%%%?%!%?%%%%%!!%%%%!%!!%?!!!%%?!?%%!%%!?!%?%!?%%??!!%!!%%?%??!?!%?%!!!!!%!%??!?%%%%%!%!!%?!??!!%%?%%%%!!%%!?%!%%!%%%%!%%%%%!!!%???%!%?!!%%%!!%?!%!?%%?%!!%%??%%%%?%!%?%!%!%%%?!%%%%%%%!!!%!%!!%?!%!!!!%%!%%%%%%!!!!%!%%??%%?%?%!%!!%!?%%?%!%!?%!%%%!!%?!%%!%!%!%%!!!!!%%?%!!%%!!!?%!?%?!%!%!%?%!!!!!%%%%?!%!%%!%%?%%%%!%%%!!%!!%?%%!%%%!!%%%%!?!!%!%??!%!!!?%%!%?!!%!%!!%%%?%%%%?%%???%%?%!!%!!%!!!%%%%%!?!%!%%!%%%?!?!!?!%!!!!%!!%!%%?%?%!!%?!!%%%!%%!%%%!!!%!?%!!%%!!?!%!?%!!%%%%%%?!!%?%??!??%!!%%!?%?%%!!?!!%%?%%%%%!?%%!%!!!!%?%?%%?!%?%?!%%?%%?%?%%%%!!!!%%?!??%!!!%%!?!%!!?%?%%%%%%%?%%%!%!??%!%!%%%%?%!%?%!%!%!!%%%!?%!!!?%!%!%!%%%??!%!%%%%%%%!%%%%!%!%%??%%%!!?%!%%!!%?%!%%%!?!?%%%%%%%%!%!!?%%%!!%!!%%!%%!?%%?!?!%%%%?%???!!%%%!?%!?!%%?!%!%??%%%!%%%!!?!%!%!!!%!??%%%%!%?%?!%!!%%!%!?%%%?%!!%!!%%!%?%%%%%%%!%%%??!?%%!!%%%!!%!%%%%%?%!!?!%%%%%%!!?%!!!!%!%!!?!%%%?%%?!!!??%%!?%!%%%!%%%%!%%%?%%%%%!%%!!!%%!%%!!%%%!??!!!!%?!%!!%%!!%%!%!!%%?!%%!!!%!!%?%%!%?%?!?!%%%!%?%%%?%??%?!?%%%%!!%?%%%?!?%!%!%!!%%!!!%%!%!%%?%?%%%!?%?%!%%%%!!%%!!%%!%%!?%!%%%?!??%%%%%%%??!%%!!!!!%%%%!%%%%!!!?%%%!!!!!%?!!!!%!%%!%!%%%%!?%!?!!!%%!!%?%!%%!%%%%%!%%%%%!!!%!!!!!%%%!!?%!!%%!!!%%%%%%%%%%%%%!%!%!%%%?%!%?!!!!!?%!?%?%!!?%%?%%!%!?!!!?!%!%?%%?!%?%%%%%%%!%?!!%!!!!!%!?%%?%?%!%%%%???%!!!!!%%!!?%%?%!%!%?%%!!!%!!?%!!%%!!!!%%?%?!??%!!?%!%%??!%%!%?!!%%%?%%%?%%!?!?%%???%%!?%%%!!?%!%?%%%!%%!!%!%?%%!%!!%!%!%%%%%%?%!%%!!!!%!%%!!!??%%%?!%!%%%!%%!%%!%%!?%!!%!%%%%%%?%?!%!%!!%%%%%!%%!%?!%%!%%!%!%!!!%!%%%%%%!%%!%%!%!!%!%?!%%%%%!%?%?!%%?!!?!!!%!%%%%%%?%?%%%%!%%%??%!!?!!%!?!!%%!%!%!?%!%?!%?!?%!?%!?!%%!!!%%!?%%!%!%%%??!%??%??%%!%%?%%!%%%%%%%?%%?%%%%!!%%%!!%!!!!??!?%!%!%?!%!%%%%!!%!%!!?%!%%!%??%%!!!%%!%!?%%!!!?%%!!!?!%%!?%!%%%%?!%?!%%%%%%?%!%??%%!%!%!!!?!!%%!%!%!%%!?!?%!%!?!?%?!!%%%%%%%%!%%?!%?!!%?!!?%%!%%!%%!!?%%%%%%%!%%%%!%!?%%!!??!%?!%!?!?!%!!!%!?%%%!%!!?%!%%%!%?%%%!%!%%%!%!!%%!%%%%%%!?!%!%%%%!!%%!?%?!%!%!!!!%%!%??%!!%?%!?!%!?%!!%%!%%%!%!%%%!!%%?%!??!%%%%%?!%?!%?!%!?!%!%%?!!!%%%%%!%%!%%!!%!%?%!??%%%!%?%?!!%?!?%!??%!?%!!?!?%?!!!%%%%%%!%?!%%%!!%%%!%%!%%!!%%!?%%?!%%?!%!???%%!%%%!!!%!%%?%?%%%?%%!!%%!%%%%!?%??%!!%?%%!%!%%!%%%%%!!?!?%%!%%%%!??!%%!%?!%??!%%?%?%%!%??!%%%%%%!%!?%!%!?%?%%%?!!%%!!%%%!%!!%!%%%?%!%%%!%!%%%!%%?%%!%%!%%%?!%!%%??!%%!%%??!!!?!!%?%%??!!%!!%%%!%%%%?!!%?%%!%?%!!!?!%%!%?%%%?%!?%%!%%!%%%%!%%!%?%%%%!?%%%%%%!%!!!%?!%??%%%%?%%!?%%?%%!!!%%%%%%%!%%!?!!%%!!%%??!%!%%%?!%!!%%?!??%!?%!!%?!%!?!!%%%!!%%!?%%%!?%!%?%?!??!%!!!?%%%?!%!!%%!?%!?%!!!!%!%?!!!!?%%%%!?%!!!%!!?%%?!%!%%%%%%!%!%!?!%!?%%!??%%!!%%!%!!%%!!%!%%%!%!!?!!%!!!%?%!?!?%%%%!!!%!%%%%?!?%!%%%!!?%%!%!?%!%%%!%?!%%!!!%%%!!%?%%!%%!?!!%?%!!???%%%!??%%%%!%%%!?%!%?%!%%!?%%%!%%!%%%!%!%%%?%%%!!!%%%!??!%?!?!!??%!!!%%?%%??%%%!%%%?%%%%%!%%?!!%!!!%?%?%!%%???!%!!!%%!%%%%?%!?!%%!%%%!%!??!%!%%%!%%%??!!???!%!!%%%%%?%?!%!!%%?%!?!%?%!%!%!?%!!%%?%?%?!!%?%?%!!!!%%?%!??!!?%?%?!!?!!!%!%%%!?%?%%%%!%?%?!!%%%%!!%%%%!!%%%!?%%%!%%!%%%%%%%!!!%?!?!?!%%!%?%%!!%!??%%?%!%%!%%!%!!?!??!??%%?%%%!?%%%!%!!????!!!%%%!%%%??!!%!%%%??%%%%%!%!%!%!!!%!!%%?%%?%%%%%!?%!%%!?%%!%%%!!??%%%%%%!!%%?%?%!%?%!?%!%!%?!%?%?!%%%?!%%%%%%!!!??%!!!!!!%!%?%???%%!!%%!%!!!!%!%!%?%%%!%!!!%%%!!!?!!%%!%%%!%!!!!%!!%%?%?!?%!?%%!%%???!?%%!!?%%%%%!?%!%%??!%?%%!!!%%%%%%%%?!!!?%%%!%%%!%%%!!%%%!?!!%!%%!!%!?%%!%?%%%??%%%?%%!%%!%%%%!??!%!?%%%!!%!%?%?%!%??%%%%!%!%?!%%%%%%%?%!!%?!!%%??%%!%%??!!!%%%!%!%%%%?%%?!!?%!!%%%!%!!%%%?%%%%?%!%!!%%%!!%?!?%?%%%!!??!%!!%%%%%%%%?%?%%%%!%%!%????%!?%%?!%%!!!%?%!!%?%!!?%!%%%?!%%?!%??%!%?%?!?!%!%%%%!!%%%!?!%%%%%!%%!!%%%%%!%!%%!?%%?!?%%%%?%!%?%!?!%?!%%!!%?%!%%%!!!!?%!?!??!?%?%?%%?%%!%?!!!!%%!%%%%!!?%?%!%?%!%%!%!?%%?%!??%%%%%?!?!%%%%!!?!!%!%!%%%!!?%%!!!%!!%%?%%%%%%%!!%%%%?!?%!!%!??!??!%!%!%%!!%!%!!%!!%%!%!!%%!%!!%!!%!!%!%%%%?!%%?%%!%%%!%%%!?%%!!!??%?!%%?!%%%!?!%%!%%!%?%?!%!%%%%%!%!%%?%%!!?%!%!%!%%%?!%%%!%%!!?%!!%%!%!!!%!!?%%%!%%!%%!?!%!%!%%?%?%%!!!?!%%?!%%%!!?!!%!!%%%%?!%!%!!?%!%!%!!%%!!%%%!%!%?!?%%?%!%%%?%%!%%!!!?%%%%%%%%%%%!!%!!%%%%%!%%!%!!%%%%??%%??%%!%?!?%%!?!%%%%!%?!%%!%%%?!!!%!%!%%!!%%%%%%?!%%%%!%%%%%!!!%%%%%%?%%!%%!!!?%!%%%?%!!!%%!%!%!??%!%%?%%%%%!%!?!!%%!!%!!%?!?!%?%?!!!?!%!?%%%?%%!%%!%!!%!!%%%!%%%?%%%%%%!%%%!???!%!%?%!%!%!%?%!%%%%?!!%%?%!?%%%??%?!!!%%?%!?%%%!!%?%%%!%%?!!!!%%%%?%%%!!%?!!!!!??%!?%?%%%%%%%%?%%!%%%%!?%?%!%?%?!%!%%!%?%%!%%!%!!!?%%%%?!%%?!!!%%!%%%%%!%%%%%!%%!%?!%%%!!!!%%%!??!!??!%%?%%?%?%%!??!%!!%!!!!!?!%??%!%%!!%%%%%%%%?!?!?%%%!%%%!%!!!%%%%%%?%!%%%%%?!%!%%!%?%!%%!%%%%!?%!!?!!!%!!%%%!%!%?%!!?%!%!!?%%!?%!%!!%%%!?%?%?%?%!%%%!%%%?%%!!!!%%?!!%!!%?%%%%%!?!!!!%!%!%!!%%!!%%!%!!%!%%!??%!%%%%?%%%%!!%!?!%??%!?!%%?%?!?!%%?!%!%!%!!!!!%%%%%!%%!!?%!!%!?!%!?%??%%%%%%?%%!%!%%??%?%!%!?!!?%!!!%%%!?!?%??!%%%%!%??!!!?!%%%%!%%!!!!%!%?!!!!%%?%%%!%!%!?%%%!%!!?%?!?%!%!?!!!!!%%%%!%%?%!!%%%%%%!!%!%%%!!!%!??!!!!%?!%!!%%!%%!%%!%%!%!%%%%%%%?!%%%?!!!!!%?%?%%!%?%!%!!!%%%?%%!!%%?%!!!%!%%%!%%!%%%??!!?%%%%!!%%%?!%!%%?%%!?%?!?!%!%??!%%%!%!?!!?%%?%?!!!%%!!?%%!%!!%%%!%%??%!!!%%%%%!!?!!%%%?%??!%%%?!%?%!%%%%%%?%%!??%%?%%!%%!!?!%%%%%%?%!%??%!?!!?%%%?%%%%?%%!!?%!!?!%!!%%?!%!!!%!!%%%%!??!!%!!%%?%!%!!%?%%%!%!!%?%%%??%%%!!%!%!%!%?%%!!%!!!%??%!%%!%%%!!%%%?%%%???%%!%!%%%%!!!?%??%!%?!%%!??%??%!?%!!?!???!!!!%?!!%!!?%!%!%%%%%!%!!!%%!!%!%!?!%%%%?!%?%!%%??%%%!%%!%!?!%%%!%%%!%!%%!?%%%%%!!!?%%%!!!?%%%?!!!%!%%!%%!%?!!%%%??!!%?!%!!%?%??%?!!??!%!%!%%??!%!!%?%%%??!%!?%%%%!%%%%%%%%!%%%%!%!?!!?!%?%%%?%%%!!??%%??%!?!!?%%!?!!%%!%?!%?!??!??%%!%%!%!%!%%!%!??!?!%%%!%%!?%!!%???%!%%%%!!!%%%%!!%%!%?!!%%%!?!%%%?%%!??!%%?%?!?%!%%%!%%%%%!!!?%?!%%%%%%%?%!!%??%%%!%!%%%%%?%%%!!?%!%?!!%%?!?%%?%%?%!%%%%!!??!%!!%!!%%!%!%!!%%%!?%%%%!%!!%%%?%!%!%%!??%%!!%%%!!%!?%!%!!%!!%!%%%%!%%!%!!!%!!%??%?%%%%%?%!%?%?!%%!%!%%!%%%??%??%%?%!!??!!!!!%%!%%%%!!?!%%%%%%%%!%!!!%%!%%!!%%?!!!%%?%%%!?%?!%%%?%!%?%!!%??%!%%%!?%?!!!!!%%!!%%?%%%?%?%!!?%!%?%!!%!%!??!%%?!%%!!!%?!%%%!?%!%!!%%%%?!?!!!%%!!!!!%%?%%%%%%?!%??!?!??%%!%%%%%%?%%!?%%?!!?!?!?%%!!!?!?%%%?!%?!?%%%!?%?%%%%!%%!!?!!%%?!?%!%%%%?!%!?!!%%%!??%%?!!!!!?%!!%%?%?%%%!%%%?%%???%!??%%%%%%!%!%?!%!!%?%%!!!%?%!%%%%%%!?!%%!%!%!%!!%!?!!!!%%%!%%%%%?!!!%%%%?!%!%%%!%%?!!%%!%%!!!%%%?!!%%%%%!%%!!?!!!%!!%%%!%!%%%%%%??%!%%!%!%%%!%!!!!!%%%%%?!%%??!!%%%?%!%%%?%%%%!!%!%!%!!?%%??!%!!%!%?!!!?%?!?%%%%%!!%%!?!%?!!!!%!??!!%%%%??!%%?!?%!!!??%!%!!!%%%%?!?%%%??%%?%%??%%%%!!!??!?%!!?%%%!?%!!%%%!!%%?!!?%%!%!%%%!%!%!%%%!%%?%%!%!%%!!%!!%%!!%?!%%?%%%?!!%!!!!%%!!%%!%%%%%%%%%%%%?!%%%?%%!?!%!%%!!%%?!%%%!?!%%%?%%!%%!!%!%%%?%%!%!%%%!!!!%!%%%%!%!?!!!%!%%%!?!%!%!?!!%!!%%%?%%!%?%!%?%!%!%%?%%!%!?!!%%!%%%!%!!%!?%!?%%%?!!%!!!%%%!!%!!%%%%%?!!!%!%?%%!!%%!!%?!%!!??!%!%%%!%%!%?!?%!%%?!%!!!%?!%?%?!%%?!!!!!%%!%!%%%%%%%%!!?%%%%!%%%!%%???%%!!?!!%%?!%%!!%!??%!!%%%?!!?%?%%!%%!%%%%%!?%!%%%??%?%!%%?!?%%?!%%%!%!!%!%!%!%%%?!%%%!!!%?!%%!!??!!%%!%%!!!!!??!??%%%%!!!!%!%%!!%!!%%%%!%!%!%%%%!%!?%%%%?%!?%!!%!!%%!%??%!%!?%%???%%%%%!%?%?%%??!%%?!?!%%%!!%%??%%!%!!%?%!?%!!?!?%!%%!%%!!?!%!?!%!!%%%%%%!%%!??!%?%?!!!%!%%%%%%!%%%%!%!%%%%!!%%!!!!?%%!%!%?%!!%!!?%!!%%%??%%%%%!%%%??%!!!%?!%%?%%%%!%!!?%?%?%!%!%!!%%%%!%??!??!%%%%%!!%%%%!!%%!%!?!%!!!!!??%%%!%!!!!%%!?%??!?%!%%!%%?%%%%%?!!?%?!%%!!!%%%!%%!!?!!!?%%%!%?!%%!?!?!%!%%%??!?%%%%%!!?!?%%!??!%?%%!%%%!%?%%%??%!%?!%!?%%?%!!%!!%??%%%%!?!!%?%!!%%%??!%?!%??%????%!?!%%!???!%%%!??!%%!%%%??%?!?%!!!%?%%%!!?!?!%?%!??!%%%!!?%!%%!%!!?%!%%?%%%%%?%!%%%%??!?!%%%!%%%?!?!!!!!%%%%!!!%!!%%?!%?%?!%?%%!%%%%!%?%!?%%?%%?%!!%?!?%%!%?!%%!!!?!?%%%?%%?%!%%!%%%?%%%%%%%!!!%%%?!%%%!%?%!%%?%!%%!%%??!%!%!!%%%?!!%!%%!%%!%%%!%%%%!!%?!!!??!!%%%!?%%%%??!%?%!!%%%%!?!?%!!%!!%%%%%??!!!???!!%!!%?%%!!!?%!%!%!!!%?!!?!%?%%%%!%%%!?%!!%?%%!??!%!%%!%%!!!%%!!??%%%%!?%%%%%%!!%!?%%!%%%?!%?%?%%%!!%%!%!?!?%%!%%!!%%%%!?%%!!%!%%%?%!%!!!%?%!%%!?%%!??!%%%%%%?!!%?%%?!%!!!!%%%%%?????%?!?%%%%!???!??%!%%%%!??%%%%%?!%%%%!?!%%%%%!%!!!%%?!%!?!%%!?%!!%%!%%!%%!%?!!%%?%%?%!%!%%!%%!%%%%?%%%%%!!%!%!??!?%%!%%!!%!%?%%%?!!%!!%!%%?%?!%!%%!%%!!!%!%%?!%!?%%%?!!%!%%%%%?!%%?%%!%!%%!?!!%??%%%!%!%%%!%!%%!%%%!!%%!%%%%!!!?!%%?%!%%!??%%!!!%%!%!!%%%!!!!???%%?%?!%!!?%?!!!?%!%%%%%%%!%?%!!%%?!%!%%?!!!?%!%%%%!?%?!%?%?%%%%%?%!!%!%!%%?%%%?!%%%!%?%?%%%!!%%!%?%%%%!%??%%??%?!%%%!%??!%!?!%!?!!!??!%%%?!?%%%?%!???%!%??%%?!?!!%!!%%?!%?%?!?%%%!!!%%??%%!?%!!?!%%??%?%?!%!?!!!%?!%!!!!?%%!!!!%%%??%!%%!!%%%?%%?!?%?%%!?%!!!%!%!%?!!%?%!%?!%%%!%%%%!!%!!%?!!%%!%%%%%%!!%%%%?%%%%%?!%%!%%%%?%%%%%%!%%?%%%%%%%%%%!!%%%??%%%!%%?%%!!?%%%!%%%?%?!%%!%%!??!!%!%?%%!%!%?%%%%!%%!!%%%!%%%%!%%?!%!?%%%%%!?%%!%?!%!%!!%?!?!!!!%?%%%%?%%!%%!%!!%%!!%%%%%%??%!%!%?%!%%%%%!!%!!?!%%!%!?%!!!!%!%?%!!%%!%%!%%?!%!%%%%%%!!!!!!%?%%%%?!!??!!%?%?!??%%!%%%%%%%%%%!!!%%??%!%%!????%%%!!%!!%%%?%!!%!%%%!!%%!!!%%!?%!%!%!!%%%!!!!?%%%%!!!%%%!%?%%!!%%!%?%%%%?%?%!?%%%!?!!%%%!%%%!?%?!?!%%%%%!%!%%?%%!%?!!%!?%%!!!?%%%%?%?!!%?!%??%?!!%?%?%!?%%%?%!%%!%!!%%!%!!??%!??%!%?%?%!%%%%%!!?%?%%%%%!!!%%%!%!!!%%%!!?!%%?!%?!!!%!!%!%%!?%?%%%!%?%!%%?%%!%%!%!!%?!%%??%%%?!%%%%!%?%?%%!?%!!%%!%!?%?!%?%%%?%%!!!!%!?!?%!%!%!?%%%%%!?%%%%%%%%%%?!!%%%?%%!%%%!?%%%%%%!?!!!%?%%!!%!%?!%%%%%!!%!%!!!%?%%!!%!!%?%%!!???%!!!!!%!%%%?!?%%%%!!?%%%%%?%!!!?%!!%!%%?!%%?%!?%!%%?!?%%?!%%?!%?!!%?%!?%?%!??%!!?!%?!%!%!%?!!?%?%%!%!!%%?%%%!!!%!!%!%!!%%%%!!%!!%!%!?!!!!%!%%!?%%%%%%?!%%%!!?%!!!?%!%%%%%?%?%%%?%!%!?%!!%%!%!!??!!%%%%%!!!%%%!%!%!%!%!%!%?!?!!%%%!!!%!???%%%!%%?!!!%!!??!%!%!%!!%%%%%!!%!%%?!%%!?!%!%?%?%!!%%!!%??!?!%?!!%%!!%!!%!!?%%?!!%??!%!!%%%%!?%%!?!%?!?!!!!!%%%%!!%%??%!%%!!!!%?%%!%!!%!!%!%%%%?%%%!??%%%!!%!%!%!%%!!%%!!?!!%%%%!%!%%%!%%!?%%!%!!!%%!%!%!????%!%!?%%%%%%!%%?%%!%%?!!%%%%%%%%!?%%!%%%%!!%!!!!!%!%%!!!%%??%%%%%?!%%!%%%%%%!?!%!!%!%%%%%%!%??%??%!%!%%?!%!!%%%!%!?%!%%%%%%!!!!!!%!%!%%%%%!%%?%%%?%%!%!%%!%!%%%%%%%%!%!!!%%!!?!%%?!?%%%!!?%%!%%%!%%!%!!!?%%!?%%?%%!%!%!%!?!!%?%%!%!!!?!!%%%%%?!!!!%!!?%%!!%%!?%?%%?!!????!?%!!%??!%%%?!%!?!?%%%%%?!!!%%!!!!%%!%%!%!?%%!%%?!%%?%?%%%!?!!%?!!%!%!!%?%%!%!!!!%%%!!%!%!%%!%%%%!?%%!!!%%!??!!%!?!!%?!???!!%%%?%?%%%?%!?%!!%!!%?%!!%%?%!%%%%%%?!%%?%%!%%?%%!!!!%!!%??%%%%?%!?%!!%%%%!%%?%!!?%!%!%%%??%?%!!!%%?!%%%!%?!%?!%?%%%%!%!%%?%%?%%!!%%%%!!?%!!!?%%?%!%%%%!%!%%%%%!?!%!%%%%!!!!??!?!%%%!?%%!!!%?%%!!%!!%%!!%%%!?!?!%!%%!!?!%!??!%%%?!%??!%?%%%%!%%?%%!!%%%%%%%??%%!!%?%%%!?%%!!%?!!%%!%!%?%%%%!%!%??!!%?!!%!%!%!%!%%%%%%!%%%%!?!%!!%!!!%!!?%%%%%%%%%%!%!??%?!%%%%%!!%%!%%%??!%!?%!??%!!!%%%%?!??%%%%%?!%%??%%!%%%%%%%%!%%?%!??!?!%%%!?!?%!%%%%%%??!!%%%%!?!?%%?!!!!?!%!%%!%%?!!!%%%!!!%!!!!%%!!%!!%%?%?%%!%!!%%%!!!%!%%!!!???%%%!%!?%%?%%%?!!!%!%%%!%%%%%!?!%?!!%!%!%?%%!!?%%%%%%%?!!?%%??%!%!%%!!?%%!!??%%!%?!!!!!%%%%!%!!?%?!%?!?%%!?%%!!%?%?%%!!%!?!%%%?%!!!??%%?%!%%%%!%!?%?%!%%%!%%%%%!!!!%!%!?!%!%%%??!!%%!%%!%%!%!%???!!??!%%%?%%!!?%!%?!!?%%!!!?%!%!?%!%%!%!%%%!%?!%!%%%%%%%!?%!?!?%!%!!%!?%%%!%!%%%?%?%?!%?%%%%%!%%%%%?%!!%!!!!!?%%%!%?%%%!%??!%?!%%%%!%%!!?!%?!%%%%???!%?!!?%??%%%%%??%%!!!%%%%!%!!%!!!?%%!%%?%%%!!!%%%!%%!?!?!%%%!%%?%!!?!!%?%!%?%!%!%!!%?%!?%?%%?%!%!%%%%%!%!%%%!?!?!%!%!!!%!!?%?!?!!?!%%?%??!!%%?%!%%%!!!%!?%%!%!!?%%!!%%%!%!!!%!%%!?!!%%%%%%!%%%??!??!%%%%!!%%?%%!!%%%?%%!!!%??!!%%%%!!!!!!%!?%!!%??!?!!%!%%%?!%!%??!%%%%%!%!?%%?%%%!?!%%%?!!!%!%%%?!?!%%!%%%!%?!%!!%!!%?%%!%!!%%!%!%%?%%%?%?%!%?%?!%%?!%??!?%%%!!%?!%%!%!%%%?!%%!?!!!?%%?!%?%?!?%%%%!?!!%%!%!!%!%%%!?%!!?%!%%?!%!!!%%!!%%%!!%%!!%!!!%%!!!%!%?!%?!!?%%%!%%?!!!!!!%?%?!!!!%%%%%%%%%!?!%!%!%!?!%%?%!!?%!?%%?%%???%?%!!!%%??%!?%??%!?%?!!!%!%%!%!?%!%!!!%!%?%%%!!!%%%?%!?%!!%!!!%%!!%%!!%!%%%?%!%%%!!!!!?!!%!%!?%%%?%%!??!!%%!%%%%!?!!%%%!!?%?!%%%%%!%!%?%!!%!!!%?%%%?!?!%!!?!%%!%?%%%?%%%!%!%%?%%%!%?%%!%%!%%!%!%!!%!!%!?!!%%?%!!%%%%%?!%!%%!%%%%??%%!%%%!%%!!%%%%%%%!!?%%%%%%%!%%%??%%!??%!!%%?%!!%!!!!%!!%??!!%?%%%!!!!%!!!!?%%%%%!%%%%%%!!%%!%!?%%%!%?!?%!!%%%!%!%%%??%!!?%%%%%%!%%!%%%%%%?%!%?!%!!%!%%???!%%!%%%!%!!%?%%%%%!%!!!%%!!%%?%%%!?%!%%%?!%?%!%%%?%!%%!?%!%!%%%!?!%%!?!%!!?%?!%!?!%%%!!!%!!%%%%%!!!!?%%!%!!?!!!?%??!!%%!%%!!%%%%?%%%!%????!%%%!!%!?!%%?%!%!!!!!!%?!%!!%%%%?!?%%!?!%%!%%%!?%??%?%%%%!!!%??!?%!?%%%!%%%%!%?%!??!!%!!%%!!!!!!?%!%?!!!%%%%%?%!?%?%!%?!?!!%%!%%!?%%??%!%!%%%!%!%%!%!!!!?!%!%!!%!?!!!!%%!%%%%%%%%%%%!!%!%%%%%!%!%?!!%%!!%%??!%%%%!!??!%!%%!?!%%%!%!%!!%%%!?!%%!%%?%%!%!!?%%!%%%?!%?!%!!%!%%?%!!!!%!%%!!!%%!!%?!%!%%%%?%%%%%%%%%%%%!%%%!%!?%%?%!!%%?%?!%!!!%!%%%%?%%%???!?!%!?!!%%!%%!!%!?!%?%%%%?%!%%??!%%!!!!!???!%%%!%!%%%%!%%?%%%!!%?%?!?%%%!%?%!??%!!%%!%!?%?%%%?!%%%%!?%?!%%%!%!%!??%%!!!%%%!%%%!!?!%%%%%%%%?%?????!%%%%!?%%!?%%%!!%%!%?%%!?%!!!?!!!%%!!%!%%%!%%?%%%%?%!%%%%!!%?%!!%!!%?!%%%!!??!%!!%%%%%%?%!!%%?%!%?%%%?!!!%!!%%%!!!!%?!???%%????%!!%!?!!%%%%!!?%!%%?%!??%!!%%!%%%%!!%%%%?%%?!%%%!!!%%!%%%?!!!%?!%!%%%%%%%?%%!%%%%!%%?%%%!!%!!%%!!%%%%%%??!%%??%!!%%%?!%?!%%%%%%%%??!?!?!%!%!?!!!%%!%%%??!%%!%%%%!?%%!!%!!%%!?%%%%%%%?%!%?%%%%!%!%?%!!!%!%%%%%%%%?!%%%%?!!%%?!!%%%%%?%%%%%%%%%!%%%%%!%%???!%%%!%%%?!!%%!!!%!%%%!!?!?%%!!!!%!?!?%%!%%??!%%%!%%%!!!%?%%%!!%%%?%%?%?%!%!%%%?!%!!?%%?!?!?%%%!!!%??!!%%%!%?%!%?%?!!!%??!%%!?%!!!?!%%??%!!!!%%?%%!!!%%!%!?%%!%?!!%%!!%!!%???%%??%!%?%!%%%!%%!!%???!%%%?!!?%%%%%!??!%%?%!%%!!%%%%%!%%!%%%%%!!!%%%%%%%?!%%!%!!!%%!%%%%%%?!%%%%%%!!%%%%%!%%!%!!?%!%%%%!%!%!%!!!!%!!!%%%!%?%!%%?%!%!!!%?%!%%%!%!!%!!!%%?%%%%!%!?!%!!!%%%%!!%!%%!??%?%%%!%?!%%!!%!!?!%!%!!%?%!!!%!%!%%?!!%?!!!!%%%?!!!%!!?%!!%?%%%?%%?!%!%%%%?%!%!!%%??%?%%?!!%%%%%%%?%!!!%!!?%?!!?%%!?%?!%!%%%!%!!?!!%?!%??!%%?!?!!%?%?%!!!%!!%!!!!?!%!!%!%!%!%%!?%!!%%%%?!%!%?%%!?%%!%!%%?!%?!%!?!?%%!?%%!%%%%!%%%%%!%%%!????%!%%%%%%%!?%!%!%%!?%%%%%!%%?!?%!?%??!%?%!!%!%?!!?!%%%?%!%!?%!!?%%%%%%!%%%!%%%!%!%%!%%!%!!!!%%%?%?%!%%??%!!%%%%!%%!%%!!?%%!?%%%!!!%!%!!%%%%!!?%%?%!!!%%%%%!%!%!%?%!!??!!%!%!%!!!%%!?%%%%!%%%%%!!!?%?%??%!??!!!%%!%?!%!%!%%%%%%!!%!%%!!!%!!%%?!%!%%%%?%%%%!!!!??%%%%!%!%%!!%!?!!%!?!!%%%%?%%!%%!%%?!%?%!%%!%!%!%%%%%!?%%?!%%!?%%%%%%!%!!%?%%!!?!!%%!!?%!!!%%!!%%?%!%%%%!?%?%%?!!!%%%%%?%%%?%?!%%%%%%?!?!%!!%!%!%!!!%%!%!%%!??%!%%%%?%!?%%??%%!%%!%%!%%%%%%!%%%%!?%!!%%!!!!!%%?%%%!!?%!?%%%?!%!!%?!!!%%%??%!?!%??!%!?!?!%!%?!%!!!%!?!!%%??%!%!%%!%%%!?%%?%%%!%%%%?!%%%%!!?%!%!%?!!!%!%%%?!%%%!%?!?%%!%!%!?!%%!!%?!?%%%!%%!%%%%?!%%?!!?%?!%%%!?!?!%%%%%!%?%!%!%%%!?%??!%%!%!?!??%!?!%%!%??%??!%?!?%!%!%%!!%!%%%%!?!!!!!%%%%?%!!%!!!%?!%!!!%!%%%!!!!?!%%!?%!!?!!%%???%!!!%!%!?%%%!%!!!%%%%!%!!?!!%?%?!!!%%!!%!%%%%%!%%?%%!!%!%?%%!!%!%!?%%?!!%!?%!?%%%?%%?%!%!%%%!?%!?%%!%%%%?%%%%!%!??%!?%%%%%?!!!%!%?%!!!%%%%!!!!%%%!!%%?%?!%%%%%%!!!???%%%!?%!%!%%%!%?%%%?%?%!!%%%!%%!%%!??%?!??%?%!!?!?!??%?%%%%!!!!%%!!%?!%!!!?%?%?%%!!%%!%%!!%%%%!%%%?!%?%%!%!!%???%??!%%!%!!?%%%!%%%!%%%!%%!!?%%%%%%%?!!%!%?!%!!!%%?%!%%!!?%%!%!?%!%%%!!%%%%%%%%%%?%!%%???%!!%%??%%%%!!!!?!%%%!%%?%!!%??%%?!!!!%%%!%%%%!%!%!?!!%!??!!??!%!??!%!%%?!!!%??%%!!%%%!%%%!%%%??%!!?!!!?%!!%!!!%%%%?%??%!?%%?%%%!%%!%%!!%%!%%!%!%%%!%!!??%%!?%!!%%?%!%!%%!!%!%!!!?%%%%!%%%%?%%!%!%!%!!!!!%%?!!?%%!!?%%!%!%??%%%?!%%%!%%%%%!%%%%%%?%!%!!!%!!%!!%?!!?%%%!%!%!%%!!!??%!!?%%%?%%%?%!%%%?%!%%%%%?%!!%?!%!%%!!!%!%?!%!!?%!%%%!!!!%%%!!%?!%%!%!%!?!%%%!%%%%%!?!%?%!%!!%%!!!%%%!!!?!??%%%%!!%!%!%!%!%!%!%?!?%??%!%%!!!%!%%!?%!%%%!!!%%!%%%%!!!!%%!!%%%%%!!%%!%%%?!!!!%!%!!%!%%!%%!?%!%?%%%%!%!?%%%??!%!%%!%%%%!%?!!%%?!%%!%%!!!%%?%%!?%%%%?%!%!%%!!??!%%!!%%%?%%%??%?%?!!!%!%%!?%%!!%!%?%!%%!?!??!!%!%!%%!%?%?%?!?!%%!?%?%%%%%?!%???%%?%%!!%%?!%%%!???!!%%%%%!?!%%%%%?!?%!?%%?%%?%!!!%%%%%!?!%??!!%%!%!%!%!?%!??%%!%!%!%!%?%!%%%!!%%%%?!!%!!?!!!%!%%%%%%!%?%%%%?%!%??%%%%%?%?!?%!%?%!%%?!%!?%%!%?!!%?%?%%?!?%%%%!%!!!%%%%%%?!!!?!!!!%%%?%???%??%!?%%?!!!%?%%!%!%?%!%%!!%!!!!%?%%??!%!%%%!%%%%%%?%?%%!!!%?!?%%?!%%%?%%%!?!?%?!?%%%%!!%!!!!%!?!%%!%!!%%!!?!?%%!!%!%?%!!%%?%?%%%%?%?!%?%%%!!?%%%!%!%!?!!%!?%%%!!%?%!?%%%%!%%??!!%%%?%%?%!%%%!%%?!%!?%!?!%%%??!!%%!%!%!%%%%%?%%%!%%%%!!%%%%%?%!%%!%%%%??%!!%%!%!!%%%%%%!!%%%%?%%?%%%%!?!%?%!!%??!%%%%!!!!!!%!%!%%%!!%%!%!%!%%!!%?!%%%!?!!%?!!!!%!%%!%??!%%%!%!!!!!%%!!%?!%!%!%!?!%!?%!!%%%%?!?%!!!!!%!%!?%%%?%?!%%%!%?%!?%!%?%%!?!!%?%%!%?%!!!%!%!%%%%%?!!?!%%!%%!%?%??%!!%%%!!!%!%?%%!?%!!%%?!%%%!%!%!%!!!%!!!%!%%%%%!!%%%%%!?%?%%%?%%!!%%%%%%%%%?!!!%?%?%%%!!!%!%!!%!!!%!%!%%%??%%!?%%!!!?%!!%%!!%!!!%!%%!!?%!?!!??%%%!!?%%%%%%%%?%%!???!%%%?%%!%?!!%!%%!%%!%!%?%%%!?%!%%?!!%!!%%!?%%?!%!%!%%%%%!%!%?!!!%!?!%%!!!!%%???%!%%!%%%%?%%!%???%%!?%!!%%%!!!%%%!!!%!%%!!!?%%?!!!%!%%!%%!?%!!%%%%%!%!%!%%?!!?%%%?%?%%!!!!%%%%!?!??!?!!%!!?%!!???%!%%!!%!%?!%%!%%%%%%!%!?%!%%%!%?!%%??%%%%%!%%%%!!!%%!?%!?!%%!?%%?!%%%!%?%%?%%?!%%%%%%%!!%%%%%!%?%%%%%%?!%?!?%%!%!?%%%%%%%%!%%%!!%!%%%%!%!%?!!%%?!%!%!!%!%%?!???!%%!%!%%!??!!%%!%!%%!%!%%!%?%??%!!?%%%!?!%%%??%!?!?%%%!%%%!!%?%%%!!%!??%!%!?%%!!?%!%!%%%%%%%!%%!%%?%%%%?%%!%!!?%%%%%%%%??%?!!?%%?!?!%%!?!!%!%!!!%?!%%%?%%%%?!?%%%!%!!%!?%%?%%!%?%%!%%%%!%%%%!%%!!%%%!!%%!?%!%?%!!%%??%!%%%?%%?%%%%?%!!!!%?!?%%!%!!!%!%%?%%%??!!!!%!??%!!%%%%!!?%%%?!!%?!%?%?%?%%!!%?%%!??!%%%%!!!%%%!%%%%%!?!%!%%%!%!%%%%!!%%%%%%%%??%%%?%%%?%%%?%!!%?!!!%%!!%%%!%%%?%!!%%%!!%%!%!!!%%!!%%%%%!!%%%%?%%%%%%%!%%%%%!!%!!%!%%?%!!%?!%!%!!?%%%??!%!!!%?%!%%!%?%%%!?!%%%!%%!%%%!!%?%%%?%?%!%!!%%!!!!%%??%%%%!%?!%!?%?%??!%!?%%?%%%%!%%%%!?!%%?!%%!!!%%%?%!%%?%%%%!!%%!!?!%!%%%!%!%%%%%%%!!%!!?%%%?%!%?%%%!!!%%?%!%!%%%%%%!?%!?%%!!!!%?!%%%%%%%!?!!%!??%%?%%!!?%%%%%?%%!!!?%%%?%!%%!?%%!%%!!%!%?%%!%!!?%%%%?%!%!?%%!%%%%?!?!%%%%!%!%%%!!%!%!?%!%!%%!%!?%!!!!%%!!%!%?!%!?!!%!?%%!!?%!%%!%?%?%%?%%!!%?%%%%!!!%!%!%%%%%?!%!!%%!!?%%%!%%?%!%!!%%%!%%????%!!%%?!!?%!%%%!!!%%!!?!%%!?%!%%%!%!%%%!%%%%%?%%%!%%%%%?%%%??%??!!!%%%%?%!%%%!%!!?!%!!%%!%%!%!!%%%!?%!%%%%%!%%%!%?%!%?!!%%?%???%?%%%%%?%%!!!!?!?!?%?%?!!!%%%%%!!!!!!!!!%!!%!%%?%?!%?%!?!%%!%?%%!?%?!!%!!??%%!%%%%%%?%%!%%%%?%%%?%!!%%%%!?!%!%!%!!!!%%%%%%%%%!!!%%!!!!!%%??%%?%?%%!%%!!%?%%%?!%!!?%%!!?%%?!??!%%!!%!!?!%!%%!%?%%%!%%!%!%!!%%!%%!!%%%%%!%?!!?!!%%!!!%%??%!!?%%%%!??!%%%%%%!%!!%!%???%%??%?%?!?%%?!!%!!??!%!????%!%?%!%%!%%%!%!!%%?%!%?%???%%!!!!!!!%?%%%%!%%!%!%%!%!!%!?!!%?%%%%%!!%%%%?%!!%%!?!?%%%%%!!?!!%%!%%%%!%%%????!%??%%!?%?!%!?!%?%%!!%?%%!!??%%!%!%?!%!!%!!!!!%!%!%%%%?%!??%?%%?%%%!%%!%%!%%%%!%%!?%?%%%!%!!!!%%%?%!%%%%%%?!?%%?%%!!%!!%%!%!?%!%%%!?%%!!?!!??!?!!%%!%%%%%%!?%%%?!%%!%%%!?!??%!%%?!!?%%%!!%%!%%!%%!%!%%%?%%?!!%?%?!?!!!%%%!?%%%!?%?!?%%!%!%!%%!!%%!%%!!?%?%!?%%!?!%%?!?!%!%!%!!?%?!%?%%%%!%!%%!%!?%!!%%%%%???!!%!%!!%!%!%?%?!%??!??%%!%%%!%!?%!?!%?!?!!?%%%%%?!?!!!%!%%??!!%?%%%%%%%!%%?%!%!!%%%%!!%?%?%%!%%?%!%%%!%!?!!??%!%!%%%%%%%%!!%%?%%!!?%!%?%%?%%%%%%!%?%!?!%!%%%!!%%!!%!%%%?%!%!%!!?!!%!!%%%%%%%?%!?!!?%?%%!?%%!%%%!!!%%!%%?%%%!!%%!%!!%%!!%%!%!?%!?%?!?!?%??!!!%%!?%!%!%%%%!!!%!%%?%%?%!%%!%%%?%%%%!!%!!!%%!!?!%??!%%%%%?!%%!!%%!%%!!%%%%?%?%!%?!%!%!!!??!!%%%!%?%%%%%%%%?%%!!!!%!!!?%?!%!%?!??%!%%%!%!%%?%!%?%!?!%?%!!??!%!%!%%%%!%?%!?%!?!%%%?!%!%!%%%%!!%%?!%%!!?!!!%???%%%%%%?!!%%!%%!?%%?%??%%%%%%!!%!?%?!%%%?!!%%%!?!!?%%!%?%%?!!%?%!%%!!%%?!?!!!%%?%!%%%%%!?%%!%!%%!!??%!!%%!!?%%?%%!%%!?%!%%%%?!!!?!%?%%!??%!!?!!%?%%!?!%?!%!?!%%!%?%!?!%!%%%%%%%!%!?!%%!%!%%!!?!!!%!%!%%%%?%!!%!%%%%%!!!%%!!!!!%!!%%?%%!%%!%%!?%!%!?%!%!%%!?%%!!%?!!?%%!%%%%!!?%!%!!%%%??!%%%?%!%!%%%!%%%!?%%%?!!%?!!%?%?%!!!%%%!%!!?%%%!%!%!!?!??%!!%?%%?%!%%%%%%%%?%%!!!%!!%?%%?%!?%?!!!%??!%?!!!?%!?%!?!%!%%%?%!!!?%%%!?!%%%!!!!??%%!??!!!%%%%?!%%%!?!!%!!%?%?%!%!%?%%%%?%%%?!%!!!%%%%%!!%%!!?%%!%!!%!!%!!%%?!?%!%%!!!%%%????%?!!%!%%%?!?%%%!!?!?!%!%?!?%!%?%!%!%?%%?%%!%!%%!!!%%%%!%?%%?%%!?!?%?!%%%%!%%?%%?%?%%?%!?!%!!%?!?!!!?!?!%?!%%?%!!%!!%%%%%%!?!!%%!!?!!%%!!!%!%!!!%?!!%??!!%%!%!%?%%%%%?!!!??!!!%%%?%!?%%!?%!%%%?%?%%%%%%%%%%!%%?%!%!%?!?%!!%%?%!%!%!!!%!!%?%?%??!!!!%%?%%%!?%!!%?%%?%%!%??!!%%%%?%??%!%!!%%!?%!%!%?%!!%%%%!%%%!%%%!%%%%?!%%?%!%%!%%%??%%%!!%???!%%!!%%%!?!%%%!?%??%%%%!!?%!?%%?%%%?!!%!%?%%!!%%??%!%!!?%!?!%%!%?%!%%%?!??!%!%!%?!?%%%?%%!!%!%!%%%%%%%%!!%!%%?%??!%%%!%!%!!!?!%%%?!%%!%%?!?%!%!!!%%!?%!%?!%%!?%%%!%!%?%%%?!!!%!!!%%%!!%!%?%!%%%%!%%%!!?%??%%!%%?%?%!%!%!%%%%%%%!???%?%%!!%!!%%!?!!!%%!!%%%!!%%!?%%!?%%%%%%%!!%!%!!%%%%!!%!%%!!%%!%%%?!!?!?%???%!!%%%!%%%%%!!!%??%!!!!!!!%!%!!?%!?!!!?!%%!%%%!%!!!%%!!!%?%%?!?!!%%%%%!%%%%!%%%%%%!%!?%%%%%?!?!!!!%!!!%%%?!%%%!??!%??%%?!%%!%!??!!%%%%?!!?!!%!%%%?%!%%%%%%??!%%%!!?!%%%%%%?%!!%!!!!!%???%?%%!?!?%%%%!%%!!%!%!?!!%%!%?!%%%?%!%%!%!!%!%%%%?%?%!%!?!!!?%%%!!?%!%%%%%!!!%%%!!%%%!??!%%%%!?!?%?!!!?!!%!!!!??%?!%%?%%%!%?!?!%?%!!!%?%?%?%%%!%?%!%!%!%!%%%%%?!!!!!!%%?%%!%%?!%!%!%!!?%!!%!!%%%!?%!%!!%%%%%%!%%%!!%!%!!%!%%%%!?%?%%%?!%%%%%?%?%!%!%!!!%%%%?%?!%!%?!%?%%%%%%%!%%!%%!?%!%?!??%%!!?!?%%%?%!!%!%!%%!%!?%!?%%%?!%?%?!%%%%!%!!!!%??!??%%%%!!!?!%!%%!%%!%%?%!%!!%%?!%%?%?%%??%%%!%!!?%??%!!%%?%!!%!%!!?!!!%%??%!!%%%!%%?%%!%!%%%%%%%%%!%%!!%%!!?%!?!%%%%!%%%!%%!%!!%!???!!!%!!!?%??%%%%???!%!!%%%!%!%%!%!%%?%%!%%?%!%%?!%%%!!%?%?%%%!!%%?%%?%!?%!%!%!%%!!%%?%!!%??!!!!!!%%!%!%!!%%%%%%?!!!%!?%?!!%%?%%%%%%%%?!?!%!!!%?%%!!%!%!%?%!%!%?%%!%!!%!%!%%%%%%%!%?!%%!%%?!%!!%!!%!!!%%?!!!!%!%%%%!!!%!%!!%%%%!?%!%%?%!%!??!%%%%???%!%?!%!%???!%!%!%%?%?%!%!%?%%!!!%%!%%!%%%!%!%%%!!!%!!!!!%%!?%!!!?!!?!!!!%%!!%?%!%!%%!!%!!!!?%%%?%%??%%%?%!%!!%%!!%%!!%%%%??!?%%%%%!!!?%!?%%!%!!%?%%%!%!%!%!%??!%??%!%%!%%?%??%!!%!%%?%!%!%%!%!?%%%!%!?%%%%!%%%%%%?%?!!%%%!%%!%%%%%!!?%!%!!!%?!%!!%%!?%%!!%?%!%%%%%!!%!%%!%%%?%!!!%!!%!?!!%%?%%%!%%!!??%%%%%%%!%!?%%%?!%!%%%%%!!?%!?!%%!%?%!?%!!%%!!%%%!!!!%!!!?%?%?!?%!?%!%?%%?%!%!??!%%%%!%!%?!?%%?%?%%?%!!%?!!?%?%?!%%!?%%%??!!%!%!%!!%?!!!!%%!%!!%!%%!%!%%?!?!?%!?!%%%%%?%%!%%!!!!%%?%!%!!?%%!!%?%%%%%%!!%!!%%%%!%%!!?%%!%!!!!%%!%!%?!!!%!%%%%%%!%!%?%%%%%%%%!!!!!%!?%!!%%!%%!!!%%?%!?%!%%%%!!?%!%%!%!%%%?%!%?%!%?%%%??!?%%%!%?%?%%%%%%%?%??%%%%%!%%!!%%%%%%!?%!%!!?%%!%%%!?%!%!!!%?!%%%!%?!%%%?%!!!%%%?%%%%%?!%%!!?%%%%?%!?!?%!?%?%!%!?%!!?%%%!!?%%%%%?!%%?!!?!?%%%!!%!!!%%%!%%%%!??%!!%??!?%%%?%?%%!!!%%%!%!!!?%!!%%%%%%%!?%??%%?%!?!%!%?!!!???%%!!%!!?!?!%%?%%%%%!!!%?!%%%%!!!??%%??%%!!?!%%%!%%%?%%%%%%%!?!!%%%!%?!%?!%!%!!%%%%%!%%%%%%%!!%%%??!%%%%!!!%%%?%!%?!%??!%%!%%!?%!!%?%%%%%%%!%!?!%%%%!!!%!%%%?%%%!?!%%%%%!%%%!%%!%!?%?%!%%!%%!%!%%!!!!!%?%%%%%%%%%%!%%?%?%!!%?%!%!!%%%%!%%%?!!%%!%!%!%!%%%%%%%%!!!!%%%?%%!!%%!%%!!%%!!%%!%%??%%%?%!!?!%%%%%%!?!!%!!!%%??!!!%?!%%%%%!!!!%!%%%%??!%%!%!%%%%%%!??%!%%!!?%!%%?%?%!%!%?%!!%%%?%%!!!!%!%%%!!%!%???%%%?%!%!%%%%%?!%!%!!!%%!%%!!!%%%??!%!%%%%%!!%!%%!?%!!%?%%!%%%%%%!??!%%%!%%%%%?%!%!!!??!%%?%%!%?%!%%!%!!%!!%%!!%?!%?!%%%%%%!%%%??!!%??%!%%%!%%%%%%!!!!%%!!%%%%!!%%%%%?!!!%!??%!!%%!%?%!!%%!%%!%%%%?%%!%!%%%!?%?!!!?!%%!?%!?%!%!?%!!%%!?%?%!!%%%%!%%!%%?%%!%%%%!%!%!%%%%!%?%!%!!%!%%%%%%%%%%%?%!%%%%%%?%%%%%%?%%?%%!%%!!??!%?!!!%??!!!%??%?%%%%?%?%%%%%%?%!%%%??!%%%%%%!!!%%%??%?!%%%!!!?%?!%!%%%%!?!??%%?%!!!!%!!%?!%!%!%!%!%!%??%!!?!%%?%%!!!%!%%%?%%!%%!%!%%!%!!%%!?%!%%?!%?%%!??%!%%%%%%%%%!!%!!%%!?!%!%!%%%%!%!!!!%!?!%!?%%%!!%%%%!?%%??%?%??%%!!!%!%?!!!!%%!%!%%??!%%%%!!%%%!?!%%%%?%!?%%!!%?!%?%!%!!!!?!!!!%%%?%%%!??%%!%!!%?%%%!!?%%%!%??%!%!%!%!%%%!!?%%!?%%%?%%??!%%?!!%!!%%!%%%!!!!%!%?!?%?!%%!%!??%!%!!%??!!??%%?!%!!!%?%?%%%%!?!??!!%%%!%%%%!!!%%%%!!%!???%%??!!%%%%!%%%%!%%!?!!??!%%%!!%%%?%??!%%%!%!!%!!%!%?%%%!%%%%!%?%%%!%!%?!%!??%%%!??%%!!!!%?%%?%!?%!%!?%?%%%!!!%%!%!!%%!%%!?!?!!!%!!%%%!!%%!%%!%%%!?!%%%!!%%%!?!?%%!?!!!%%!%%?%!%%?%!%!%%?!?%%%%!%%%!%%%%!%!!%??!!?%%?!!%%%?%!%%!?!%!%?!!!%%%!%%!!%%!?%%!%!%%!%%%!%%!%%%%%%%?!!%!%%%%?%!%%!!%!%%%??!!!%%!%!%!?%!?%!!%!!%%!%?%%%%!%!%?%?!?%%%!!?!!!!%%%!%!%?%%!%?!?!%!%!%!!%%%?%%?!?%%?!!%%%!?%%!!!!%%%%?!!%!%!?!!!%!%?%?%!%%%%%%!!!%%!%?%!%!%%!%%!%!?%%%?!?%!!!%!%!%?%%%%!!%%?%!!%!!%%%!?!?!!!%%!%!?%?!!%!!!%!!%!%%!?%?%%!%?%%%!%%%%!%%!%%%%!!!!!%?%!%!%%!!!!!!%!%!!%%%!!%!%%%%!!!%%%!?%!%!!!!%!%!?%%?%?%?%!!!%%!!%!!!!%%%!%!!?%%%?!%%%!!%%%?!%%!%?%!??!!%%?%%%%!!%%%%!%!!!%%?!%%%%!!!%!!!%!%?!!!%%%!!!!!?%%!!%%%%!!%!%!%%%!?%!%!!!%!!?!!%?%?%!!?!%%%%!%?!%!%!%?!%%%!!%%%?%%?!%!%%%%%%?%!?!!%%!%!%%%?%%!%%!!%?!?!%%!%?!%%%%%!!%%%%!!%%?!!!!%%!?%%?!?!!%%?!!!?%%%?!%?%%%%%!%%%?!%%!%?!%%%%!!%%!%%!%%!%?%??%%%??%!%%?!%%%!!?%!!%?!!%%%%!?%%!!!!%%?!!%!???!!??%!%%%%%%%!%?%%%!?!%%!%!%%?!?!%?%%?%%!?%%%!!!%%!%%%%%?!!%!?!!?!%%?%?%%!%?!%?!!%?%%!%%%!%%%!??%!%?!!?!%!%!?%%!!%%%%%!%!%!%%%%%%%?%!%!!%!?%??%%%%%%!?!!%%%???%%%%!%!!??!!%%!!!%??%%!%!%%%!%%%!%?!?%%%%!%%!%!%!????!!%!!%%!%%!%%%%!!%!%%%??%?!?%%%!%!%!%!!!?%!?!%%%%!%%!!!?!%!??%%%%%?%%%%!%!!%%%%%!!!!?%!!%!%?!!?%%!?!!%%%%%!!%%!?!?%!%!?%%%%%!!!!!!!!!%!!%%%%??%%???%%%%%%!!%%%%%%?!!%%!%%??!%%?%!!%!%!%?!%%%??!%%!!!?!!!%%%!%?%?!!!%?%%!!?!%!%%%%%!!!!!!!%!%%%?%!?!!!?%!?!!!!%?!%%%?%!!%!!%%%%%%?%?%%!%%%%%%?%%?!%%%%!%!!%??%???%?!!!?!%%%%%!%%!?%%!%!%!%!%%!%%%%%?%?%!!?%!?!%?!%!%!%??%%!%?%!?%!%!%%!!?!%%%!%%?%!%!!%?!%!%%%%%!%?!?%!?%%%%%!%%!%!%!%%%!%!?!!?%?%%!!!!%%?%%%%!%%%?!%!!%%!%!%!!!!?%!%!?!!??!!!!%!%!?%%%!%!%%!%%!%!%%%%!%!%%!!%%!!%%!!!!%!%%?!?%!%!%!?%!%%!!%%%!%%%%%!?!%!%!%%!?%%?!%!%!%!!%%!%!%!%%?%!%%%!??%%!%%%%%!%!%!?%%!!!%?!%!!%!%?!?%?!%!!!!%%%!!?%!?%!%%%!!!?%%%%%!!!!?%!!%?%%%!!??!!!?!%%%%%?%%!%%!!!%?%?%!?%!!%!%!%%!!!%?!!%!?!!??%!!?!!!%!!%%%!%?%!%%?%??!%?%!?%%%!?%%??%%!%%!%%!%?%!!!%!!!%%!?!!?%!!?%?!%!%!%%!?%%%!?%!!!%?%??!!?!!%?%?!!!?%%%%%%%%?!%?%!?!%%%%%%!%%!!?%!!!%!!%%%%?%%?%%%%!%%%!%??!%!%!%!?%%%%!!%?%!!!%%%%%!%!%%!!?%!?%%!%!%%!%%%!%!%%%%?%%!%?%%!%!??%!!!!!!?%%!??%%%?!%%!!%!%%!?!%%%!%%????%%%%%%!!!%!!%%%!?!%%%%?%%!%?%%?!!!!%%%?%%?!!!?!%%!%!%!%?%%!?%%%%!%!%!!%!!!!!%%!%?!!!!!%!%?%!!!!%!?%!!!%%%%!%%%!%%%?%%?%%%%%!!%%%?%%%!!%!!%???!%%!!%%!!?%!%%%%%%%?!%?!%?%!%?%!?%%%%%%!!%!%!!%%?%!??!!%!?%%!%!%%!?%!%!%?%!!?!%%%!!%%!%%%%!?%!!??!!%%%%%%!!%%!%!!%?%!?!!!!?!%!??%%!%%%%?!%!%%%!%?%!%%%%%%%%%%%%%!%!?!!%%%?!%?%%??%%!!!!%!%!%?!%!?%!%%!%%%%?!%!!%?%!!%!%!???%?%!!?!!!%%!%???%?!%%?%!%%!!?!!!%%%!%%%%?%?!!%!?%!!%?%?%%%?!!?%!%!?!%!!?!!!%%%!%%?%%!!%%!%%%%%%?!?!!%!!%%%??%!?!%%%!%!%!%%%!!!!%!%%%%!%%%!!?!!??%?%?%%%?%%%%%?%?%%?!%?%!%?%?%!!%%%%%%%%?%!!%%!!!!%!%!!%!%!%?!%?%%!%%%!!!%%%%!%%!%%?!!!!%!%%%%%!%%!!%%!!?%!%!%%?%?%!%!!!%%%%%%%%!!!!%?%%%%%!!?!%%%%%%!?%!%%!%%%!%!%%%!!!!%?%%%%?!%??%!!?%%!!!!%%%?%%%%%!%%%%!%%!?%?!%%!?!!!%!%%%!%!%?%!!!!!%!%!??!!!?%%?%!!?%%%???%%!!!%!%?!?!!!%!!!!%!%!!%!!%%%!!%%%!%!%%!%!?!!%?%%!?%%%?!%!!%??%%!%%%%!!%%%%%!!%!%%?%!?%!?!!!?!??%!%%%%%??!!%!?%?%!?!%%!?!%?%%???%?%?%!%!!!%!%!?!!%!%%%%!!!%?%!%!?!%%!%!%!%%%!?%%%%!%!?!%%?%%%!%!%??!??%%?%!!%!!!%?%!%%%?%!%%?%!!?%%!!?%!!?%?!%%?%%!?%!!%!%%%??%!%%%!?%%!!%!%%!%%%%?%%%??!%?!%%%??%?%??%?%%!!%%%!?!?%%%%??%?%%%%%?%%??%%!!!!?!??%%%%%!%!%%??%%?%?!!???!%!%%!%!!%!!%?%%!%??%!!%%%!!%?!%%!%%??!%?!%%?%%%?!?!%!?!%!%%%!?%%!!%!%%?%%?%!?%!%%!!%%%!?%?!!%!%?%%%%%!!%!?%??%!%%!%!%%?%?%?%%!%?!?!!!!!?%!%%!%?%!%?%%!??%!!!%?%!!!!%%!%%%%%%%!!?%%%!!!%%%%%%!%%%????%!!%?%?!!?%%!!%??!%!%??%%!%!%%%???!%%%!!!%!%!!!%%!%%?%!!%%%!?!!!??%%%%!%%!%!!%?!%%%%%%%!%%?%!%!!%!%%!%?%!!%%%%%!%!?!?%!?!!%%?!%%%!%?%?%%!%%%?!%!%%!%%%%!%!!!%!?!%!%!%!!?%!!%%?%!%?!%!%?!!%%!%%%%%!??!???%%%%%?%!?%%!%!!!%??%%%!%%!?%%!%%%!?!%!!%%%%%!?!!??%!!%%!?%%%%!!!!!%!%??!?%%!!%%!??!?%!%%%!!?%%%!%?!!!!%%!%%%!%!?%%!%%%!%%?%%%!%%%%%%!%%!%%%%?%%!%!%%?%%%!%!?%%%%?%%!%?%!%?%!!%?!?!!?!%%!%%%%%!%%%%%%!%%?!?%%%!??%!!!?!!%?%?%?%%?!%%%!!!%%%!%%%%%??!%%!?!!%%%!??!%!%!%????%!%!%%%%!%!%?%?!%!!%%!!%%!%%%!%!?%!?!%!!%!?%!%%!!%?%??%!%%%%?!%%!?!%%%%!%?%!!%?%!%%???!%!!%%%%!!!!!?%?!!%%%%%?!%?%!%%!%?!!%??%%??%%%!!!?%%?%%%?%%!%??!!%?!%%%%?!?!!%!%%%?%%!%?%?%!%!%%%!?!%%%%!%?%?%%%%%%!%%%%!!%%!!%%!%%!%%?%!!!!%!?%?%%??%??%%!%%%%!?%!?%!%%%%??!?%!!!?%?%%!!!!??!%!!%%%%!%%!%!!!!%?!%!?!%%?%?%%%!%!!%!%%!%!!%?!%!!!!%?%?%%%%%%!!!!%!!!%%%!!?%%!!?%%!%%%%%!%%%?%%!!!%%!!?%%%%%!%%!?!%%?!%??%%!%!?!?%?!%%!%%!!?%???%%%%!%%!%%!!%%%%%%%%%!%???%!!??%%%%%%!!!%!?%%!!!%%%%%%%!!!!%?%%!!%!%?!%!%%?%%?%!%%%!!!!%%!!!!?%!%%?%%!!%!%%%!%%!!!??%%?!!!%%!%!%%%%!?%!%%!%%%%%%??%!!!?%%?%%??!?%%?%!!%%%%?!%%%?!!!!!%%!%!!!??!%?%?%%%%!%%%%!%%%%!%%%!!%!!!!%!!?%%%%!%?!!!!%!%!!%!!%%!%%!%!!%?%%%%!%!%!!%%?%%%?%!%%?!%%?%!?%!%!%!!%%!%?%%%%%%???!%!!%!%%!?!%%!!!%%!!%?%!%%?%??!?%??%!?%!%%%%?%%!%!%!?!!!%%!%?%!%%?%!%!%%%%!%!!%%%%%!%!!%?%??%%!%%%?%%%%%!!!%!%???!%?%%%!?!!%%!!%!%%%%%!%%!%?!%%!?%!%?%%%%%%%%%!%%%%%!%%%%?%%?%%%%!%!%%!%!%%!%!?!%!!!%?!%!?!%%!%%%?%!%%?!%!%!!%!%%%!!%!!%%%?!!%%%!!%%%!!!%%%%?!%%?!%!!!%%%%%!!!!%%!!!%%%!!!?%!!?%?%%%%?%!!!??%!%%!!?%!!!%?%%%!%%?%!%%?%%%!!%%!%!?%%%!!%%!!%%%%%%!!!%%??!!%??%!!?!!%?!!%%%!!?!%%?%!!%!%%%!%%!??%%%%%!%%!%%!%!!%%!%%!%%%!%!%%%?!!!%!%%!?%??%%!!%!%%!%?%!!!%%?%!%!%%!%!%%%%!%!%!?%%%%!?%!%%%%%!%%%!!%?%???!%!!%%%??%?%?!!%%?!??%%!%!!??%?!!%!!??%!??!%!%%%?!%!%%!%%?%%%!%!??%!%!%%?!%!%!??%%!%!%!%!!!!!!!%?!?%?%?%!%?!?%?!?!%!!%!%%%%??!%!!!!!?!?%%?%%%%!?%?%!?%?%??!!!%!%%%%%%?%%!%%?!??%!%!%?%%%%%%%%%%?%%%%%!?%%%%!%?!%!%%%%?%%!??%??!?!!%%?%!%!%%%%!!!%%%%?%%%!!%%!!%!!%!%%%?%%%!???%%%%!!!??!?%%%%??%!!??!%%%%!!%%%%%%?!%%!!%??%%%!%!!!%%!?!%%!%!%%!%!%!?%!!%!!%%!%!%!%%%%?%%%%?%%%%%%!!%%?%%!!%%??%%!%!!?!%!%%%%%!%?%!!?!%%%%%?!!%%?%%?!%%%%%%!%%%%!!%!%%?%!%!%%%!!%%!??%??%?%%%%!!%%!%!!!%%!%!!!%%!?!??%?!!%%!?!%%!%%%?%%?%%%!%!?!!%%!!%%%%?%??%!!!%!!??%%?%%!%%?%?!?!?%?!!%%!!!?%?!!!?%%%%%!%%!%%%!!%%%!%!!%%!%!!?%%%%%%!%!??%%%%?%%%?%?!%!%!%!!!!!?%%%!!!!!!!!!%%%!!%!%%%%%!%!!%%%!?%?%%!%%%?%%%!%??%!%!%%?%%!%!?%??!!%%??%!!%%%!%!%?!%%%%%!!%%%!?%%!!%?!%!??%%%!%!%%!?%%!%%%!%%%!%!!%%%!!?!!?%?%?!%!!?%!!!%!%!%%!%!!?!!!%%%%!%!?%!!%%!%?%%%%!%?%%??!?!%!%%!!%!%?!!!%%!%%!!!%?!%%!%!%%%%!!%!%%?!%%!%!?!?%!?!%?!??%!%%%%!%!%%%%%!%%%!%?%%%%?%%%%%%?%!%%%%%!%%%?!%%!%!!%%%!!%%?%%!!!%%%?%%%?%%!!!%%!?!!!%?%%%?%%%!!%!!%%!!%!%!!%?%?!%%%%%!!!%!%%?%%??%%%%%%!%!?%%%%%%%%!%%%%%!%%!?%%!%??!!!!?%%!!!???!%!%%!%%%?!!%%??!?%??%!%%%%%%!!%%%%%%!?!%%%%%!%!%?%%!%%??%?%%%%!%%!!!?%%%?!%%??!%!!%!%%!!!?%!%!?!?%!%%?%%%!?!%%?!%%%%?%!??!!%!?!!%?%%!?!%%?!!?!%%%%%%%!%!%!%!%%%?%%!%%!%!!!%!!!%?!%?%?!!%!%%%!%%%?%%%!!!!!%!!%%?%%!%!!?%!%%%!!%!%??!%%%!!!?%!%?%!!%!%%!%%%?!%%!%!%!?!!!?!!??!%!%%?!?!?%?!!??%!!%%??!?!%!!%%%%!%%%%%!?%%%!?!%%!%?%!!!???%%!!%!%?%%%!???!%?!!!%%??%!!!!!?!%!!?%%?%!!%%%%%!%?!!%!!%%!%%%%!!?%!!%%%!!%??%%!??!?!?!%!!!%!%!%%!%%!!!?%%!!%%!!?!%%%!%!%%%%!%!!?%!?%!!%%%?%%%%!%%%%%%%!!%%%%%%?!%!!!!%%!!%!?%%???%%%%%!?%???!%%??!%%!!!%%%%?!%%???!?!%%?!!?%?%%!!?%%!%%%!?!?%%%%!%%?%%!%%?!%%!?%%%!?%!!%%%%%!!!!%?%%!%!!%?%%%?%?%%?%%!?%!%!?%!?%%%?!!%!%%?%!?%!?!!%%!%%!!?!%!!!?%!?!?%%%!!!%%!!%%!%!!%%%!!%!%%%!%%?!%%%!%!!%?%!%!!!!!??%!%%!%!!?!%!!!%!?%?!!!%%!%??!!!!!%?!!!%!!%!%!%%%%%%%!!!???%%%%!%?%%%!?%%%%??!!!%?!!!%%%%!!%%%%!%%?%!!!%?!%!!%!!%%%%!!!%%?%!!%?%!!%%?%%%?!?!%?%!%%%!?%%?%%?%%!?!%%!!%%!!%!!?!%?%%!%?!?!%?!%!%!%%%%%%!!%!%%%!!%%??!!!!!%!!%%?%!%?!%?%!!!%%!?%%%!!%!%%%%!?!%%%?%!%?!!!%?!!%!!%?!%%%?%%%%?!!%%!!?%!?!%%%%?!?%%%!%!!%!%!%%%%!!!%!?!%!%%%%%%!%%%!!!%%%%%%?%%!!!!%?%%!!%????%!%!??!!%!%%!?%??!%!%%?%%?!%%%%%%%?%?%!%%%%?%%%!%!%!?!!?%!%%!?%%!?%%?%!%?%!%!!%!%!?!!%%%!?!%?!%%%?%?%!%%!%%%%?%?%%%%%%!%%%%??%??%????%%%!!%!%%!%%?%%!!%%%!%%?%%%!%%!%%!%!%!!!!%!?!%%!%%!?%%!%%!!%%!!!!?!%!%!!%%%!%!!%%?%%%%?%!%%?!%%%%%??%?%!%??%!%???!!!!!%?%!!?!!?!%?%?!%%!%?!%!%%!??%%%!%%%!?%?!!!%%!%!%!!%%!??!%%?!!%%%!%%%%???!!%%!%?%!%!%!%?%%%!%!%!!?!?%%???%%%%!%%!%?%!%%%%??%%?%%!%%!!!!%??%%!!%!%!%%%%%%%??%%!%%?!%!%!%?!!%!%%!%%?!%!!%??%!!!?!!%!%?%%!%!!!%!%%!%%!??!!%!%%%!%!%%%%%%!!%%%%!%%!!!%%!%%!!%!%%%!%%%%!%!!!%%%??!%%!%%%?!%%%%!?%!%%!%%!%%%%??%%!%%!%!%!%!%%!!!?%?!!%!!!%!!!!!!!%?%%!!!?!?!!!!!!%%%%!!%?!!!!%!!!!%%!%!%%?%%%%%%!?%!!?!!%!!%%!!%!!!!%!!%!%!%%?%%%%%%!%!%%%!!!%!%%?!%%%%!%!%!%%!%!?!%%%!%??%!%?!!%!!!?%%?!%?%%%!%!?%?!!%!%?%%!%?!%?!%%%%%?%!!!%!%%%%%!%%%%%%%%!%!!%?%%%!%%?!?%%!!%%%?%%%%%%!?!?%%%!!%?!!!%!!!%!?%?%??%%!%%%!!!!??%!%%%%%%?!!%%!%%?%!!%%!%%?%?%%?!%!!?!%!?%%%%!%?!%!%!!%!%!!!?!%?%%!!%%!%!!%!%%%%!%%%?!!?%?%!!%!?%%!%!!%%%!%%!!%%%%!!??!!!%%%%%!??!%?%%%?%!%?!?!%%??!%%%%!%?%%%!!%!?%%!?%!!%%%!%!%?!%!!%??%%!!%!!?%!!??%%%?!%%%%!%?!%?%!%?!%!%%%?%!%%%!%%%%%!!%%%%%%?!%%!%!%!?!%%%!%!%%%?!!?%?!!!??%%%!%?%!%!%%??%%%!%!!?%%!?%%%%%!???%%!!!%!%?%%?!!%%%%!%%%!!%!!!!%!%!?!!!!%?%!%%%!!!!!%%%%!%%?%!!%%!!?!!!%%%?%%!%!!!%!%%!%%!%%???%%%%%?%!!%%!%!!!!!%?%?%%%!%%%!!%%!%?%!?%!!!!%!?%!%!???!%%!%%%%%!%%!!%!%?%?!!!%%?!?%%!%!!!!!%%%!!!!!%%%!%!%%%%%%!?!??!%!%%!%%!%%!%!%!%?%?%%%%!?%?!%%%!!!?%%?!%!%?%%!!%?%%?!!%%?%%!%%%!!%%%%%%%!%!%%?!%!%!?%%?!!!?!%%!%!%%!%!!%%?!%%%%!%!%%%%!%%%?!%%!%%!%%?%%!%%!%%!?%%?!%%%!%?!%!%%??%!%!%?%??%%%%?%!!%!%%%!!%%%?%!%%%!?%?!%!%%?!?%%%%?%%!%!%%%%%%%?%!%!%%%!?%?%!?%%%%%!?%?%%!!!!%%!%%?!%!%!%????%%?!??!!!!?!?%%!!%%%!!!???%?%%%%%%%!%!%%%%!%?!??!?!%%%%!%!%%%%%%!%?!!%%%!%?%%!!!!!?%!%%!%!%!%!%%%!%?%?!%!?!%%!!%!%!?!%?!!%?%%%?%?%!!?!!%%!%?%%%!%!???!%%!%!!!%%%%!%?%%%%%?!%!!!%%?!%%?%%%%%!%!%!%%?%!!%?%%%!%%%%%?%!?%%%?%%!!%!?%?%%%!!!?!!%?%%?%%?%%!%%!!%%%%?%!%%%%?%!!?%%!?%%?%%!?!!!%!?%!%!%!!!!%%%%?%%%%%%%%%%%%!!%%%%%!??!!%%%%!?%%%!%!!%!!???!!%?%?!?!%!%!!%%??!%!%!%!%!?!!?!!!??%%?%%?%!!!!!!%!!?%!!%%%%%%%%?%!??!!?!%%%?!!%%!%%!%%%%%!!!%!?!%%%%?!%%%%!!?!!!!!!%!%!%%?%??!?!!!?%%%?%?!%%%!%!?%!!!?!!!%!?!??!%%?!??!!!%%%%%!%!!%%%!?%%?!!!%%%?!!!?!!%%%!!!!%%!!!?%?!%%%!!%%!!%?!%!%%%!%!!%!%?%???!!!?!%%%!%%%%!!%??!%?!?!!??!%!%?%%!!%!%%!%%!%!!!%%??%%?%%??!!??%!?%!%?!!!!%%!!!!!?%%%!%?!!!%?%!!%%?!%!!!??!!%!%%%%!%%%%%%%%%%!%%?!%%!%!!?%?%%%%!%%%!!%%%%!?%!?%%%!%!!!%%!%%%%%%%%?%%%!%%?%!%%%!%%?!%%%!%!%!%!%?%%%%?%%%?%%?%!!%%%%%!%!%%!!?%%?%!?%%%%?%%%?!%%%!%!??%%??%!%%!%!%!!?%%!%?%?%!%%!%%%%!?%!%%!%?!%%!%!%!%%%%%!!%%%%!!??!?%!?%%%%!!%!!!!%!!%%%%%!!!%%!%%%%%%!!!%%%%%%%%??%%%%%%?%%??!%%?%!!?%%%%%%!!%%%?!%%%!!%!%!!?!%%!%%?%%%!%%!%!%!%?%!?%!!%?%!%%%%%!%!?%!?%%!%?!!%?%!%!?!!!!!%%!?!%!?%!%!%%%%%??%%!%!%%!%!?!!!?!!!!?!%%!%%?%?!%?!!%!?!%%%%?%!!%!%!!%%!!%!??%!??!!%!!?!!!!%%%%?%%?%?%!%!%?%?%%%%%%!??%!!%!%?%?%?!!?%!?%?%??%%%%!%?%%%!!%%%%%?!%!?%!%!%%?%!!%!?!!?!!%%!%?!?%%%%!!%%?!%!%%!!%%!%%!%!%!%%%!!%%!%!?%!%%!%?%%!?%%!!!!!%!%%!??%%%?!!??%!?%?!!%%%%!%!%%?%!%!%!?%%!?%%%%?%?%!%!%!%!%%%?%!%!?%!!!?!!?%!!!%%%!%!%??!!%%!!!%?!%?%?!%!%%?%?%%%?!%?%!!%?%?%!?!!!%%?!?%!???!%%%%?!%!%%%!%!%%%%%!?!%%%!!%%!!%%%!??%%!!!!%%?%!%!!!%%%!%!!!%%!%!???!%?%??%!%%!%%!!%!!%!?%?%!??!%!!!!!!!%%!!%%!%%%!?!!!%?!?%?!!!%!%!%!!!??%?%%%%%!%?!?%!!!%%%!%%!??!%?%%!%?%%?%%%%?!?%%!?%%!!%?!!%!!!%%!!%%%%%!%%!%%?%%%%%!%??!!%%!?!!%%%!?%?%%!?!%%!%%%%!?%??%%!%%%??%%%!%%%?%!!%%!??%!%%?%%%%!!!!%%!%%%?!%%%?%?%??%?%?%%!%!%?%??!!%!?!%%?!!!%!%%%!!!?%%!!!%%!!!%%?%!!!!!!?!??%%%%%%!%%%!!%%!%!!!?????%!!??!%%!%%?!%%!%?%%%!!!!!%!%%?%%%%%%!?!%!?%!!!%%!!!%?%?%??%%%%%%%?!%?%%%?!?!!?%?%!!!%!%?%%??!%!?%%!!%!!?%!%!%!?!%%%!%?!%%!%%!!??!!???%%!%!?%??%%%%!!!!%?%%%%%%%!%!%%%%%?%%!%?%%%%%%%%%!!!!!%%%?!!%?%%!%??!?%!!!!?%%%!?%?%!?%%%?%%%!%%%%!!!%%%%%%?%!!%!??!%%!%??%?%%%%%%!%!%%%%%%%%!%%!%%%%%%%%!%?!?!%!!?%%!%%%%?!%!?%?!!%!!!%%%!?%!%!%!%!%%!%%!!%%%!?%!!??!%%?%%!?%!!%?!%!%??%%?!%!!!?%!!%%!?!!!%???!%?%!?!!!??%%?!!!%%%?!?%%?%?!%!!%%?%%!!%%!%!??!!%%%%%?%?!!?%!!?%!%?%%%!!?!%%%?!%%!!??%!!!??!!%?!?%!%%?!!%%%!!!%%!%!%!%?%!%!?!%!%!%!%%!%%??%?!!?%%!!!?!!!?%%!%%%!%?%??%%%?%??%!%%!%!!%%?%!!%!?%!%?%!%!!!!!%!%!!%%!?%!%!!%%%!?%?%!!!%!%%%%!!!!?%%%!!??!%!%!!%??!%!%%!!!?%%!?!%!%!!%%!?!%!!%%?!?%%!%!!!%%%%!%%!%!%%?%%!!%%!!%?%%%%%?!?!%%%!!!%%%%?%%%!%%!!?%%%!%%?%!!%%%%?%%!%%?%!!!!!%%%?%?%%!??%!%%%%%?!!!%!?%%%%!%%!!%%%?!!%%!!%?%%%%!%!?!%!?%!!%%!%%%%%!%%%%!?%%?!!!!?%!!%?!%?!%?%!?%?%!!%%!!!%%!%%!!%!%!!%%?%!%%%!%%!!!?%%!%%!%!!%%%!!?%%%?%!?%!!!!?!!%%%%%?%?%?%%!!!%?!!%?!%!%!%!%?%%!!%%%!!%%??%%?!%!!?!!%!!%!%%!!%!%!%%%!%!!?!%%!??%%%?%!%!!%?%%!%!%%!!%?!%!!%%!%%!!%!!%%%!!%%%%%!?%%!%!!?!!!!%!%%!!!%%!%%!?%?%%%%%?%!%%%%?%!!!%%%%?!%?%%%??%!%%%!%%!?%!?%%%?!%?%%%%!%%?%%!%%%%%!%%!%%%%%%%?%%%%%%!?!?%?%%!!%!%?%!!%%%!?!!!!!!%%%%%?!%!!?%%?%!%!!%%%%!!%%%%!!%!%?!!%%%%!%!%!%!??%?%!!%!?%%!%%%?!%!!%%!!!!!%%?!%%!!%%!?!%??%!%%%!%%%!%?%%%%!!!!%?%%%???%%%?%%!%!%?!%?%!%?%!%!!?%%!!!!!%%%%%!%%!!%?!!%%%!%??%?%!?%??%%?%%%?%!%%%!%!?%?!!%!%%%?%!%!?%%%%%?%?%%!%?%%%%%!?!%!%%%%!%%%!%%????%%!!%!!?!%%!!%%?!%%%%%??!?%%%%?%!%%?%?!%!!%?%!%%!!??%?!%!%%!?!%!%!??!!%%%%!%%!%!?%%?%%!!??%!%?%!!%!%!!!%%%!??%??!%?%%%%%%!?!!%%??!%!?%%??%%????!!%%%%%!%%!!???!??%!%%!%%?!?%!%!%!!?%%?%!%%?!%!%!%%?%%%%!?%%!!%%!?!%!?%%!%%%!!%?%!!?%?%!!%%!%%?!??%!!?!!%!!%!!?%!!??!?%??!%!%%%%!%%!!!%!%!%!!!%!%!!!??%!?%!!?%%%%!!!!!??%%%??%%%!?%!%%%?%%!%%%%!%!!%%!%%?!!!!%%%%%!%!!!!%%%!%%%%%%!?!!%!%%%%?!!!!!!!!%?%!%%?%!!??!!%%!!?%%!!!%?%!!!?%%!!????!??%%??%%%!!%%!??%%?!!%!?!!!%!%%%%??!%!%??%!%!!%%%?!?!?%!%!%%%%%%%!%%%%?%%%!%?!!%?%%%?!!%!%!!%?!%!!!!%??%!?%!%??!?%!%!!!?%!%!?%!!?!%?%%%!%!%?%%%%!%%???%%?!?!%%%!%%!!%?%?%!%%?%%???%?%!%!?%%?%!%!%?%!%!%%%%!?%?%!!%?!??!%%%%%%!!!!!%%!!!%%%%!!!%%%!!%!!%!%%%?!%!!!%%!?!%!!!%!?!%%?%!!%%%!?!!%%%%!???!%!%!%%?%!%?%%!%%%%?%!!!!??%!!?%?%%?!!!%%!!%!!%?%!!%!%%!!%!%!%%%!%%%%!?%%%%!%%%!?!?!!%?%??%%!!%?%???!!!!%%??%%%%!!?!%%%!!%???%??%%?%?%!%!%%?%?!?%%%!!!!?!!!?%%%!!!%?%?%%!?%??%%%!%!%%%%!!!!%%?%!?%!%%%%!!!!%%%?%!!%%%!%!!%%!%!!%!??%?%%!%?%%%%%?%%?%!!!%?%!!!%%!%%%!!!?%%!%%%?!!!%!!%%!%%%%%%!?%!?!%%%???!%!%?!%%%!%!%?%!%%%%?%%?!%%%!%%%??%%%?!%%%%%%?%!?%%?%%!?%%%%%?!%!%!%?%%!%%%%?%!%%!%?%!%!%!?%%?%?%!!?%?!??%%!!%!!!!?!%%%%!%!?%?!!%?!%%?!%%!%!!%%!!%?%%%!%%!!%?%?!!%%%%%!!%!!!%!!!?%?%%!%?%%??%?!%?!!%%!%%?%%?!!%%?%%%%!!!!?%%!!%!!%?%%%!!%%%%!%%%??%%%%!%!%?%?!%!%?!!%!%!%?%!%%%!%%?%%!!?!!!%%!%?%%!!!!!!%!!%!?%%%!!!%%!!!?%%%%!%%%!?!?%?!%%?%!??%%!?!%%?%%?!%%%%%!?%??%!%??!%?%!%?!%%!%%!%?!%%%%%%?%%?!!!%!??%%%%?%!?!%%!%%%!%%!%%%!!??%!!!!?!!%%%%!!?%!??!?%!%!!?%%!!!?!!%!!%%%?%%%%?%%%%??!%!?%%%%!!?!%%!%%!!!!%!%%?!!%%%%%?%!%%!?%%!!%%?%%%%%%%%!%%!%%??%?%!%!?%!%!!%%!?%!%!%%?!!?%?%%%??%?!%!%?%!%!%%!%?%!?!%??%%!!%%?%?!!%!%%%%%%?!!!%!%%!?!%!%?%!!%%%%%%!%%%?%?!%!!!%%!!%%%%!!%%%%!?%%%!%%%!!?!%!!%!!%?%%%%%!!%!!!%!%%%%%!!!?!!%%!%%!%%%%?%!%%!%%!!!%!?!%%!!%%%!%%!!?!!!%%%%%%%!?!%?%%!!%?!%%??%!!!!%%%!!!!!%%%?%%?%!%%!!!%!!!!%!!!%%!%%%%%%?%!!!%!!%!!!?%%%%?%%?!?%!!%%?%!%??!!?!!%%%%%%??%!%%%?!!%?%%%!!%!%!!%?%!%!?!%%%!%!?%%%!%%%%!!!%%!%!%%?!?!%!%!????%??%!%%?%%%!!%%%%!%%%%!%%%%!!%%??!%?%!%!!?!%!!%?!!!%%%!%%%%%!%%?!!%%%?%%%%!!!%%?!%!%%!%%!?!!%!%%%%%%%%?!?%%?!%%?%%%!?!!%?!%%!!%%!!!%!!%%??%%%?!%!?!%?%?%%!!!?%!%%?!%!%?%?!%?%%%%%%!?%?!%?!?!?!%%!?!%%%?!%%%!!%!%%!?%?%%%%!!%%?!%%%%?%%!%%!!!??!!?!%!!?%!%%%!?!???!%?%!%?%%!%!?%%%%%%%%?!!!?%!!%!?%!?%!%!%!%?%%!%?!??%!%??%%!%!!%!!?!%!!?!?%%%?!%%!!%%?%!!%!%%%%!?%!%!%%!!!%%%%%!!%!%%?!??%%!?!??!%%!!%!%%%!%?!%??%!!%!%%%?!%?%!%%!%???!%%%?%!%%%%%?%?%%%!?!%%%!!%%!%%!%%%%%%%%!!?%?!!%%?%%?%!%%?%?!%!!%!??!%!!?!!!%%%%!%%%%?%!!%%%!?!%%%?%!!%%%!!%%%!?%!!%%?%?%%!?%!?%!?!%!%%%%%%%!%?!?!!!!?!!!%%!%%%????%!%%?!?%!%%!%!!%!%%!%!%!!?%?%?%%%?%%%%!%?%%%%!?!!?!%!!%%%%%%%?%%?%!%%!%%%?%?%%%%%%%?!!%?%%%%%%!!%%%??%!!!%!%%?!?%%%!!%%%%!%%%%!???!!%%%%%!%!!!!!%%!!%!%%!%%%!!%%!?!!%!!%!!%%%!?%!%?!!%%?!%!?%%?%%?!!!!%%%%!%!?%??%%!!!!%%%%!!%%!%%%?%?%%%%%%!!!%%%?!!?%%!%!%%!!!??%!!%!?!!?%!%!%!!%!!?!??!%???!%%!%!%!!%%%!?%%%%?%?%%%%%%%??!?%!%%!!!?!?%%!%%%%%?!!?%!%??!%?%%!%%%!%%%%%!%?%!%??%%%?%!!!!!!?%%!%%%!?%?!%%!%%!?%?!%!%%%%%%%?%%%%%?!!?!%!%!!?%!!%!?%?%?%%???!?%%%%!?%!%%?%?!?%%!!%!!?%%%%%??!!!%!%%%%%%!!%%%!!?%!?!!?%!?%!?!%%%!%?!??!!%%%%%!%%?%!?!%%%?!%%%%%!!!%%!%%%!?!%%!!%%%%?%%%%%!!?%!!%%%%%%%!%%%%%!%!!%%%?%%%%%%!%!!%!%%?!?%%!!!%%%!%%!!%%%%%!!?!%%%?!?!%%!%!%%?!%%%!?!!!!%!!!%%!%%!!%%?%!%%!%%?%%%%%%%?!%%!%!!!!%%%??%?!!%%%?!!!%!%!!!!%%??!%?!%%!!%!!%!!%?!%%?%%%%%%!!%?%%!!!%%!?!!!!%!%!!%!!?!!%?!%%%?%!%%%%%!?!%%%%!?%?%!!!%!%!%%%%!%?!!!%%%%%?%?!!!?%!!!%%%%??!%!?%!??%!?%%!?!?%?!%%?%%%!!!!%!%!%!!!%%!?!?!%!!???%?!%!?%!%?!%!%!%!%%!!!%%!%!!%?!%%%%!!%%%!%%!!!%%%%%%%?!%%?%%?%%!%%%!%%%%!%!%%%%?%%!!!!!%%%!!%%!%!!!%!!%%%%%!%%!%!%?!!%%?!?!%%%%%%!!!%?%%?!!%?%!?!!%!%%%%%!%??%%?!!!%%%!?%%%!?%%!!%%%%%%!%%%!%?!??%%!?%!!%%%%%?!%%??%!%???%?!!%?!%%%%%!%!!!%!%!%!!%?%%!?!%%!!%?%?%!%%!%!!%!%%!?!!%??%!!%%!%!%%!!!!!?%?!%!!!!%!?!!%%%%!!%!%!!!%%%%%?%%!?%!%!!%%%!%%!??%!%!%%!%!?!%!%?%?%%!%?!%%?!%%%??%!%!!!!%!!%%%%!%!%?!!%?%%!!?!!?!!!!!%%?!%%%%?!?!!%%%!%%?!%%!%%%?%!!?%%!?!%%%!%%?%%??%%!%!%!!?%%%%!%!%%?!!!%!!?%%%!%%!%%%!%%!%!%%%%!!!%!%!!%!!!%!%!%%%!%%?!!%%%!?%%!%%!?!?%!%?%?%!%%!%%%!%?!%%?!%%?%%%%!?%%!!!!?!%!%%!!%!!%%!??%%%%%%!%!%%%!%!!!%%!%!%?%%!?%!%!%!%%%%%!!%%!!!!%%?%%!!!!!%?!!%%!!%%!%%%!!%?%?!%%!!!!!!%!%!%%?%%!??%%%%%%?%%!%!!!%%%%%!?!!%%%%%!!!%??%!!%%%!!%%%%%!%!!%%%%%!?%?!%??%!%!%!?%!%!%!%?%%%!%!%!%%%!%%??!%!%%%%%%?%!%%?%!%%%%%%%!%?!!!%%%%%%%?!%%%%%%?%%%?!%?%?%!!?%!?%%%!!%???%!%%%??!!!?%%%!%%%!??%%!!%!%%%!!!?!%%%%%%?!?!%%%%?%%%%!!!!??!?!%%%%%!%!??!!%?!?%%!!%?!%?%%%??%!%!!%%%%!%%?!%?!!!%!%%!?%!%%%%?!!%!?%!!%%%!%!?%%%%!?!?!?!%%?%!%?%%??%!!%%!!!!!!%%?!!%?!!!!%!%!%%%!!!%%!!%??%%%%%%%!%!!!%!!!!%%???%!!%!%??%!!!%%!?%%%%%?!%%!%%!%?!!!!!%%!??%!%%!%%!%??%!!?!?%%!%?%??%?%%%!!%!!%%%%%%%%%%?%%%!!!!?!%?%!!%%%?!%??%!%!%%!%%%%??!!!!%!?%%%%%%?!?%?%%!!%!%?%!%!%?!!%!%!!%!?!!%!%!!!!?%%?!%%??%%%!!?%?%%!!!!%%%?%%%%%?%!%?%%%?%%%?%%!!!%%%%!?%%?%??!%%%%!%!!%%?%!?%%!!%!?!?%!%!%?%!?!%!!?%?%!%?%!!%!!!!!?%%?%?%?%%%%%%%!!??!%%?%?!?!??%%?!!!!%!!%%%?%%!%%!?!!%%!!%%%!?!%!%%?%%?!!%??%%%%!%%!%!?%?!%!%!%%%%!%%%%%!!??!!%%?%?%%%?%!%%!%!!?!!!%??%%?!!%!%%%%!%%%?%%?%??%%%%!!%%!%%!%!!%%!!%%%!!?!%%!!%%%!!!%??!%%%?!!!%!?%%?!!???%?!%%%!!%!!%%!%%%%?!?%%%%?!!%%%??%%%%?%%?%??%?%!%!%!%!!%!!!?%%!%%%%%%!!%!%?%%%??%!!!?%!?%%%?%!%%!%%!?!!?!!%!!!!%%%!!!!%!!!%%!%%!?%!?%%!%%%%!%?!!?%%%%?!??!!%?!!?!%%%%%%%%!%%!?%%%%%!!%!!!??%%!%?%!!%!?%!!%!%!%?%!!!%%%%?!!!?%%%!!!%%%%?!%?%!%?!%!!!!%%%?!%%??!?%!%%?%%%%%%%?!%!!!%%%%%%!!%?%%?%%%%?%?!!%%!%%%%!!!%?!!!%%?!%!%%??%%!%!!!!%!%!!%?!?%%!!?!%%!%%!?!%!%!%!?%%?%%%%??%?%%!!%!!%!!!%%!!%%?%%%!!!%??%!?%?!%%%%!%%%!%%!??!?%%%!!%!%%%!%?!?%%%?%%%%!%%%!?%%%!!%?!!!%!%?!%%%!%%!%?!%!%%%%%!%%%%?%%%?!%%%!!!%%!!??%%!?!%%%%?!%?%??!???!%%!!!%%???!???%!%%%%%!?%%%?!!!%%%%!??%!?%!%%!!%!%%!?!?!!%?%!%?!%!%?!%%?!%!%%!??!??%%%!??%%%%!%%?!!%!?!%%?%%!%%%%?!!!!!%!!%%!?%%?!%!%?!?%%!!!%%!%!%!!%%%%!%!?%?%%!%%%%!!!!%%%%%%%%?!%?!!%%%!?%%!?!%%!%%%%!%%!??%!!%!!!%!%%!%%!!?!%!!%!!!%!%!%!%!%!!?!%%?%%?!%%%?!?!%%%?%?!%?!%!%!%%%%?%%%!!?%!%%%%%?%!%!%%%%%%%%%%%%!!%?%%!?%%%%%!!?%%%%%!!?%%%!?%?!?%?!%%!!%%!!?%!!?!%%!%?%!%!%%%?%?%!?!!??!!%%%%!!!??!%%!???%!%%%!!?%%!!%%?!?%!!%%%?!%%%?%?%%%%!!%??%!%%%!%?%!!!%%%%?!!%%!!%?%!%?%%???%??%!!%%%???%%?%!!%%%%?%%%%??%%%%!%%!!!!%%!!%!!!!?!%%!!%!%!%%!??!!%%!%?%%!%?!%%!%%!%?%!%?!!%?%?%??!?%!%%%!?%%%!%%%%%!%!?%%?%%!%%?%%!%?!!!!!!%!!%%!%!%!?!%!%%%%?%%!!!%?%!?%%?!!!!%???%?%%%??%%%%%%!!%%%%%%!%%!%%!!!%!%%%!?%!%%%!?!!%%%%%%%%%!?%%?%?!%%!%%!%%%!!%%%%%?%!%?%%!%%%!%%?!%%%!!%%!%!!%%%%%!%!!?%?%%%?%!%%!%????%!?%!%%%!%%%%%?%!?%%!%%%!%%!!%%!!?%%!%%%!%%?%?!!!%!%!?%!%!%!?%?!%?!?!%!%!%?%!?!%!%!!??%%%%%!%!!%!%!?%??%%!!?%!%%%%?%%?!?%%%?!!%%?!!!%%%!%%%%%%!%?!%%%%%!%%!%%?%%?!%!?!%%%?%!%%!%%%%!%??%%%%%!%!!!?%??%!%%?!%?!%%!!!!%!!!!%%!!%!%%!%??%??!??!%%!??!!!%??!%!%%!%%%%%%!%!%%%%%%!%!%%!?%!%!%!?%%%!%%?%%!%%%%%%!%!??%%!%%%%!%?!?%!%%%!%%!!%!!!%%%!%?!!!!%!!%!!!?%%%!%?%??%%?!%%%!???!%%%!?!%!%!%%?!%?%?!!?%!%%%%!%%%%%%!%?!!??!!%%%%!?!!%?%!%?!%%??!!%%%!?!!?!%!%%!!!!%%?%!?%%?!!!!!?!%%!??%%%!!%??!!%?%%%%??!?%?%%%%!!!%%%?%%%!!!!%%%%%%%%?%?%?%%%%!%!%!!!!%%?!?!%%!%%%%!!?!!!?%%%???%%%%%!%!!%?!?%%%!!%!!%?%%!!%!!%!?%%%%?%!?%%??%?%?!!!%!%%?!%?!!?%%?!%?!%%%%!?%%?!?%!%!!?%%%?!?!%%?%?%!!!?%%%%!%%?!%%?%?!%?%!%?!?!%!%%%%!%!%?!!%%??%%%%?%??%%%%!?%%%%!%%!%!%!%?!!!!??%%%%?%%?!%??!?!?!!%?!%%%!!%%%?%?%!!!%!%?%%%!!%!%%!!%!%%!%%%!%?%?%!?%%%%!%%%%!%!%!!?%!!?%!%%!%%%!%!%!%%!%%%%%%?%%!%%!%!%?!%%%!%%%?%??!%!?%%!%%%%%!%?%?%%%%%%?%%!?%?%%?!!%%!%?%!?!!!?%!!!!%%%!%%%%%?%%?%%!!%!!%%!%%%!%!??!%%%!%!!?!?%%%!???!!!!%%!%%%!%%!%%!%%?%??%?%%%%!%!%%%?!%?!?%!%%?%!!!!!%%!!??!??%%!%%%%!%%%%%%%!%%%%%???!?!!%!%%!?%%!%!%%!!%!%!%!!?!%!!%%!!%%!%?%!!!?%%%%%%%%%%!!%%%%!!%%%?!!!%!?!?!%!%?%!%%%%%%!!!%!%%%%%!??!%?!?%%!%%%!%%%!%!?%%!!%?!%!%!!!%!%?!!%%!?%?%%?!%!%??%!%%!?%%%?!!%%%!%%!%%%!!!!%%%!%??!!?!??%!!%%!%?%%??%!!%%?%?%%?%%!!?!!%!!%%%!!!%%?%%!!%%%?%%!!%%?%!?!%%!!!?!%%?%!!%?!!%!?%?!!??%%%%!%!!??%%!%%!%!!?%!!?!!%%!%%!!%%!%%%%?%%?%%!!%!%%%%!%%?!?!%!%!!!?%?!%%!!!!%!%!!%?%%!!%%%!%%!!!%%?%?%%%%!%?!%%!!%!!%%?%??!%!%%!%!!!%%%!%%??%%!%?%!!%!!%%!!%%%%%%%!?%!%!%!!?%%%!%%?%!%?!%?%%?%!!%!%%%%?!!!%!%!?%!%?%%%??%%!%%!%%%!!!%!%!%!!%%?%?%%%%%?%!%!!%%!!?!?!%%?%??!!!%%%%!?!??%?%%?%%?!!%!!%!!?!%!!?!%??%!???%?%%%%?%%%!%!%%?!!%!%%?!%!!?!?%!!?!%%%?%%!%%!%%%!%!!!%?%?%!%?%!%%?%!!%%%%!?%%%%%?!!?%%!%%%%?%%!!!%%%!!!%!%%?!??%%%?!%%!%%!!!!%!%%%%%!%%!%%?%?!%%%!!?%%%%?%?!!?!!%%!%%?%?!?%!%%!%%!!!?%??!%!%%%%%%%?!!!?%!%%?%%!%!!%?!???%!%!%%?!!?!!%!%!?%%%!%!%?!!%!%%%!%%!!%??%!%%??!%%?%?%?%!%%!%%!%!!?!?%!!!!!!%?!?%%%??%!%!!!?%%%%!%%!%%%?!%?%!!%??%!?%%!?%!%?%?%??!!!%!%%!%?%?!!!!%!%!%%%!?%!%!?!%%?%%!!%?!!%%?!!%!%%!?!%%%!%%?!%?%!%?%%%%?!!!?!?%!!!%!!!!%%!%!!?!%?!?%????%%%!%??%?%%%%!%?!!%!%?%%!!!!%?%%%!%!%%!?%!!%!%!!?!!!%!!!?!%!%!!!%?%%%%%!!?%?%!!%%!!?!?!%!%%!%?!!!%!!%!??%%%%!??%%%!?%?%!%?%!%?%%!!?%%%!?!%?!%?%%%!%%%%!!%???%%!!!!?!%?!!!!!?%?%??!%%%%%!%?!!?!%?!!!!??!%%??!?!!%%%%!?!!%!%?%%?%%%?!!%%%!!%%?!!%%%%%%!!%%%!%!?!?%%%!%!!%??%?%%%%?!!%!!!!%!%%%%%???!%!%%%!!%%?%%%!%?!%%%%!!!?!?!%%!!%%%!!%%!!%!!?%?!!?%%!%%%%%%!!!%!!?%%?%%!%?%!?%!!%!?!%%%%??!!%%!?!%!???!%%!!!%?%%!%%?%?!%%%%!%!!%?!%!!!?!!%%!?%%%??%%%%!!%%%%!%%%!%%?!!!%%%?!!??!%!?%?%%%!%%!%?%%%%%%%%%!??!%!%?%!%!%!%%!!%%!%??%%%!%%%%!?!!%%?%??%!%?%?!%%!!!!!%?%!%!%?!%?!%%!!!?%%!?%?!?%!!??%%!?!!?!!!!!%%%?!%%!%%!!%%!!?!!%!%!!!%%%%!!%!%%!%!!!%%%!!%?%%%%%!!!??!%!%!!%?!?!%!%!%%!%?%!%%%%!%!%?!!%!!?!%%!!%%%!%%!?!%!?!?%%!%%%%%!!?%%!%%!?!!?%??%?!!??%%%%?!!!!%?%%%%?!%?%!!!?%!?%?!%%%!!%%!!?!%!!!!!!%%%%%?%!%!%%?!%%%!!!%?%%%%!!%?%%!?!%!!%???%?%%%%???!!?!!%?%%!%%%??!%%%%?%%!%%?!??%%!!%!!%%%??!%%%!%%%%%!!?!%!!%!%%%%!?!!%!!%?!%!%?%?%?!%%%%?%?%!%!%%%%!%!!!?!%!!!!!%!%!?!!!%%%%%%??%!!!%%!!?!%%%!!!%!%!%!?%%%%!!%%?!?%!%%%?%?%?%!??%%%%!?!%%?%!!%!%%!?!!%!!?!%%!%!!!%%%%%!!%!%%%?%%!%%%??%!!!%!%?%%?!%??!%?%!!%!%%%!%%!%?!?%%%%!%!!%!!%%!%%!!%?%%?!!%%%!!%?%?!!%!%%!%%%!%%%!?!??%!!%%?%%%%%%!?!!%!!!%%%!!!%%%%%%%!!?!%?%%%%?%!!??!%%!!!!?%%%??%%!%%!%%%%%%%%%!!!%%%%%!%%%%%%%!!%!!!%!!??%%!%!%!!%!%%%%%%%?%!!!!!??%%!%%%%%%?%!%!?%%%?%!%!%%!%!!%%!%%%?!?!!?!!%%?%%%!!??%%%%?%%!%?%%%?!!%?!!!!%%%!%%%?!!%?!!!%!%%%%!!?%%%%!!%!%?%!%%?!!%!?%%%!!??%!!?%%!?%!!%!!%!%%!!!%?!?%%!!%%%??%!%?!!?%!%!%!!%%!%!??!%!?!!%!%!%%%%?!%%%%%%!??!%%?%%!%%%!!%!??!??!%%%%%?%%?!%??%!!??%%!%!!%?!!???%%%!!%%!%%!%?%%!%%%%!!!!%?%%%%%!?!%!%%?!%%!%!%?%%%!%%!!!%?%!!!?%?%??!%%%%!!%!%!!!%!!%%!%%%%!%!?!!%!%!%%!%!%%!!?%?!!%!!%!?!%!%??!%%%!?%%!!!!%!%!%?!!!%!%%%!?%!%%!%%%??!%%%???!%?!%?%!??!!%?%?!?!%%!!%%%!?!%!?!%!%%!%?%%!!%!!%!!!!%%!%?!%!!!!%!%!!!!%%!%%!!%!%%!%!%%%%?!??%%!!%!?%?!%%%!?%%%%%%!?%!?!%!%!%%?!%!%%?%!%!%%%%%%%!%%%%?%%%?%!!!%%%%!?!!%!!?!?%?%%%?%%%%%%!%%%%!%!%%!%%!!!%%??!!%%!%%!%!%!!%!%?%%%%!?%%?%%%%!%??%!%%!%!!%%%%%?%%!!%%!??%!!!!%!%%??%?!!%!!%!%!%?!?%!?%%%%%%%%%!%??!??%?%!?!%!?!!%!?!?%%!%%%!%?!!!%%??%%%!%%?%!!%%!!!?%!!%%%%!!%%?!%!%?%%%%!!%?!!%%%%?%!!%!!%%%%%!%%!!!!?%!%!?!?%%%%?%%?!?%?%%!?%%%!%??!!?%%%%!%%%!%?%%%%!!!?%!%?%!%%%!%%!!%!!%?%!?!%%!?%!%?!%%%%!%%%!!%%!??!??%?%%?!%%!!??%!!?!%!!???%!%%%%%!%!!?%%!%?!?!%!%%??!!%%%%!!%!!!??!!%%!!%%%%%%%%%!!!!%%?!%?!%%%%!?!%!!%%%%%%!?%%%%!!!%!!!%!%??%%!!%%%!!%!%%%%%!%!!!???!?!%%%%!%%%!%!%!?%!!%%!!?!?%%??%%!!!!%%!!?!%!?!??%!!!%!%!%!?%?!%%%!%?%%%%?!!%%!!%%!!?!%!!!%!%%%%%!!!!?!??%!!%?%???!!?!%%?!%?!!%%%%!?!!%%%%??%%?%!!!%%%!!?%!?!!%!!!%!?!%!%!%!%??%!!%?!%%!!?!%!!!%?!!%!!%?%!%%%%!?%%%%%%%!%!%?%?%!!!???!!%%%??!%!?!!!!%!!?%%%!!?!!?%%%!%!!!!%%%%%!%!%!?%%%!!%?!%%%!!%%?%!!%!%%%!!%%?!%%!!?%%!%%%%%?%!%%!?!!!%?!%!%%%!%%!?!!?%%%%!%%%!%?%!?%%!%!?%!!%!%%%!!!%%?%!%%!%!!!!%!%%!?%!!%%!!!%%%%!!%%%%%%%!!%??!%%!!!!!%%%%%%%!%%!!!%!%!!%!%%!%!%%!?!!%%%%?%!%%%?%!!!!!!%%!%%!!!!%!?%!!%%!!%%%??%%%!%!?%%!!%%%!%!%%!%!%%%!?%?%?%??%!!%!?%?%%?!!%?!%%!!!!%%%?%!%%?%?!%?!%?%%!!%%?%?%?!%%%!!?%%!%?%%?%%%%%!!?!%%!?!%!!%%%%!!!%!!!?%%%%?%!!%!%!?%%!%%%?%%!!%%%%?%?!???!!%!?!!%%!%%?!%%%!!%%!%!!%%%%%!!!%!!?%%!%!%!%?%%%%!?%?!!!%!!!%!%%!%!!!?!!!?%!!!!%?!%!%!%%%?!!!%%?%%%!%!%%!!%%!!!%%!%!%!!?!%%!!%%!!!%%!!!!!%%!%?!!%!%%%!%%%%%!%!%%%%%?%%?!%?!?!%%!%%%?%!%?%%%%!!!%%?%!%%%%%!%!!?!%??%!!%?%!%?!?%%!!%%!!!!%!!?!?!%%?%%?%?%!?%!%%%%%%!%!!!%!!!?!%??!?!!!%!%%%%!%%!!!%%%%!!?%!%%!%?%!?%%%%!%%%%%!%!%?%%%%!%?%!?%?!?%?!?%%%%!%?%%%%!%!%%%%?!!%%%%!?!%%!%%%%%%!!!?%%?!%?%%?%%!?!%!%%?%!!!?%!%!%%%??%%%%!%?%%?!!!??!??!?%!%%%?!%!%%%%!!%%%%!!%!%%!!?!?!!!!%%!!%!!%!!!?%%!!%%%%%?%%?!!%??!%!!%%?%!!%!%%!?!%!%!%?!%?%!!!%!?%%%%%!??%!?!!!!?!%%%%!??%%!%!%%%%%%%%%!%?!%!?!?%!%%%?%!?%%%!%!!%?%%!%!!%%?!!%%%?!%%!%%%!%!!!%!%?%%?%%%??%%%?!%%??!?!%!%!%%%%%!!%%?%%%%!!%%%?!%?%%?%!?%!%%%%!?%%%?%%%%?%%!?!?%%?%%%%%?%!%!%%!%!%%%!!%!%!%%%%%?!?!!%%%!!%%%%%!?%%?!%???!%!%!!?!!%%%%!!!%%?!!!!!%!%%%%%?%!!!!%%?%!??!!%%!%??%%%!%?!%?%!%%%!!%%%%!%%%?!%?%?%!%?%%%!%%%%%%!%!?!!!%!%?!!!%%%!??!!!%!?%!%%%%%%?%%%%?!%%?%%!%!!%%%%!!?%%%%?%%%%!?%??%??%%!%%%?%!%?%%%!%?%!%%%%?%!%!!%!!!!!!%%%%!%%!!!??!%!%%%!!!%!?!!!!%%%!!!!%?!%!%%%%!%?%!%%%?%!%%!?!%%!!?%%?%!%%%%%%%!%%%!!%%!%??!%!!!%!?%%?!!?%??!!%?%!?!!!!!?!%!!!!%%%!!%%%%%!%!%%?!%!!!%!%%!%?!%%%%%%?%?%%??!%!!%??!!%%?!%%!!%%?%?!%!%%!%%%?!%!!!%???%??%%!%%!!!%!%%!%!%%%?%%!?%%!?%?%%?%!?%%!?%!%!%%%!%%?%!%!%%?!%%%%!%!!!%%?%!?!%!!%%!?%?!%!?%%!%!%%%%%%%%!%%?%!!%%!!%%!!%!!%??%%%%%%?%%%?%%%!%?%!?%%!%%%%!!!!!!%!%%%%%!!%%?%???%%%%??%?%%%??!%%!!!%?!%!!%%%%!%%%!%!!?!%!%%%!!?%!%!!!%%%!!!%%%%!%%%%%%?%?%%!!%%%%!%!%?%!%?!?!?%!%%!%!!%%%%?!%%??%%!%%%?%%!%%!%?%!%%!!%%%?!!!%!!!%?%!%!%%!%%!%!!%!%%!%%%!!%%%%!?%%%?%?!%%!%?!!%!!!!%!%!?%!!%%%%!?%?%?%?%%%!%?!%!?!%%%%%!!%%?!!!%%!%?!%%!!?%?%?%%!%!%?%!!?!%?%!%%!%?%!!?%?!!%%!%!%!%!%%!!?%%%!%?%?!?!%???%!!!%!!??%%%??%?!!!%%!!%!%%%%%%%%%?%!%!?%!?%?%%!!%!?!!!!%%!%!%%!???%%!??%!!!?!?%%%%!?!!?!%%%%%??%%!%??!%%%!?%?%%%%!!!!%?%%%%%!!!%%%%!?%%!!?%%%%%%?!!!!!%!?%%?!%%?%!%!%!%?%%!%%?%%!!?%!%!%??!!%?%%%!%%%!%%%!%!%?%%!!%%!?!%!?%%%?%?!!!%%!!!!?%!%?!??%%%%?%%!%!!!!%!!%%!!%!%%%%??%%%!%%!%%?%%??!%%!%%?%!!%!!?%!%!??!?%!%%%??%%!%!!%!%!!!%%!%%!%?!!%?!!?%!!!!!%!%?%!?!%%!!!!?%!?!%%!!!!!!?%%%%%!%%%!%??%%%!?!!!!%!?%%%%%%%%%!%!?%%!!!???%%?%%%%%?!%%%%!?!!!%%!%!!!!!%???%!%%?!%%!?%%%?!%%??%?%%!%!%%%??!%%!!!!%!!%%%%%%%%!?%!!%%%!?!%!%?!!%?%!?%??%%%!%%!!!!%%%%%%!!!%!!!!!!!%%!!%%??!%!%!!!!!?%!%%!!?%%!%%?!%!?%%!!%%!!!?%!!%?%%!!%?%%%%!%%%!%?%%%%!?!%?%!?%%?%!???%?%%%%%!%%!%?%%%%%!!!%%%?%%%%%?%!?!%!%%%%!%%%%!!!!%!%%!!!?!%%%?%!%%%!%?%!%!%%?%!%!!!!!!!%%!%?%!?%!%?%!%!?%!%%%!%%%%!!?!%%?%?!!!%!%?%%%?%?%%%%%!?%%%!!%%%!?%!?!%%%%!%%!?!%!!?%!%!%?!?%%%!?%%%%!%!%!!!%!?%%!%?%%%?%!%!!?!%!?%%!%!%!!%%!!%!!%%!!!%!!%?%!?%%%%!!!%!??%%?%%%%%?%!%%!%%%%%%%???%%%%?%?%%%!%%%!!?%?%%!%!%%!!%?!!!!?%?!%%%?%??%!!%!?!?%!%%!!%?!%!%!%%%%%%%?%%%%?%%!!%!%!!!%?%%!%%%!%!?%%!!!%!!!!%%!?!!%%!%!%??%!?!%%!%!?%%%%!?!!!!%%!!%!?%%%%!%%%?!!%%?%%%!!?!?!!%!%%%%??%%?!!!%!!?!%!?!%%%!%%!%%%%%?!!?%!?%%!%%%?!%?!%%%!!???!!?!?!%%?%!!!%!???%%?%!!?!%?%!!%%!?%%%!?%%!%!!!!!!%!%%%%%%%!%%!!!?!%?%%%?%?!%!!!?%%!!!%%!!%!%?%!%%%!%?!?%%%%?%%%%!?%%%!!%!!?!%%!%%%%?!%%%!!%%!%!??%!%!%!!!?!%!!!%%%%%%!%?!%!%%%!%!!%?!%%%!%!%!%%%!%?%!%%%!%!%%%%!!!%!%!!%?%!??!%%%%%%!%%%!!!!%!%!!%??!!???%%%%!?!%%!%!%?%!?!!?%!%%%%??!%?%%?!%!!!%!!!%?!%!?!!!%%!%!!%%%%!%%?%%!??%!%!!%%!!!!!%%???%%!!!?!%???%%!%%%!%!??!%%%%!%?!%?%%%%%!?%!?%!%!??%%!?%%?%%?!!%!%??%%!!!!??%!?!%%%??%!%!%!!?%!%%%?%!!!!%??%??%!%?%?!?%%?%!!!!%%!%!!%%?!?!%!%%?%%%%%%!!!%!!%!%%!!!%?!!%!%!?!%%!%%!%%%%!%!!!!%?%?%%!?%?%!!%?%%!!%?%%?%!?%%?!%%?!!!%!?%%%%!?%%%%%!%%!%!??!%!%%%!?!!%%!!%%!?!%%%?!!%%%!!?%%%%%%!%?%??%%%?%??!?!%%%!!?%?%!%%%!%?%%%!!%?%?%!%%%!?%!!?!%%%!!%%!?!%%%%?!%%!%%!%?%!%%!!%!%?!%??%?!%%!%!%%!%%!%?!%!%%%%%%!%!??%!?!!!%%?!?!!!%?!%!?!?%%?%?%!%%!%!%%%%!?!?!%%%!?%!%%%%%%!!!?%!%%%!???!!!!!!!%!!!%!!?!?%!!%!%?%%??!!!%%%%!%%%%%%??%%%!?!!%%???!!%!%%%%!?%%!!!?%?!!%!?%?%%!%!%%%%!!!!?%?!!%!!%!!%!%?!%!%%%%?!%!%!!!%!?!%?%!%%!!?%!%?!%!%!%%%!!!??%%??%%%%?!%!!?!%?%!!!?!%%?%%%!!%??!!?%%%%?%%%%%!%!?%%%%????%%!%%%%!%%!!%????!%%!%?!?!%%!?!%?%%!%?%!%%%!?%%%%!!%%%?!%??%!%%!%%?!%%!%%!%%%!%%%%%%!?!%%%%%%!%?%!%!%!%??!!%?!!%%%!%%%?!%%%!!!?%!%%%??!%%!!%%!%!%%?%%%%?%%!%%%%%?%%%%%%%!%%%%????!?!%????!%%?%%%%!??!?%?%!%%?%!!%!%%%%!%?%%?%!%?!!!%!!!!%!!?!!%%?%?%!!%%%%!%%??%?%%%!!?!%!%%%%%!?!!%!%?%!!%%%?!!!!!%%%%!!?!%%%%%?%!%%?%?!??%%%?%%%!%!%!%!?%%!!%%%%!%!?!%%%%?!%%!%!%%!%!!!%!%?%!?!!!!!%%!%!%!?!%!%%?%%%%%?%%!?!!%%%!?!!%!%?%?!%%%%!?%?%!!%%!!!?%!%%!!%!???!%%%?%!?%%%%%?%!%!%%?%%%%%%?%!%!!!!%!!%%%%!%%%%%?!%!%?%%!%?%%!?%%%%%%!%%!%?%%%%%%%%%!%%!%!%!%!%%%!?%!%%????!%%%?!%!%%!?%!%%!??%%!%%%!!%%%%%!!%%%%!%%!?!!%!%!%!%?%%!!?!!!%?%!%%?!%%!%!%%!!%?%?%%%%!%%%%%%%%%!%?%%?!!%%!%%!!%?!%!!?%%!%!%%%%!!%!?!%%?%%%%%?%%%%%%?%%%!%%!?%%%%%!%!%?%!%%?%?%%!%?%%%!!??%!!%%%%!%%!%?!!%!!?%!!%%%!!%%!!?!!!%%?%!!%%!?!!!?%%!!?%??%%%!%%!%%?%%%!!%!??!%%?%!%%%!!%?%%!!?%!%%%?%!%!%!!%?!!!%!!!?!!?%!!?%%%!%%?%??!?%!%!%?%%?%!?!!%%?!%?!!%%%!%%%??!?!!%%%!??%?%%!??!%!%%%%%?%!!!%!%%?%%%!!%!%%?%%?%!%%!!!%%%%%!%%%%%%%!%!%%?%%!!%?!%%%%!!%!%%%?%!!!?%%%!!!?%%!!%%%!%!??%!!?!!!!!%?!??%%%!%?%%%!!%%!??%!!%!?!%%?%?%!%%%??!%%%%%?%%!!%%!%???!%!?!%%?%!%%!%%%!%%??!%?%%!%%!!%??%!%?%%%%!%!??%%?!%%?%!?!!?%!!!?%%?%?%%!%?!!!%%!!!?%%%!%!%!!%!?%%%!%?!%%!%!%!%%!%%!%%%?%!?%!%%%%%!%%!%%%!%!!!!%!%%%%%%!%?%%%%!%?%%%!!!%%??!%!%%!!%%!%%%%%%%?!!!%%!%!?!??%%%%?%!???%!%%%?!!?!?!%%%!%!%!%%!%!%??!%!%?%!??%%??!!!?%!!%!!%%?%%%?%!!%%%%%?%??!!%!%!!%!%%%!!!!%%%%!%?%%!%!!!!?!!%%%?!%%!!?%?%%%!!%!!!?!%%!!%%!!%%%%%!%%!%!%!?!?!!?%%%!%?%%!!%!?%!%%!!%!%%%%!%!%???%%%%%!%%%%!%?%%!%%%%!!%!%?%!%!?%%!%!%??%!%?%%%?!!%!?%%%!?%!%!%%!%%!!!?!!%%?%!%%%!%%%%!%?!!%?%!%!%%!?!%%%%!%%!%??%!!!!!!%%!!%!%?%???!!?%??!%?!!%%%%?%%%!??%%!?!?!%!%%%%%?%%%?%%!%%!%%%!%!%??!%!?!?%%?%?%?!!!%??%?%%!%!%?%%%!!%%%!!%!!!%?%%%?%%!?%%%!%%!??!%%%??%%%?%%!!%%%?%??%%%%!?!?%!%!???%!?!%%!%%%%%%??%%?!%!%%%!!%%%%?%%%%?%%!%!%!%!%%%%!??%%%%%%!!%!!!%%??!%%!%!%%?!%%!?%%%%?%!!!%?%%!%%%!!%!!%%%!%?%%?!!%%!?%%%%?%%%!!%!%%%?%!%%%%!%!%%%?%!%!%!%?!%?%%?!%!!!!%?%!%!%%%?!%%!??!%%%%!!%%!!!!!?%?!!!!%%!%%!!?!%%!!?!%!!!!%!!%???!%!%!!?!%?!%?%%%%%??%%%!!%!!%?!??%%%!?!!!!!%%%?%%?%!???%!??%!!%!%?%!%%%!%??%!%%%!%%?%%%%!%!!!%%%%!?%???%!!%!!%!%!!%%%%%%!!?%!%!!%?%%%?%%%%%%!%%?!%%%?%%?%%%%%!!!%%?%%%!%!?%%%%!?%?%%%%?%%!%!?!!?!%%!!?!!%%%%%!!%%%?%%!!%%%!%%%%%%!!!?!?%!?!%?%%!%%!?!%%%%%!!%?%%%!%!!!?%!%?!!!?%%!%%!!%!%?!!%?%?!??%!!!%%%%%%%%!%!%!%%%?%?%!%%?????%??!%%?%!!!!?%!%!%%!?!%??%!!!!!!%%?%!!%?%%%%%%!%?%!%%?%?!!%%!%%%!%%%%??!?!!!%%!%?%?!%%%%?%!!%!%!!%!%!!%%!%%%%!%?!%%%%%%%!!!?%!%!%?%%!!!?%?%?%%%%??%%??%%%!!%%%??%%%?%!%!!?%%%!!??%%%?!%%?!?!!%%!!%!?%?%%!!!!!%!%?%%%?%!!%%!%%%%%%!!%??%!?%%%%?%%%%%?%%%%%?%!!!%%%!?%!%%!%!!%!!!!%!!%?%%?%!%%%%%%!!%?!%?!!!?%%%!!%%%%?%!!%%!%!!%%!%!!%%%%!%?%!%!%!%?%%%??%%%%%!!%%!%?!?%%!?!!?!%?!%!%!%!%!%%%%%!%!%%!%?%%%%%%%%?!%?%!?%?%%%!%!!!!%!%!!!??!%%!!%!%%%!%%?%!!!%??%%?%!%%?!!!?%?%%!?%%%?!%%%%%?%%%?!!?%%!%%?!%%%%%?%%%%!?%?!?!%!?%%!!%!%??!?!!%%%?!?!??%!!%!%?!%!!%?!%%!!??!%!??!%?%%!!%%!%%%%??%??!!%%%!!!%!%%!%??!%!!?%!!%%%%%!!%!%?%%%%!%%?%%?!%%?!%%%%%!!%!!%%%!!!!!%%!%%?!!%%!?%!%!%%!!?%%%!?%!??%%?!%!!%!!!?%!%?%%!?%%?!!!?!!!%%%%!%!!%%!%??!!%?!!%%!%!!%%?!!%?%%%%?%!%%%!?%!!!?%!%!!!!!?!%!??%!%%%%%%???%%!%!!%??%!?%?%%%%%!!?%%%!%!%!%?!%!%%!%%!%!%%%%%%!%%%!!%%!%?!%%?!!!%%%?!!%??!%??!!?%%!%!%?%!%%%?%?!%%%!%%%!%!%%!%%!%?%%%%!!?%%?%!%!%?%?!!%%%%%%%!%%%?%?%??%!!!?%%%%%!%%%?!%%?!??!%!%!!%!?%!?%!!!!?!%!%?!!%!!%?%%!%%%%%%!!%!?%%!%%%!?%!!?!!?%%%%!!!?!!!%!%!!!!!?!%!?%%?%%!?%%%%%!%%%!?!!%!%%%!?!%?%!%??!!?!!!%%%%?!?%!?%%!%%!%!%%%?%!%!!%!!%%%?%%!?!%!%%!?!!!%%!%%!!?%%%%!!!%%%!!!!%!??%%%!!!!?!!?%%!!%%?!!?%?%%!?%!!%!!??%%?%%?!%%%%%%%%!!?%?%%%!%%!!!%%%!%%%%!!!?!?!?%%%%%%!%!%%!!!!%%?%%%%%!%!!!%%%%?%!%%%%%%%!%%%!%%?%%%%%%!!!!%%?!%%!%!%?!!!?!?!!?%%!%!!%%%%%%%%!%?%%%%%%!%!%!%!?%%%!!%%%!%!!%!%%%?%!!%!?%%!!%%%%%%?!%%!?%%%!?!!%%!!%!%%?!%!?%!%%%%!!?%!!!%%%%%?%?!?%%%!!!?!?%?%%%?!?%%!%!!%%%%!?%!%%??%%%%%%?!?%%!!!?!?%%?!%!%%%?!!%%?!%!%!!!!%%%!%!%%!%!%%%%%!%!?%%?!!%%%%%!%%!%%!?%!%%%%%%%!?%?%%?%%?!!%%%%%!%%%!%%%!%?%%%!%%?%!!%?!%%!%%!%!%!!%%%!%%%??%%!!!%%%?!%?%?!!!%!!%??%?!%!!?!!%!?%%%?!%?!%?!%%%%%%%?%%??%?!%!!?%!!%%?%%!%%!?%%!%!?%!%?%%!%!!%%%!%!!%%%%%!?%%?!?%!!%%!!%%!!!!%!%!!%?%!%!%%?!%%!%?%!%!!!%??%!%%%%%?%??%%%?!%!!%%!???!!!%!!!?!%!%%?%!%%%!!%%%%???%!!%%!??%%??%?%%%%?%!!%%?%%%!?%?%?%%!!%%%!?!!!%!%%%%%%!!!?%%?!!!?%%?%%%%%%!%?!!%?%!?%%?!!%!%!?!!%%%%%!%%%!!%!%!%%!%!%!%??!%%%!%?%!!%%%%!%%!!!?!%!%!%!%%%%%%!%?!?!%%%%!%!!%%!!%%?!!%%!%%!%!!???%%!%?%%!!%!?!%??%%%!?%!!%%%!!%%!?%%?!%!%??%%%!%%!??%!!?%!%?%%!%%!?!?%!%??!%!%!%!??%%%%%%!!%!?%?%%!?!?%!?%!%%%?!%%%!??%?!??%%%%%!?%!%%%?!!??!%%%%%%?!!%%%%!%%%!%???%!%%??!?%!!!%?%%!!%!!%%!%!%!%%!%!%%%%!!!!?!!%%%!!%%!%!!%!!!!%??%!!%%%?%!?%%?!!%%%!%!?%!%!!%!%%!??%%%%!%%%%!!!%%!%!!%%%%%%%!%%?%%%%!%%%!%!%%%!!%%??%!!!%%?%!%?!%%%%%%%%!%%?!!%%??%%%%??%%%%%%!%!%%!!%%?%?!%?%?!%!%??%!%!!!!!%%%%%%%%%!%%%?%%!?%%?%?%%%%!%%!!%%!%%?%!%%!!!%%!%%!!!?%%!!%%!??%%%!?%%!!?%%!%!%%!?%!%!%%!?%!%?!%%%%%%%%!!%?%%%%%!?%!%!!!%!%%?%!%%!?%?%!%%%!%%!!?!%%!%!%?!%?%!%!%!?%%%%??%!%!!?!%!!%%?!?%%%%?%%%%%???%!!!?%%?!%%%!!%?%%!%%!%%!??!%!%%%%%%%%??%%!!%%!%%!!?!?%%%?%%!!%%%%%?%!%!?%%!!%?!%%?!!%%%%!%?!%!%%?%%%?%%%???%?%!%%%%!%?%!%!?!%%%%%%!!%!%!%%!%!%%%!%!%%%%!!!?!%%%?%%%!%!?%?%%%!%!%!%%%%%!%!%??%%%%!?!%%!%?%?!!!!%%%%?%%%?!!!!!%%%!%?%%?%!%!%!!%!!!!%!!?!!?!%%!%!!?!!!!%??%?%!%%!?%%%%%%%!%%!%%!!%%??!?%!!!%!!%%!%!%%%%%%%!?%%!%%!!!%%%%!!%!%!!%!%%?%!%%%!%%%?%%%%%%%?%%??!?!!?%!%?!?!!??%?!%!%%!!%%%%%%%?!%??%!!!%?%?%%?%%%!%!%%%?%%?%!?!!%!%?!!?%!%?%!!??%!%!%%%!%!%?%%!%!%%%%?!%%!!%%%!?%%%%!%!%%?!??%%!%%%%%%?!?!?!%!!!%%!%%!!!!?!%%!%%!!!%?%!!%%%%?!%%!!%%%!%?!%!%%%!%%!%!%%!?!!%!%%%%%!%!%??%!!%??%?%!%!!!%!!!%??%?!%%?%%%%!%%%%%?!%?%%%?!%%!%?%!!!!%%??%?%??%!!!%%?!%%!!!%!!!%%??%!?%%%%%%!%!%!?!!!%%!%%!?!%!%%%?%%%%?%!!??%!%!??%%!!%%!!!!%%?!%!%?%%%?!%!%%!!%%%%!?%!%!?%!!?%!!?!!%!!??%!?!%?!%!%%%?%%!%!!!!%!%?%%!%%%!%%?!!!?!!!?!!%%!?%%?%%!%!%%%%%%%%!%%%!%%!%?????%!!%%?!!%!?!%???%?!?!%%%??!%?%%%%%%%%??%%%%%%%%?!?%!%?!%%?!!!!%%%!%?!!??%!%?!?!?%!??%%!%%%%!??%%%%!?%%%%%??%%%%%??!!%%?!%!%%%%!%!!!%%!!!%?!?!%%%!!%%?!%!%!!?%%%!!!!!%!%?%!%!%%%%%%%%%!?%!!%%!!?%!%??!%!%!%!!!?%!!!??%%%?%!!%!%%%%%%%?%!%?%%%!??!%!!%!%%%?%!!%%%?%!%!?%!!?%!!?%%%!??%%%%?%??%%%%?%?!%%%!!?!%!%!?!%%?!%!%%%%?!!?!!?%%!!!!%!%%%!%%%%!!%!%!!%!!%!!!!%?%%?%!%%%?!?%!%?%!!!%%%??!!!%%%%??%%%%!%!!%%%!!?!!!%%!%%%%?!!%??!%!%!!!%%?%!%!!!!!%%?!??!%!%?%!%?!%?!%%??!%!%!!%!!%!%??%%%%%?%%%!%%!?!!%?%%?%%?!%!!!?%!%?%%%%%%%%?!%%%!!!!!!%%??!%%!%%!%!%!%%!!%??%!?!!%?%%!%!!!%?%%%%%%!%%!!%!%!!?!!!%??%?%%!%%!?!%%%%%%?%!%!!%%%%%!!%%!%%%%%!%!!%?%??!%%!?%!%%!!%%?!!?!%!!!%%?%!!?%!%%!%!%%%%?%??%%%%%%%%%%%?%%%%%!!%%?%?!%%?%!%?%?!%!%%%!!!%%%%?%!%!!?%%!%!?!?%!!!%?!!%!!%!?%%%%!!%%%%!??!%%%?%%%%%%%!?%??!%%!%%?%!%!%!%!?%?%!%%?%%?!!%?%%!%!%%!!%%%%%??%%%%%%!!%%%%%??%?%!!?%!!%%%%!%?%!!?!%%!%%%?!%%?%?!?%!!%?!!%!%%%!!!%!%!%%%?!!!!!!%!!%?%%%%!!%?!?!!!!%?!!!!?!?%??!!%%!!%?!!%%!%!?!!%%!!!!!!%%?%??%!?%%%%!?!%%%!!%!%!?!%!!%%!%%?!%!?%!%%%?%%!!!%%%%%%!%!!%?%!%?!??!%??!!%!%%!!%%!%!%?!%%!!%%%%??%%%!!!%%%%?!?!!%?%!!?!%!!!%??%?!%?!%%!%%%!%!%!%?%???!%%%!%%!!%%?!?!%%%%!%%%?!%!%%%!!!%!!%!%?%%!?%?%%%%!%!%%?!!%%%%!?%!??%??%%!%%!?!!!!%?!%?%??%!!%%!%%!%!%!!!?%!!?!%%%%?!%%!%!%?!?!!!!!%%?!%%%?!%%%?!!%!!!!!%!%!%%%%!%%%%!%!%%?!?!!!%!%!!%!!%%%?%?%!%!%!%!%%!?%?%%!????%%%!!?!%%!!%%%%!!%!?!%%%%?!%?%%%%%?%%%%%%%?!?!!!!%!%!!%!?%!%?%%!%%!!%%?%%%%%??%%%%%%%!!%!???!!%!!%%???%%!%!?%%?%?%%%%!%!%!%%%?!%%!%?!%%!?!%!??%!!!!%%%%%?!%%%!%%!%%%%!%!?!?%%%%%%%%??%!%%%!%!%%%!??!%?%!!%!%?!%%?%?!%?%??!?%!%%??!!%!%?%%??!%%?!?%%%%!!%%!!??!!%%%%%%?%%%?%?%!?%!?!%?!%?%%%?!%!%%%%!%%??!%%%%%%%%%!!%%%!!!?%!%%%?%!?%!%%%!%?!%?!?!!%%!!%%!!%!!%%%%!%!%!!%%%???%?%!!%?!%%!!!!!!!!%%%%?!!%!%!!%%?%!!?!?%%??%!!%!%!!?!!%%%!!%%!%!%%%!!!!!%%%%?!%%%!%%%%??%?%%%%%%!%%%%?!%%%?%!!%%!!%!%%!?!%???%!??!!%%!%%%%!%%%%%%?!%%!!!%!?%%%!?%?%!!%%?!!%!!%%%!%%!%%?%%%%?%!!%%!%?%?%%?%%!%%??%%%%%?!%%!%%!!%%%!?%%%!%!%!%%!%%?%!%!!%%!%%!?!%!%%?%%?!?!%%!!!%!%?%???%!%%?%!!%?%!!%??%!!%!%%%%?%!!!%??!%%%%%!%!!%??%?%!%%?!?%%%%%%%!!?!%!%?%!%%%%?!!%%!%%!%??!!%%%%!?!!%!!!%?!!?!!!%?%%?%%%%%?%!!%?%%%%%%%!!%%!!%??%%?%%!%!%%%!%?%!?%?%%%???%%!%!?!%!!?%%%!%!?%%%!??!%??!%!%?%!!%!?!!!!?!%%%?%!%%%?!%!!?%%!!??!!%%%%%!!%!!%!%?%%%%!!?!!%%?%!!?%%!!?%%%%%!?%%%%%!%!?%%%%%%?%%%%?%!%%%!%!%!?%%%%%?%!%%!!!!?!%%%%%%%!!!!%%!%???%!%!%%%%%!%?!?%%?!%%?!!?%%%?!!%?%%%%%%!!%!!!%%%?%!!%%%%%!%%?!?!%%?%!%?!!%!?!%%%!%%%?!%%%!%!!?%%%%%?%?!!%!%!?%!%%%%%!!%%!?%?%%?%!%%%!???!%!%%!!%!!??!!!%!!%%%%!%!!%???%%%%%%%??!!%%?%%!!!%?%%%???%%!!%!!%!%!%%!!?%%%%%!%!!!!%%!%%%!!!%%!%%%%!%%!%?%?!!??%!%?%%!!!!?!%%!%%%!??!%%%%%!!!?!!!!%%%%!%?%!%!!!%?%!?!??!?%?%%!?%%!!!????!%!%%%?!!%!%%!!?!?!?%%!%%%%?%%%%!?%%!???%%%%%!??%%?%!!?%!%%?%%%!!!!?%%?!%%%%%%!!?%!!!!%%%!!!?!%%%%%?%%!%%%%%?!!%!!!!?!!?!!?!%%?!!!!?!%!?%%!?%?!!%%%%?%%%!!!!!%%%%%??!!%%%%%%!?%%%%%!%!%!%!!??!!!%!?!!!!%%!%%!%?%%?!%%?%%%!%%%?!%%%%%%!%?!!%%%!?!!%!%!???%!%???%%%%%%%%!%??%?%?!!%!!%%%%%%%!!%%!%%%%%%?!?%%%%%?%%!?%%??!%!!%!%%%!!?%!%!?%!%%!!!%%!!!!!%!%%!!!?%!%%!%%!!!%%%%?!!?!?%%!%%!!%??!!%??%%!%!%?%%%?%%%!!!?%!??!%!?!%?%%%%?!%!%%!%!?!?%%%??%!!%%%?%%%%%!!%!%%%?%!!!?%?!!!%%!?!%??%?!%%???%!%??!?!!!??!%%%%%%%?!%%?!!?!%%?%!?!!!%%!%%?!%!!?!!!%!%%%%!!%!%??%%%%??%?!!?!!%%?%%%%??%%!%!%%?!%?%!%!%!!%%?%!%%!%!%%%%%%!%?%%%%!%!?!!?!%%!%!%%%%%%?%%!!?%!!%!!!%!%!!%%%!!%!!%%???!!!%%%?!!!%%%!!%%%%?%?!%!!???%%?%!!?%%%!!!!%%%!%%%%%%?%%!%?%%!%%!??!%%!!!%??%!?!?%%%?%!!?%!%%!?%%%%!!!%??!%!?%%%%!?%%%?!!%??%?!!!!%!%%!!?%%?!!?!%!!%!%%%!!!!%!!!%!%%??!?%%!%!%%??%%?%!%!?%%%!%!?%%!!!!%%!%?!!%!%%%!%%!%??!!!%%!%%%!??%?%!?!?%?!!%?%%!!!!?!%%%%!!%%%!%?%%!?%%%!!!?%%!%!%!!%!!!%!%!!!%%%?%%?%!%%!%?!%%%%!%?%!!%!%!%!%%!?%%%%!%%%%%!!!%!??%%%%?!!%%%%%%!!!!%%%!%!%!!%!%%?%%?%%!%??%??%!%%%%!%%!%!%%%%%%??%%%%%%!%%%!!%%?!%%%!??!!!!!!!!%%?%!!%!!!!?%%??!!%!?!%%%%?!%%!%%%!%?!!%!?%%%%!?!%%!%%%!%!%???!%!%%%%%!%!!!!?%?!%?%!?%%!%%!%!%%%!!!?!!%%%!%%!??%%%!%%%!%!%?!?!!?%!%%%%!%!?%%?!!!%%!%%??!%%%%%%!%!%!!%!%%%%%!!?%%%!%!!%!%%%!%%!!!%!?!?!%%!%%%!!%%%?!!%??%%%%!!?%%??%?%!%%!%%?!!%!!%%?%?!!%!!!%?%!!%!%%%!%%%!%%%%!%!%!%%%?%%%%!!!%???%%%?!?%%!!%!%?!!!!?%!%?!%!?!%%%%!%%%?!?!%%%%%!!%!%!?!?%%?%%?!?!!!%%?!%?%?%%%?!%!!%!??%?%?!!%%!%%?%%?%%%!%%??!%?%%!??!%??!?%!!%%?%!?%?%%?%%%!%%?%?%%!%!?%!!%%%%!%%%%!?%%%?%?%%!!%%%!!%%%%!?%??!%!%?%%%!!%?%%%?%?%!!!%!%%!%%%%?!%%%%%%%!!%!?!%!%%!%!%%!?!%%!%%%??%?!??!?%!!?!%%!?!??!%%%!!!?%%%%%%%!!%?%%!?!%!!%!%%?%%%%!!!%?%%!%!!?!%%!%!!%!%%%?%!%?%%!%?!%!!%%%%!%!?%%%%!?!%%!%!%%!%%%%!%?%!%?!%%!?!?!!%%%%!%?%!%%%%!!?%!%%?!%!!!?!%%!%!%%%?%%%?%!!?!%??!!%%%%%!%%!%%?!!?!!!!!%%!%!!%%%%%%?%!%%?!!%!%!!%!%%??%!?%!?!?!!!%%%!?%?!%%!%!%%%?%%%%!%%!%!!%!!?!%!!%!%%?%!%!%%%%%%%!%??%%!%?%%%?%?%%!%%%%%%?%%!%%!%?!?%%%!%!!!%!%?%!?%!!%%%!%%%%%%!!?%%!?!%%!%!?%!%!%!??%!?%%%!!!%?%!?%%!%?!!?!%?%!%!%??!!%%!%?!?!%%%%%%%!?!!?!%%%%?!%!%!%!%!%%%?!?%%!!!!%!?%%%??!%!%!?!?!!%?!%!!%!%!%?%?!!%!!!%%?!!?%!%!?!!%%%%!!?%%!%!%%?!%%%%%??!?%!!!%?!!%!%%!?!!!%!?!?!%%?%%?!%%%%%!%%%?!?%%?%%%!%%%%%%?!%%?!%!%%%!%%%?%%!%!%%%!%%%!!%!!!?%%?%!!?!%?%?!%!??!%%!%%!!%!!?!%!!%!%!???%%!!?!??!%!%!%!%%!%!?%!!?%%?!?!!!!%!%%!%!%%%%%!!%%%%%%!!%%??%%%!!%!%%%!%%%%%!!!?%!!%%?!!%%%?%!%%%%%!%%%?%%%%?%%%?%%%%!!!?%%?!!%!%%%%%!!%%!?%!%!!%%%%!?%%??%%%?%!!%!?%%!%!?%!?%!!!%%!%%?%?%!!!!%%%%%%!!!%??!%%%!%!%%%!!%%?%%!!%?%??%!?!%%?!%!!!!%!%?%!%!!%%%%%%%%!%!%%?!%!?!%%!!%%!?%%?!?%?!!!%?%!%%%%??!%%%%%!%!!%%!%%%%%%?!%??%??!!%?%%%!!%!%%!%%%%?!%!%%%%!!?%%?!%!!%%%!!%%%%%?!!!!%%%%%!??!!!%%%!?!!%!%%%%%!%%%??!%?!%!!%!%%?!!%%!?%%%%!?%!!%%%??%!!%%!%%%!?!%?%!%?!?!??!%%%?%?%?!!?%?!!!%%%%!%!!%%??%%%!%%?%%%%!%!%?!%!?%!%%%%%%%?!%!%%%%%%%!!%!!%%!%!!?!?%!%!!!!%%!%!%%%%%%%!!%%!?!%%!%%?!%%!!%!?%?%!!!!%!?%%!!!!%!%%%%?%%?!!!?!%%?!!!%%!?%!!?!?!!%%!%?%!!??!%%!!!?!%%!?%!%?!%%?%?%?!?%%%??!%%%%%%%%%%%!????%%?%%!!%%%!?!!%!%!%%%%!%!?!!!%%%%%!?%!!!%%!!!%%!?%%%!?!%%%!%!%!%!%%%%%%%%%!%!!!%%?%?!!!%%%%%%%?%?%%%!!!%!!%%!%%%%?%%%%?!%!%?!%%%%!!%%!!%!!%?%%!%!%!%%!%!%!?%%%!?!%%!%?%%!%!!???!%?!%%%!%??%%?!%!%!??%??%!%%?%%%!%%?%!?%!%%!%!!%%!?%%??!%%!?!!%%!%!%!%!%!!!!!!!%%!!%%%%%%!%%%%??!%!!%%%??%%!?%!!%%%!!?%%%!%!!!%!%%???!!%!%%!%%%!%!!?%%%!?%%%%%%%!!!!%%!%??%!!%!%!%%?%?!?!?%%??!%!%!%%%%??!?%%%?!!%!!%%!!!%!?%!!%?%%!%!%!!%!%!%%?!%?%%%!%?!?!?%?%!%??!%!?!!!!!%%!%?%?!?!?!%%%!%!!%%!?%!?!!%!!%%!%!!!!%%!!%%%?%%!%!?%!%%??!%%!!!%%!!%!%%%%!?!%%!%%%%!%%!!?%!%%!%!!%%%%%?%%!%!%%%%%%?%?!%?!?%?!%!%!%%%?%!%%!%%!%%%%?%!??!?%%!%%%!!!!!!!%%%%!!!%%%!!%!?%%%%!!!%%%!!%?!%%%?%!%!??%%?%!!%%!%?%%%%!%%%!%?%%?!!%%??%%%%%!!%!!!%!%!!!%%????%%%!%!!%%%%?!%%!%%%!!%%!!?%%?!%!?!!?!%!%%?%%?%%!!%?%?%!??%%%%%%!??%%!%%%!%%!!%!?!%%%?!!!!!?%%%%!%%!%!%??%%%%%%?!%?%!%!!%%!?!%!%%?%%!!!%!%%!?%%?%%!!?!!!!%?%!?!!?%!?%%!%?!!!!%?%?%!?%?%??%%%%!%?%%?%%%!%%!?%%%%%!!%?%!!!%?!%%!!!%%%!%!?!%?%!!%!!%!%%!!!%?%%%%!%!%!?%!%!!??!?%%!%!%!%!%%!%?!%%%%!%?%%%%!%!%!!!!%%%%%%!!!!!!?%?!%!?%%%%?!%%%!!?%%!!%%%%%??!!!!%!%%%%%!!%%!%%%?!?%!?!!?%??!?%%%%!!%!%!!%!%!%!%%?%%%!%!%%%?%%!%%!%%?%%%%?%!!!?%%!!!!%!%%!?!?%%!!%?!%%%!!%!!!!!??!!!%%!!!%?%%%%?!?!%!!%!!%!%%?%!%%!?%!!%!%!!!!%?!%?!?%!!!!!!%?%%!%%%!?!%!!!!%?!?%!!!!%%%%?!???%!%!%%?%%%!%!%%%?!%%!%!!??%!!!!!??%!!!%!%%?%%?%!!!%%%!%?%?%%!%%%?%%!%%%?%%%!!?%!%!!!%%%%%!%?!%!!%%%!%?!!!!%%%%!%%%%!%%%!%%%%!%!%!%%%%!%%%%%%%!%%%?%%%!%!!%???!!%%!%?!%%%?%%%%!%%%!%%!!!!%%%!!%!%?!%%!%%!?!!!!%%??%%%%!%%%!%%%!!%%%%%?%%%%%!??%%!!%%%%%?!?%%%!!!!!%%!!%%?%?!??%%?%!!!!%%%%%!%%%!%!!!!%!!!%%%!!!!%!%!%!?!?%!!!%%%!%!%%%???%!!%?%%!%!%%%%%!!!!%!!?!%!%%!%!?!%!!%%%!%%?%!%%%!!%??%%%??%!%%%%!%!%%!%%%%%%!!!!!%%!%%%%%%!??!!%!%%!?%?!%%?!%!%!?%%%!!%%!!%%!!%?!%%!%%%!%??%%?%!%!!%%!%%%!%!%!??%%!!%?!!?%!?%!!%!%!%!!%%?%%!?%%%!%!!%!%!%????%%%%!?%!?!!!%!%%!!%?%%!!?%!%%?%%%!!%!%!!%!!%!?%!!!%!%?%%%?!!!!%%!%%%!%%%!!??%!%%%%%%%%%!!?!%!?!!!%?%?%%%%?%%?%%%!%%%%?%!%?%%?%?%%%%%!%%?%%!?%!!%!%!%??%%%?%??!%!!%!%%%!?%%!%!?%??%!%!?%!!%%%%!%%??%??!%!%!%%%%!%%!?%%%!%%%%%%%%!!%!%!%!%%!!%%!??%!%!!!%!!!?%%??!?!?!%!%%!?%!!?%%%!%!!%%!!!!?%%%%%!%%!%!%!%!!%%%%%%!%?%%%!?%%!??%!!!%!!!%%%!%%?%%??%%!%?%!!!%!%%%!%!?%%%%%!?%?%?%?%%%!%??%!%%%%!%%!!?!%%!%%?%%%?!%!%?!!!%!!!%!%!!%?%%!%!%%!%%?%?%%%%!?!%%?%%%%%%%!%%!%!%%%?!%%%!!!!%!!?%%!!!!%!?%%!?%!%%!!?!!!%?%!!%%!%%!%!%%%%%%%?!!%%!!!%%%!!!!!!?%!!%!%!%?%!%??!?!%!!?%%%%!%%?!!%%!%%%!%!%!!%%%%%%?!!!!%!!%!?!?!!%%%!?!%%!!!%%!%?!%%!!?%%?!!%%?%!!!!%%!!%!%!?%!?%%%!!!%%%%!%??%!?!!%!%!?%!%%%%%!!%%%!!%!%%%%%?!%%%%%!%!?%%?%%%%%!%%??!%!!!%?!?%!!%!!%!%%!%%%!%!%%?%!%!%!%%%%%?!%%!!?%%!!%!!%!%!!!!!%!!%%%!%?!!%%?!!%%!%%?%%?%%%%%%%?!?!%?!%!!%!!!?%!!!%?!??%?!%!%!%!?%?!!%%%%!!%%!?!%!%%?%!%%%!?!?%%%%!!!%%%%!%%%!?%!%%%?%%%!!%??!!?!!%!!!!%!!?%%!?%?%%?%!%!??%!%%!%?!!!%%!!!?%%!?%%%!%!%%!!??!!!!!%!!%%!!%%!?%!!!!%!!%%?!%!%!%%%%%!!%!%!!%!%!%%%%???%!!%%!!!%%!%!!%%!%%!%%%!%!!%!!!?!?%!%!!!!%%??!%%!!%%%?!%%!!!%!!!!!!%?%?!?!!%%%?%!%%%!%%%?!%!%%%!%!%%?%%%%%%%%%%%?%%!%!!!!?%?%!!%%!%!%!!!?!%!%%!!!?%!!%%!?%%%!?%?%!!!%?!!%?%!?%%%%%%%%%%?%?!!?%!%!%?!%!!%%%!%%%%?%%%%?!%!%%%%%%%!!?!!!%%?%%%%!%%%%!%%%%!%%!%%!%%!!%%%!%%?!%%%%%%!!!?%%!%%%%%?%!!%%?!%?!!%%%!?%!%%%%%%!!%%!?%%%%!%?!?!?%!!?!%!%!%%%%%!%?%%%%!!!%%%!?!!%!?%!%%%!!!%%!%!?%%??%?!%?%%%%!%!%%%!?%!%?!%%!?%%!?%!%!%!?%%%!%!!!!%!%%%!!!%%!!?%!%%?%!%%!%!%!!!!%%%!%%%%%%%%!%%%!!??%%%!%!?!!!%?%%!!!%%%%??!%%%?!!%!!%%?!%%%%%%?%%!??%!!!%%!!%%??%%!%%%!%%?!?%%!%%%%??%!!!%??%%%!%?!!!%%!%!?%%%?%%%?%!!?%?!%!?%!%%%%%?%!?%!%%%!%%%%?!??%%%!%%%?!??%%%%%!%%!!%!!!!!%%%!?!%!%!%?%%??!!!%?!%%%%?%!%%%%%%?!%??!!!!?!%%!%?%%!%%!?!%%%???%%!?!?%!%%!%%?%%%%%!%!%%%%!!%!%!?%%!%%%!%%%%%!!%%%%%?%!%%%%%!!%%?%!%?%!!%?%!?%!%%%%%%!%!%%%%?%!!?%%!%%%%%!!%?%%%??%?%%!?%%%!%%%%?%%?!!!!%%?!?%!?!%!?%%?!!%%!!!!%!??%?!%%!%%!%%?!%??%%?%%%%%?!!%!!!?%!?!??!?%!%%%%!%?!!???%%!?%!%!!%%!?%%!!%%%!!%!%??!%!?!%?!?!?%%!?%%?!%!!%???%%?!%?!%%%!%%%!%%?!%!!!!?!?!%%?%%%%%%%?%%!!!%?%%%!%!%%%%!?%%!%%?!%%?!%%?%%%?%%%!%%%%%?%!!%!%%!!!%%!!?%!%!%%!%%!!!%%%!%%%%%!%%%?%!!%?!!!!%%%%%!!!?!%%?!%%?!?%%?%?%!!?!!!!??!!%!%!!?%?%%%?%%%!!%%%!%!!!?!?!%%!!!%%%%%!%?!!%!%%!?%%!!!%!%?!%%!%??%%?%!%%%%%%?%?%%!%%%%?%%!!%??!!%%?!?%%%%!%!?!%%!!%%%!!!!%!?%!%!%%%%!?%!%%%%%%%!%%%%!%!!?%!!?!!%?%!!!%?!%!%%!!%!!%%!%!%%%%!%%%%%!%%?!!???!%%%%%!%%??!%%%!%%?%?%?%!!%!!!!!!%%!%%%%%%!?%??!?%%!%!%!!%%!%!%%%%%%%%%!%!%!%%%!!!%?%?%?!%%!!?%!???%%!?%%!%!%!%%!!%%!?%!?%!!%%!!%!%%%%%%%%!%!%!!!%!%%!!%!%!??%!!!?!?%%%%!%!?%%!%!?%%%???!!!%%!%!?!!!%%%!%%%%%?!%!!!%!!%!!%!!%%?%!%%!%%%%%%!!!!!%%%!?!%%%?%??!%%!?%!?%%!%!%%!?%%!!!?%%?!?%!%%?%%%!??!!?%%%%%!!%?!!%!!%%!?%%%%%?%!?!!%?%!%%%%%%%%%%%!%%%%!?!?%%%!%!?%%!?%%%!%%%%%%?%%??%?%!?!%%?!%%%%!%%!!!?!!%%!!!?!%%%!%%!%%?%%!%!%!%%%%!%%!%%%%%!!%%%%%%!!%?%%%!?%!%%?%!!!!!!!%%!%%%%%%!!%!%%%!!!%?%%%!%!%?%%!!%%!%%??!!%%%%!!%%%!!?%!%!?%!%?%!%!%!!%!%?!!?%?!?%!?%%%%??!?!!!!!?%!!%!!%??%?!!!!%!!!%?!%!%%%%!!!!!%!!%!?!!!?!!%%%?%%!%?%%!%!%?%%%%%%!%!!!%!?!%%!%!!%?%%%%!!%%%%?%!?%!%!?!%?!%%%%%!?%!!%%!%?%!%%!!??%!%?!%?%%%%%%!%%!%!!%!!%?%%!%%?%!%?%!%%%%%%%!%%?%%%%!%%??%%?%!!%!%?%%?!!!%?%!?!%!%%%%%?!!!%!!%%?!!?%%?%%%%%!%%%%%!%%%!!?%%!!?%%%!?%%%%!!!%!%!%!?!%%%%!%!!?%%%!!?%%!!!%!?!%%?%!%%%!?!%%%%%%%!!%?!??!!!%!%%!??%?%%%?!%%%!%!%??%!!?%!%!!?%?%!%%?%%%!%?%%!%%%%%%%?!%!!!%!??%%?%%%!%%!%%%%%!%?%%?%%?%?%?!!%%%?!!%%%!%?%%!!!%!%?%!%!%%?!%?%%%!!!??%!!!??!%?%?%%%%%!%?%?%%%%%%!?%?%%?!?!%%?%?!%!%!%%%%!%%%??%%!??!!%%%%?%%%%%!%%??%!%%%%?!!%!%%!?!%%%%?%!%%!!!?%!?%%%!!%!%%%%!%!%%%%!%%!!%%%?%?%%%%!?!!?!!%%%!?%%?%!%%%%?%%%%!?!%!!!?!!?%%%%!!!%%?!%!?%!?!%%!?%?%%!!!%!?!%!?%%%!%?!%?%!??!%%!%!%?%?%%%%%?%%!%%!%!?%%!%?!%%!!?%!!%%!%!%???%!!!!%?%!!%!%!!!%%%!%%%%??%%?%!%%%!%%!?%!%%!!%??!!!%?%!??!??%%!!%%!?!?!%!%?!%!%%!%?!%%%%%!??%%%?!!!???!!!%!!%?%!%%!%?%!%!!%%!!%!!!?!?%!!!!!%%%%!!%%???%%%??%%!%!?!!%%?%!%!?%!!%!!%%%%!%%%%%%?%%?!??!!%%!!%%%?!%!%!%!!%%?%%!?%!%?!%?%%!%%!%%%!%?%%?!?!%%!%??%%%%%!%!!!!%!!!?%!!%!%?!!!%??%!?%%%!!%%!!!%%!!!!%!?%%!!%!%%!%%%%!?!%!!!%!%%%?%!%%%%!!?%?%%%!!%!?!%%%!%!%!!%?!!??%!!!?%%%%%?%!%?%%!%%!?%%%!%!?%?%!%%%!%%%%%?%!%%!%%%%%!!?%?!??%%!!%%%%%?%%!!%!%%%!%?!??%?%?!?%!?%%%%!%%%%%!!!%%!%%%!!%%?!?%%%??%!%!%%!%!%%%%!%%?!!?%?!!%%%%?!%%!!!%!%?!?%??!%!%?%!%?!!%%%%%?!?!?%?%%!%?!%%%?%?%%%!%!!%%%%!%!!?%!!%!!!%%?%?%%%%%!!?%%!?!%%!!!?%%%%?!%%!?%%%?!%%%!!%!%%%%%?!?%%%%!%!%!%?%!?%%!!!!!%??!!%!!%%%!?!?!%%%!%%!!%?%??!%!!%!%!!%!!%!!!!!!%?%%!!%%!!%%!!!%%%%?!%!!%%!%!!!?%!%!?%%!!%%%%!%?!!!!%?!%%%!??!!%?!?!%%!%!%%%?%%!%!?%%!%%?%!%%%!%%!!!%!%?%!!%%?!!%!!!%!!%!%%!!!!?!!?!?%!%%%??!%!%%!%%%%%!%%%!!?!?!?!??!%?!%!%%!%!!!!%!%?%%?%??%?%%!%??%%???%%!!!?%?!?!%?%!%!!%?%?!?!%%!?%?%!!!!!%?%%!%%%!%?%!!?%%%!%%%%%%!!!?%%?%!%!!%%!%%!%%%!%%!!%!%?!!!!!??!%%%!%!!!%?!%%%%?!%!!!%!!?%?%%%%%!%!%!!%%%!?%!%!!%!%%!%%??%%%%%%?%?%%??!??%%%!%?%%!!%!%?%%%!!?%%?%%!!!!!%?!!???!%%!?%%%%??!%???%%%%?%%!!?%%?%%%!?!!!!?%!%%!%%%%!!!%%%!%!%%!!!!!%%%%%%%%%%?%%%%%%!%!%%!%!!%?!!?%?%%%!?!?%!%%%!??!%??!?%!?%%!!%%?!%%?%!!%%!!%?!%?%%%?!!%%?!%%!!!%!%%!%!!!%%!%?%%%%%%?%%%?%!!!%!!!?%?%?!!??!%%!%%%%%?%!%??%%!%!????!%%!%%%!%!?!!!%?%%%%?!%!%?%!??!!%!!%!%%%?%%!%%%!!!%!!%%?%%!?%%%!%!!%!%%?%%!?%%?!%!%!%%!!!%!%%%!%%?!%%%%%!?%?!?%?!?%%!!!?%?!??%!%?%%%?%%!%%?%!%%!!!?%%%%%?!!%%%?%!%%?%!%%!?!%!!!%%?!!%%!!%?!?!!!!%%%%!?%%!%%?%%%%%%!%!%!%!%%%%?!!?!?!!?!?%%%!??!!!%!%%!%!!!!%!%!!!%?!%%!%%%%!!?%%%%%%%%%!%%!!%%!!%?!!%%!%?%%!?%!%%%?!%!%%%!!!?!%%%%!?%%!!!!?%%??!!%%!%!!!!!%%!%%%!%%!!?!?%!!!?!!!?!%%%%?!!%!!%%!?%?!?!%!!%%!!%%%!?!!!%!%%!!?%%?!%!%!!%!%%%?!%%%!%%%%%%%!??%!!!%%!%?!!%%%%!%!!%%!%%!%%!%!!!!%%!!!?!?%%%!!%%!%!%!%%%%?%%%!%!!?%%!!%%%!?%!%%!%?%%%?%%!%%!%%%??!%!%?%?!%???%!%!!%%%%??!%%?%%%%!!%%%%!!%!!!%??%!!?%?%%%?%%!%%%%??%??!?%!!%%!%%?!%%%?%%%%%%!%!?!%!%??!%%?%%!?!%?%%!%?!!%?%%%%%%%?!!%?%!!??%?%%%%?!%!!!%?%%!%!?%%???!!%%!!??%???!%!!!%%%!%%!%?!%%%!!!%?!?%!%?%%!!%!%%!!%%%!%!%?%%%%?%!%!!?%!!!%%!%%!!!!?%?%?%?%%?%?%%%!?%%%%%%!%%!!?!!%!%%%!%!%?%!!!!%%!!??%?!?!%%%!!?!!%!%%%!%!%!%%?!!!%%%?%!!%%%%%%%%%?!%%!?!%!?%?!%%%!!!%%!%%%%%?!?%%%?%%%%!!%%%!?%%!!%!?!%!%?%%?!%?%%%%%?%?%%!%%%%!%!!!?%??!%!%?%!!%?!!!!?!%%!!!%!%?%?%!!!%%!%?!%!?%!!???!%%!??%%?%!?!%%%%%%%%!!!!%!%!!%!%%%!?%!!?!%!%??!!?!?%%%!!!!%?%%!?%?%%!%!%!!???!%%!%!%?%%%%%?%%!!!%!?%??!??%%%!!!%%!!!%!!!?%%%%!!%!?%!%!%!%%%!%!!!!?%%%!%%%%?!!%!!!%!?%!!%!%!%!%!!%%!?%%%!%%??!?%%!%%!%%%%%%!%%!!!!%%%%%%%%%%%%???!%!%%!!%?!!!%?%?%!%%%?%%!!%%%%%!?%%!%??%%?%?!%?%!%??%!!?!%!?%??!%!!%!!!%!!?%!!!!?%!??%%?!?%?!%%!%%%!?!%?!?!!?%%!%!%!%?%!?%!%%%?%!%!%!???!!!%%%%%?!?!!?!%??%!?!%?!!!%%%??%%%!%!??!??%%?%!?!%!%%!!%%!!%%%%%%!%%!?%!?!%%!!!!%%?!?%!!%!!%%!%%%%!!%%%%!%%%!%%%%%%%%%!?!%!%!%!!!%!!!%?%%!!%?%!%!!!%%%%!!%%??%%!%%%!!%%!%?%!%%?%!%%%?!%!!!!!%%?!!%%?%!%%!!%!%?%%?%!%%%!%%?%!%%?!!?%??%?!!%%!%!?%??!%%!!!%%?!%?!?%%!%!%!%%!%!%!?%%%%%%!!??%%%%?%?%!?!%%!!?%%%!%%%%%%?%%%%%%?!?%!%%!%%%?%?!%!!?%%%%!!?!!!??%?!%!%%%%!?%??%?!!!%%!!%!%!%!%%!%??%?%!%!%?!%%!%%!%?!%%!!%!?!!%%!!!!%%!!?%%%?!??%%%!!%%%%!%%%?%!?%%!!!!%!??%!!!!!?%%!%%!!!%?!!!!!!?!%%%??%!%!!??%!%!%%%!%%!%!!!%%!?%!%%!%%!?%!%%?%%!%!%%%%%%%?%%%%!%?%%?%%!!!!%!%?!%!%%%?!!!%?%!?!!!?%%!?%%?%%!!%!%!%??%%%!%%?%!%?%??%?!%!%!!?%?!!!!!!?!%%!?%%%!!%!%!%!%%%%%?%!%!!%!%?%%!%!%%%%!%!%?!!%??!!!%%%%!!!!%%?!?!%%!%!!!%!%%%!%%%?%!??%%%%%?%%?%%%%!%?%%!!%%!%%!%?%%%%%!!!%?%!%!!!%?%!%%%%!?%%?!?!%?!%!!%%!%!!%%%%????%??%%!?%%%%%!%%%%%%?!%%%%!!?%?%!!!%%?%%%???%%!!%%%?!!!%%!!!!!%%?!%%!!%!?%!!!%??%!!?!%!?!?!!?!%!%!%%%%!%!%%%%!?%?%%!!%%%%%!%%%%%?!!!%%%!!%!%%!%!%!??%!!%%%%!%%%!%?!%!%?!%?!!!!?!%!?!?!?%%?!%?!%!!%!%%%%!%%!?%%!!%%%%!%%%%%%!%%%???!!%%!%%?%!!%!%?%%?!!!%%%!?%%%%%%?%%!%%%%!%!!%!%%?!!%!?!!%%%!!!?!!!%?%%!!%?!?%!%?%?!%%?%%%%?%%!???%!%!%%!!%%!%%!%!!%?%!?!%%%%%%%%!%%!?%!!%%??!?%%!?%!!!%%?%%%!!??%!%?%?%%!%%%%%!%?%!!%%%!!!?%%!!%%%?%!%%?!%!?!%!!!!?%!%!!!!!%?%%%!%%%!%%!!%%%%!%?!!%!?!%%?%?!%%%%!%%!!%%?%?%?!!%%??%%%!%%%??!%!?!%!%%?!?!?%%!!%%%%%??%!??%%%!%%%!%%%?%%?%%?%%%%!%!%%%!?%!!%%%%!?!!?%%!%%%%%%!!?%?%!!!%!%%!%?!%%!%%!?%%!?!%!!%?%!!?%?!!!?%?!%!%!!!?%%%%??%%!!%!%?%%%!%%?%!%%%!%%%%!!!%%%%%!%%?%%!?%%%!%%%%??%%%!%?!%%%%%?!%%!!%?!??%%%%%!%?%!%?%!!?%!%?!??!!!!!%!!%!%%?%%%%%?!%%!%!%!?!!!%%%!%%%%!%?%!!!!!!?%?!%%%?%%?!!!!%%%!%!!!!%!%%!%%%%%!%?!!??%?!%?%%%%!%%%!?!???!%!%?%!%%%!?!?!?!%%%!%%?%!%!%!!?%!!?!%%!!%!%%%%%!?!!%!%%%?%!!%%%?%!?!%!%!%%%%!?%!!!!!%!%!?!?%!!!%!??!!%%!!%!?%%%!%%!%!%%!%??%!?%%%!%!%%%!%!%%%%!%!!%!%??!%%%%!?%%?!!%%%%!!!!!?%%!%!!!%%%??%%%!%%%%%?%%%?%%%%%?!?%%%!%%%!%?!%!!%!%%%%%!%??%?%!%%?!%!!%!%!!%!!!!%%!%%%%!!?%?%?%!!?%%!%%%!%%!%%%!%?%%%%??!!?%?%%!%!!%%!%%%!%%%%%!%!!%!!!?%!?%%%!!!!%%!!%!%%%!?%%?%!!%%%%!!%?!!%%%%%?!%%?!?!%%%!!%!!%%%%?!%!?!%?%!%%%?%?!%?%!!!%%!!?%?!%!??%?!%!!%!?!%!?!%!?%!!!%%%%!?%!?!??!?%%%%?%!!!%%?%!%%?%%%%?!%!!%?%%%!!%!%%%!%%%%%%!%%%%!%%%%?%%!%%%%%!%%%%%%!?%!%%%%%?!%%%%!%%!!?%%%%%!%%%%!!%%?%%!!%%%!%!!%!!!%%%!%%!%%%!!?!?%?%!?!!%%!%!%%!!%%%!%!!%%%!%!!??%%!!%%?%?%!%%?!%%!?%%%!%?%%%%%%%???!!%?%%!%%%?%%!%%%!!%!%!!!%%%?!!%%%%?!%%%%%!?%%!?!%!!!%%%?%?%??!%%%!!!?%!?%%%!%???%!!%!!%%!%%%%?!%%!%%%!!%!?!%%%!!%%%%%%%%!%%!!%!!!!%%!%!?%%%!%%???!%!%???%%?!!%!?%!%%!%%??!!!!%!%?!%!%%!?%%!%%%%%%%!!!?!!%%!!!%%%??%%?!%%!%%%!!?!?%?!%%%%!?!!?%%%%!%!%%%!!%%%%%%%%%%%%!%%!%%%%%%%%%%%%%%!%%!%%%!%%%!%!?%!!?%!?%%%!!%!%!%!!!%%?%!%!?!!?%%!?!??!!%%!%%!!%?!%!!%%%%%!%!%%?%%!%!!?!!?%?%!!?!%%%%%%%%%%%%%!%!?%%%%!!!%%!!%!?%!?%%%%%!%?!%??%%!?%%%!%%?%%%!!?%!%%!!!%!!??%%!!%!%%?%%%%%!?!??%?%!?%?%!%%?%!!%%%%?%%%!!!%?%%%?%!?!%?%%%!!!!!%%%%?!%??!!!!%%!%?%?!!%!%%%?%%??%!!!%%!?%%%%%%?!%%!!?%!!?%!?!%%%%%%!!!!!?%!!?%%%?%??%%?!%%?!%%?%%%%!!!!!%%%!!%%!%!!%!!?%%?!?!!%%!!?%%%!!!%!%!!%??!%?%%%!!!!!?%!%!?%?%%%!%%%%!!!!%!%?%?%%%!%?%%%!%?!%?%%%%%!!?!?%%%?%%%!!%!%!%%%%%%%!?!%%!?!?%!%%%%%!%!%!!%?!!?%?%%%!%?%%!!%%?%!%%%%%%%!%?%%?!%!?!?!!!%%?%!!!!?%%?%%?!!!?%%%?!!?%%!%!%%!!%!%%!%!%!%!?%?%%!%!!%%!%%%!!%%%?%!%%!%!!%!%?!%!%?%%%%!%%!%%!!!%!!??%%%%!%!!!!%%%?!%%!%%%!!?!%!%?!%!%!!%!?%%%!%?%%%?%%%!?!!%%%!%!!!!%!!%%!%%!%%!!%%%?!%%%%%%?%?!?%!!%?!?%?!!!!!?%!%%!!%!%?!?%%%%??%%%!%!?%%%!!?!!!%%%%?%%%??%!%%?!!%?%%?!%%!??%!?!!?!!!!!%%!%%!!%!%%!%!%%!!!%%%%!%!???%%!%!%!!!%%%%!?!!%%!%%!?%!%%%!%%%?%???%%???%%!%!??!!!%!%?!!%%%%!%%!%%%%!%!!?%%!%%%!!!?%?%%!?%%%%%%?%!?%%!%%%%!%?%%?!%%?%%!%!%!?!%%%%!%?%!!!?!!??%%%!%!!%%!%%!!?%!%%%???!%%%%!!%!%%%!!%?%!%%??%%?%%%!%%%%%!!!%%%!!%!?%!%%%!%%?!%!%??%%?%?%!?!?%!%%%!%%%?%!?!?!!%%!!?%%!%%!%?%?%%!%??!%%%%%!%?!%%%%!?!!%%%?!%??%?!%%%?%!!!%%%%%?!?%%%%%%?%!%!!%!?!!%%!%%!%!!%%?!%%??!%!!!%?%!!%%?%!!%%%!!%?%?!!?%%%?%%%%!!!!?%%!?%%!%?%?%??%!%%?%!%?%%?!%!%!%%%!??!!%%%%!!%%%?%!%%!%%%?!%!%%%!%?%?!!%?!%%?!?!%!%!!%?%%%%%%%?!?!%?!%!!%!!%%!%%%%%!%!%!%%!?!%!%%%%!?!!%!?%?%???%?%%%%!!%?!!?%!%%%%%%!%%%%!!%!%!%%%!%%%%??%?%!!%!%%!?!%!!!%!!!?%%%%%%?!%!??%%%%?%!!%!!!%!!?%%%%?%!%!%?%!?%!%!%!!??!?%?%!%%!?%?!!!%!!!!%!!?%!%!%%%!!!?!%!%?%?%%%?!!??!%!!?%%%%!?%!!%?!%%%%!%!%%%!%!%%!!%%%%%%%%%%%%!%%%%?!!!?!%?!%%!??%%%%%%%%%%!!!%!?!%%%?%%%%%%%!?%!%%%%?!%!?!%!%%%?%%?!?!%%!%?!?!?%!%%?!%!!?%?!!%%!!%!?%%!%!!!%?%%?%?!%%%%%%!%!?%%%?!%?%%%?%!?%!??%%!%%?!!%%%!!%%%%%!%!!%!?!%%%%%%%%??!%!?!%?!??!%%!!!%!%%!%%!?%!?!?%%%%!!?!%%%%%!%?!!!%%%%!%!%%%!%!!%!%!!?%?%%?%%!%%!!%!%%!%%!?%?%%???%!!%%%%!?!%%%%!!%%%?%%?%%%%%%%%!?%%?%!??%!!!???%!%!!%%%%%%%!?%%%!%!!!!!%%!%%%%!%%??%%!%!!!%%!?%%%%%%!?%?%%%!?!%!%!%!!%%%%!!!!!!!!?%!%?!!%%!%!%!%!!%%%!%%?%%%%%%%?!!%!%%%??%!%?%!?!!!%?%?%%!%!!%%?%%!!%%!%?%%%!%%?!%!%%%?!!!!!!%!%!%%!!%%?%%!?%!%%!!%?!%%%%%%%%!%!%%!%??!!%%!%%%!%%%?%%!%!!%!!!%!%%!%?!?%%%?%!%%%%%%??!?%%!?!!%!%?%%%!!!!%!!?%%%!!%%!?!%?!?%%%%!!?!!!%?%%!!!%!!!!%%!%!!%%?%%!!%%?%??%?%!%!!%%%?!?!%%%%%?!%?!!!!!%%!!!?%%%!!?%%%%!%%!!!%%%!!!%!%%%%%?%!?%?!?%%%%!%%%!%!?%%!?%%!!??%!%!?%?!!!%%%?!!%!%%%%%?%%%?%?%!!%%%%%?%%!%%!%!%!%?%%??!!%?!%%!%!!%!!%!%!??%%!%!?%??%!!%%%??%?!!%!?!!!%%%%%!%??%%!%!%?!!%%%?%%?%%?%%%%!??!???%!??!%!%%%??!!%!%%!%%%%%%!%%!!%?%!!!%%!?!%%!!!!%?%%!%%%!%%%!!?!%!%!%%%%%!%?%?!%!?!%%%%%%%!%?%!!!!!%!!%%!%%?%%%%!%%%!%%%%!%!%?%!!!!!%!%%??!?%%!%%!!!%?%%%%%??%!%!%%%%%%%%?!%???%%?!?!!%!?!%%!%!!?%%!!!??%?!!%?%!!%?%!%%%%%%%?!?%?%??%!%!%!?!%?%%%!%!%!%!%!?%%%??!!!?!!!%?%%!?!!%%!!?%!!%!%%%!!!!%%!??%%!%%!%!!%?!!!%!?!%%%?!!%?%%%!!%?%!%%?%%!%?%?!%!%!!%??%%%%%%%?!%!%!!?%!?%!%%!!%%?%%%?!!%?%!?%%?%%%%%%?!%%?!%!!!%%%!%%!!%?!%%!%!%%%!?!%!%%%%!%!%!?!!%%!%%?!?%!!%!%??%?%?%?!!!?%!%%!%%?%%%%%!%%%%?%!!%%!%%!!!?%%!%!%??%%%!?%!%%%!!%!???%%!!?!%!??!!!?%!!%%%!?!%?!!!!%!!%!%!%%%!%%%%%!%%%%!?%%?!%!!??%%%?%!%%!!!!%!%%%?!!%%%!!!!!%?%!%%!%%?%!%!%?%!%%%!%%!%%%!%!!%!?%%%?%!%%%%%%?%%%%?%?%%%%?%%%%%?!!!!%!!%??%%!!!!%%!!%!%!!?!%%!!!!!%%!!!%!%!!!%%!%!?%%?%!%%!%%!!!%!%?%!??%!%%%%%??%%%%%%%%%!%!!%%?%%!%!%%%%%%!%?%%!%!%%%%%!!!%?%?!??%?%!!%%%!?!%%%!?%%?%%!!?%??%?%%!%?%%%%!%!!%!%!%%%%%%%!%%??%!%?!%!%%?!%%!%%%%%?!%%!?%?%?!%!!???!?%!!%%!!%?!%%!!?%!?%!%%!%%%%?%!%%%!%%%!%%%%%%%!!!%%!%?%!%?!%%?%!%!!!!%!??%%!!%!%?!!!?!%!%!%!%?%%%%!!%!%%!%%%%!?!%!%???!%?!!!?!!%%?!??%%?%?%!%%!%%%%%%%%?%%%!%%%%%!%%%!?%%%%!%%??%??!!!%!%?%%%%??!!%%%%!%???%!%%!%%!%%%%!%%%%%!!?%%!?%?!%%!%%!!%%??%%?!!??!%!%??%%%%!!%?%%%!!!??%%!%%%!%?!%!!?!%%%%!%?%%!?%%!%%!%?%!%!%!%!%!!?%!%!?%??!%%%!!%?%?%!!!!%!??%!%%?!%%!%%%!%%!!%%%!%?%!!!!%%%%%%%?%?%%!%!?!!%!?!?%?%%?%!%%%%%!??!%%%%!!!%?%??%??%!!!%%!!%!!!!?!%%%?%!!?%?%?!%%%!?!%?%%%%?%!!%%%%%%?!!?%???!%%?!!%%%%!!!?%%?!??!%%%%!%????%!?!%%%!?%?!!?!%?%!%!%!!%!%%!%%%!?!!%%%%!!%??%%!!?!%%???!%??!?!%%?!?!%?%%%%%!??%!!!%?%%%%%%%%???!??!%%%%!?%%!!!!%?%???%!!%%%%%%!!%%!%!!?%%!%!!?%%?%!!%!%!!%!%%%%!???%%%%?%?!%%%%!!?%!!???%%!!%?%%%!%%%%%%!!!%!%!!?!!!?!!%%??!!!%!!%!%%%?%?!!%!%%%??%%%!??%%?%%!!%%%%!%!%!!!%?!%%!?%%%!%%%%%!!!%?!%%%%%!?!%??!%!!%%%?%%%?%!!%%!%%!%!!!%!%!%!%!!%%%?!!%!!??%%!!???!%!!%%!%!%!!%%!!!?%!?%!%!%?!?%%!!%?!%%%!%!%%%!%%?!%%%!!!%%!?%%%?!%!!%%!?%!!%!?!!!%%%%%%!!!%!!!!?%!!%%!?!%%!%%%%%%%?!%?!%!!%%%%!!%%!?!%!%?%%?!%!%!?!%%%%%!%!%%!%!!%%!%%?%??%%!%!%%%!!!%?%%??%!!%%?%%%!%?%%%?%%!!!??%!%%?%!!%!?!%?%%!%%?!%%%!!!%!%%?!%%!%%%!?%%!%%!%%!!!!%%!%!!%%!%!?%%!!%%?!%%%?!%!!%!%?%!??%?!!!?%!!%%?%!%?%%%!%%%?!!?%%?!??%%!!?!!%?%%%%?!!?%!?%%%%%%?%!%!!%?%!%?%!?!!%?!%!!!%%%!?!%%?!!%%?!!!%?!!?!%!%!%%!!%!?%?%%%%!%%%%!!%!?%%%!%%%%!%%??%%%?!%?!%%%?!%%%?%%%?%%%%%%?!!%%%!!??%%%!!!!%%%%!!!!??%%!%%%%!%%%%%!%%!%%!?%%!!%?%%%%%%%%!%?%%!%%?%%!%!%%%!%%%%?%%%%%%%%%%%!!!%%!%?!%%!%??%?!!!%!%?%!%%!%!%%!?!!!!!%%%%%?%?%%%%%!!%!%!%?%%%!!%!%%%!%!%!%!?!%%!%!%!%!?%!%!%!!%?%!!%%%!%%%!!!%%%%%!%%%!?!!?%?%%!%%!%%%%%%%!%?%!?%%!!!!%%%%%%%?%!%%?!!?!!%%??%??%?%%%%!!?!%%%%?!%%%%?!!%?%%%%?%%!%%?!%%%%??!?%?%!%%!!!??!!!?%!%!%%%?%%%!%%!%!%!%%%%%%%?%%!!%%%%!!!%%!!%%!?%!%%%??!%%%%%!%!?!%%!??!%?!!%!%!?%?%%!%%%?%!!%%%%%%!%!!%?!%!!%!!!!%%%?%?!%%%?!%?!!%%%!!?%!!?%%%%?!%?%%%!%!%!%%%%!??!!!%%%%!%!!!?%%%%!%!!%!?%?!!!%%%?!%?%?%%?%!%??%%!%%!%%%%%!!?!%!!%%%?%!!!%!!!!%!%%%!%%%%%%!%%%!?%%%!%??%?%%%%%%%!%!!%?%%%%?!%!%%%!%?!!%%%?!!!!%!!%%%!?!%%!!?%!%??%!!!!!?%!%%%%%%??%%%%%?%%%%?%!!!???%!???!!%%!%%!%%?%%?%?!?!?%!!!%!%%%%!?!??%%%%?%%!?!??%!!%?%!%!!!%%%%%%%%%!?!?!!%?%%%?%!%!%!%%!!%%???%%???!!%!%!!%%%?%!%!!!%%!!!%%!!?%%%?%%%!?!%!!%?%%?%?%!??%%%!%%%?%?!%%%?!?!%!%%!%!!%%%%!!!!?!!%%!%%!%?!%!?%!%!%%!%!%!!!??%!!%!!%%%?!!!?!!%%!?%!!%!%%!?%%????!?!????!%%%%!!!%%%%%%?%?%%%?%!%?%!%!?!%!%!!!???!%%%!!!%!%!?%?!%!%!!?!!%?%!!%%%%!?%%?%%%%%%!%?!!%!%?%?!%?%%?!!??!%%!%?!?%!%%%%?%?!%!!%%!%%!%%!!%%!!!%%%???%!!%%%?!?%%%%!?%!%%%?!!?!!!%%!?%!%!%!?%%!!!%%!?%%??%!%??%%%?!!!%!!!%!%%!??!%%%!!!%!%%?%%!!!!!%!!%!%!!%%!%%%%%%!%!!!?%!%%!!%!!!!%!%!%!!%%!%!%!!%%%?%%??%!%!!%%%!%!!!!%!?!%!!??!!%?!!!!%%%%?!?%!?!?%%!%!%?%%?!?!!!%%%!%!%%%%%!%!?!!%%!!!%%?%%%%%%%%!!%!?!%?%%%!%%!%%%%%%!%!!%?!!!%%%!?!!%%%%!%?%!??!%!!%?!%%?%!%!%%%%%%%!!!?%!%?%!!!%!%?%!%%!%!%!??%%%%!!%!!%%!!!%!%???!%!%%%?%?!!!!!?%?!!%%!?%%%%%?!!!%?%%%%?%%?%%%%?!%%%%%%!!!%%%%?%!!%%%%!%!%!%%?%?%%%%!%?%%!!!!!%!%%%%!%%%%?%%%!?%%!%?!!%%!!%%!!!!%%%?%%!%%!%%!!%%%!%?!%?%?%!%%!%!%%%!!?!%%?%?%%!%%%%%?%%%%?%%%%%!%!%?%%%%%%%?%!!!?%!!%%!%?%!%!!!%%?!%%!%!!?%%%%%%%%!!?%%%!!%!!?!%!%%%?!%%%%?!%!!?%!?!%%?%%?!!?!!%%!!%!%!%%?%%?%%!?!%!%%!%%!%?%!%?%%!!!%%%!!?%%%???!%%%%!?%!%!?!?%%%%!!!%!%!!%%%%%!?%!%%%!!%!%%!%%%%!!!?%%%!%!%!%%?%!%?%!??!!!%!%!!?%%%%!%!%%??%%%!??%!!!!%%%%%%!!!%?!%?!??%%!%%%%%%%!%%!%!%%%%?%%%%???%%!??%!%%!%%%%%%!%%%%?%??!%!!!%?%?!!?%!??%%%?%%%%!!%??!%%??%%?%%%%!!?!!%??%%%?!!?!%?!?%?!!!%!!%%%?%?!%%?%?%!!%%?!%%!!%?!!%%!!!!%%!!!%%!%%!!%%!?%!%!!!?%!%??!??%%!!%%?%%%%!!!!%%?%?%!!!%!!%%!!%!%!%!%%%%%!%%??!%%%!?!%!!%!?%%%!?%%!%%%%%!%?%!%%%%!%?!!!%?!%!!!%%??%%%%%?%%!!%%!%%%%%%%!%!%!%!%???%!%!??%!%!%%!%%%!!?!%!!%%%!!%!%!???!%!%!%!?!%%!?%!!%%?%!%?!?%?%!%?!?%!%%%?%!!%%%!!!%%%!%%%%?%%!!%?!%%!?!%%%?%%!!!%!!!%!?!!%%%%%!%%%%%!%?!%??%?%%!??%?!?!%!%!?!?%%%%%%%%%%!?%%!%%%%%%%%?%%%?%%%%%?!?%!%!!%%%%!%!%?!%!%%%??%!!%!%%%??!?%!!%?%%?!%!%!%%!?%%%%%?%?%?%!!?%?%%%!%!!%!%!%%!?%!!!%%%!!!%%!??%!!%%!?%%?%%!!?%%!%%%%!?%%?!!%??!%%%%%?!??%!%%!%!?!%%??!?%%%??%%!?%%?!%!%!%!%%!%!!?%!%?%!!%???%%!!!%%%%%!!%!%!%%%!%%!%!?!%!!!%!?!?%?%?!%!!?!!%?!!!%%??%%!%%!!!!??%%%%!?%?%%%?%!%%!!!%%?!!!%%%??%%%!%%%%!!!%%?%%?!!!%%?%?%%%?%!!%?%!%%?%%!!%?%%?%%%%?%??%%%?!%%!%!?!%%?!%!%%!%%%!%%!%!?%!??%%%?!%%%%!!?%!%!!%?!!%%%!%!!%%%!%!?!!%%!%%?%%%%!?!%!!!%!!!??!!!%%%?!%%!!!!!%%!?!!%%!!%%!%?!!%!%?!!%%%%%!%?!%!!??%%!%%%!?%!%%!%%!%%%%!%%!!%%?%%?%!!!%%!?%!%%%%%%!%!?!?%%%%%%%?%!!%%?%?%?%!%%!%??%%?!%?!?%%?!%!??!!%!!?!%!!!!%?!%%?%!%%%?!!%?!!%?!?%!%!!!?!?%!????%%?!!!%%%!!%?!%%%!?!%?!!!!!?!%%%?%!?!%%%%%!!!?%%!!%!%%%!!!?%?!%%%%!%%?%!%%!!%??!!?%!?!?!%!!?%%%%?!!%%%%%!%!???%%!%!%!?%?!!%?!%%%?%!%!!%%%%?!%!?!%%%!!!?%?%?%?%!!%!%%!%%%%%?!!%?!?%!%%!??%%!!%%%%?!!!!!!??%%%%!%!%%%!%!%%?%!%%%?!%%%?!!%?!?%?!!!!!%!%!!%%%%%?%%%!%!!?%%!?!!%!!%?%%%???%%!%!%%!%%!!!!?%%%%%%%%!?%!%!!%%%!%%!%!?%%%?%!!%%?%%%%%!?%%!?%?%!!!!%%!!!!?%!!!!%%%!%%%%!%%!!%!!!%!%%!%%%!%!%%%?%%!!%!!%!!!?!%%%%!%??%?!%%%%%%%%!%!%%?%%!?%%!?%!%!!%%?%%%%%%!%%!%!%!!!!%!?!!?!%!!?%!!%?%%!%??%%?!%%%?%%!%!%%%?%!?!%%%!%!!%%!!%%%%!?%%%!?%%!!!%!!!%%%%%!!%%?!?%!%!!%!?!?%%!!!!%%%%%%%%!%!%%!!!???!!%%?%%%%!!??!%%!%!%%%!!%?%%!?%%%!!!!%!!!!??%!!!%!%?%?!!!%%%?!%%!%!!?!%%?%?%!%??%%%!!%%!?%%%%!!%!%%%!%!!!%!%?!??%%%?%%?%%?%??%!!!!%!%%%!!%!%!!?!!%!!!%%%%%%??%!%%?!%?!%%%%?%%%%!?%%!!%!%%!%%!!%!%?!%%%%?%!!!?!%!?%%%%!!!%%%%!!!%!?!!!!!%%%%%%%!%%!%!????!%?%%%%%%!%%%??!!%%???!%!!%?%?%%%!!%?%!?%%%%!%!%!???!%%!!!%%!%%%%%%?%!%!!!??!!%!%!!?!!!!%%%?%!%%!%%!%%!%%%?%%!?%%!%?%!!%!%%?%!!%%%!%!%%!?!!%%%?%%!%%%?!%%%?%%!%%%%!!!!!?%!!%!%!%?%%!!!%%%%!%%%%!%%%%!%!?!%%?%!%!%%!%%!?!%%??%%%%?!!???!?%!!%%%%%%%!%%%!%!!?!%%%?%%%%%%!%!%!%%%?!%!%%%%%%!%!!?!%%%?!!?!?%!?%%?!?%%?!%%!%!!%!!%?!%%%!%%!??%!!%%%!%%%%%?%!!%!!%%!!%%%%!%%%!%!%!?!!???%!?!!%%?%%?%%!%!%%!!%!%?%?!%!%%%??%%%!%%!%%%%?%!%%?%??!??%%!?!%!?!%%!!!%!?%?%?!%%%%%%%!?!!?!%%%!%!!!%!?!%!!%%!%!%!?!%?!%%!%%%?!!%%!!!??%%%%%%%?%??%!%%%?!?!!!?!?%%!%%%!!%?%!%%!?!%!!!%%!%%?!!%!%?%%!!!%?%!%!?%!%?%%%%!!%%??!?%!!!%!%%?%!!!%%?%!!%!?!%%!!%%??!%!%%%%!%?%!%!%?%!!!%!%!!!%!!!%?%?%!%%!?%!!?%!%?%!!%!%%?%%%%?%%?!!??%%!!%?!%%!!?%%?%!%%!%%%!!%%%%!%%!%!!%!%%%%%!?%%%%%!%?%%%!!%%!!?!!?!%%%%!%%%!%!%!%%?!%%%%!!??%!%%!!%%!%!!?%!!%!!!!%!%!!%!!%?!%%%%%!%%?%%?!?!%%%%%!!%!?%%?!%%!!%%%!!!!?!%?!%%%!?%%?!%%?%?%%!%%%!!!?%%%%!!!?%%!%%!!%?!!!!!!?%!%?!%%?%%!%?%!?%?!%!?!%%!%?%%%%%%%!%%%!%!%%%%%%!%!%%%!!?%%!%%!%%?!%%%%?!%!%%%%%%?!%%%%%!!?!%%%%!%%%%!%%!?%!!!%!%%%%?%?%!%?!?!%?%%%!!%%%!!%!!!%??%%%!?%%!???!!!!!%%??%?%?%?%??!%!%%%%!%%%%%%?%!!%%%%%!%%!%!!%%!%%!%%%?%%%??%%!?!%!%%!!%%!!%%!%!?!%!%!!?!!??%%!%!!!!%%?%!%?%!!%!%!%?%!!!%%%?!%?%!%?%?%?%!?!?%?!%!?!%!!?!%%%!!%!?!!?%%?%%%%%!?%?%%%!%%!!!%%??%!%%%!%%%%!?%!%%??%?%%!%?%%%%%%%!??%%!%!%!%%%!%%%%?!!%!%?!%%?%%%?!%%?!%%!%%%!%%!?%?!!!%!?!%%!%!!?%!%%!%?!%??%!!%%%%%!%!%%!??%%!??%?%%?!?%!%%%%?%?!%!%%%?%%!%!!%%%!%!%!%%%?%%%%!!%%!!%!!!!?!%%!%%?%%%??%%%!?%??!%!?!!%%%!?%?%%!!%!%%!%%%!%%!!?%?%%!%?%!%%!?!!%%?%?%!%%!%!!?!!%!!!!?%%%!!%%!%?!!!%!%!!!%%?%?%%%!!%!%%%%!%%!!%!!?!%%%?!!!!?%%%%%%%!%%%%%%%!%%??%!%%%?!%!!%?%%!?%%%!%!%%%%!%!!%!!%%%%%%!%%%%%%?%!!?%%%%!!??!!?%%%%!%!???%?!!%!?%%%!??%!%%%%%%?!%%?%%?%?%%%!%%!!%%!?!!!!%%%!!%%%!%%?%%%?%%%%?!%%%%%%!!!!!%%??%!!%!%%%!!%!!!%%?%!%%%%!?%%%!?!!%%!%!?%!%!%!!?!%%!!!!%??!%?!!%?!%%%%%%%!%??!%%%%%%!%%%%?%%!%%!%%!?%%?%!??%?%!!!%%!%!?!%%??!?%%?!%!!%%%%?%%!?%%%!%!??%%%%%%?!%%%!!!!?!%!!%?%?%%%!!??%%%?!%?!?%!%%!??!!?%!?!?!?!!%%%!!%%?%!!?%!%%!!!!%%?%%%?%%!%!!!%!%%%!!%!?!?%???%?%%%%%%!!%?%!?%!?!!%!!%%%!%!?!%%!%%%%%%%??%%!?!!%%?!%%!%%!!%%!?%%%!!%%!%%!%?!%?%?!!%%!!??%%%%%%%%%!?%!?%%%?!!?%%%!%%!%%%%%%?%%%!??%?!%%!?!%!%!%?!%%%!!%%%?!!%%%?%!%??%%!?!%?!?%!??%%!!!?!?!%?%%%?!%%?!%%!?!??!%?%%!%%!%%!%%%?!%?%!?%%?!%%%%!?%!%%!%%!??!?%!%!?!!%!??%%!%!%%!!!!?!%%%%%!?%%?%!%%%%!%%%!!!??%%!!!?!%!!!%!?!%??!!%!!!?!!!%%%%%%!%?!!%?%!!%%!%!%%??%%?!%!%!%%!%%!%%!!%!!?!?%!%!%%%%%%%%!?!%%%%%%!%%!?%%%%%%!??%%!%!?%???%?%!%?%%?%%?!%%%?%%!!!!?!%%%?!%%%%%??!!%%%!%%!%?!??%%%?%%?!!!!%!?%!?!?%%!??%%?!?!?%?!!!%%!?!?%?%%%!%%?!??!?%!%%%!!%%?%!%%!%!!%?%!%?%%!!%!%%%%%!?!!%!!%!?%%%%%!%%!!%%%%%!!?%%%%%?%%!?%?%!%%!%%?!%?!%%%!%!%%%!!%?%!?!?!%!??!!?%%!!!!%%%%?%!!%??%?%!%!?%%%?%%%?%?%%!%!!??%!!%%%%!%%%%%%%%!!!%%%%%!?%!?!?%!%%!%?%%%!%%%%?%%??%%!!%!!!%!%!!%!%%%%%%%!%?!!?%??!%%?%%?%?%?%!!%%%%!?!%?!%!%%!%%!!%%%!%!?!!?%%%%!%%!!%?!%%?!!%%?%%!!%!%%!%!%%!!%%!!%?!%!%%%?%?%%%!!!!!%!%%!!!!!!%!??%%!%!%%%!%!%!?%%?!!%?!!??%%?%%%%!%!?!%%%%%!%%%!%%?%!?!%%%!%!%?!?!!!%!%!!%?%%%%?!%%!?%?!!!%!%!%?%%?%!%%!!%!!%?!!!!%%%!%!!?!?!!%??%%!!??%!!%?%!%!?%%%!%%%%%!%%%!!%?!%%!!?%%%%%??%%!?%!!!!!%?%%!%!!!%!?%%!??%%%!%?%%!%?%?!%%?!?%!%%!?%?!!!%%%!?!!%%%%!!%%!%!!%%!%%%%!%?!!!%%%!!?%!!!!%%!%!%?%%%!%!!%!?%%!?%!!!!%%?%?%%%%%%%%%%%%!%%!!%%?!!%%%%!!%%!!!?%%?!??!%!!!%%?!%?!???!?%%?%??!%?!%!%%%%!%??%%%!%%?%!?%%%%!!!%?%%!%!!%!%?%%%!%%?%%!!%!?!%!%!%%?!%?%%!!!!%!!!!%%%?%%%!%%%!%%!%?!!%!%!%%?%%!!%%%!%%%?%?!!!!!%?!?%%!??%!%%?%%?%?!!%%%!%!%!%!?%!!%!!%%%%%??!!!%!!!%%?!!??%%%%!!?%%%?!?!!!%?!%!%%%?%?%%%!%%!%%%%%?!!!?!!%?!%!?!!%%!!%!!%%!!%%!%!?%%%%%!!?!%%%!!%!%%%!%%%%%!!%!!?%??%%%!%%%%!%!!?%!!%!!%%?%%%?!%!%%!%%%%!!%%%%%%%%%%!?!?!!%!!%%%?%%%%%!!!!!%!!!!%%%?!!%?%!%%%!%%%??!?!%%??%%%%?%!?%?%?!!%%%%!!??!?!!%%%!%!%%%?!!!?!%%!!%?%!%%%???!%%!%%??!!??!%??%%%!%!!%%!%!!!?%%???!!!?%%%!%%!!!!??%!%!!%!%%%!?%!%?%!?!%%%%??%%%%!!%?%!%!!%!%!!!%%%%!%%%%?!%%!%!%!%%?%?%?%?%!?!!!!%%?!?%?!%%%!%!!%%%%%!%%%%?!?!%%%%!!%!%%%!%!!!!!%!!%!%%%%??!%%%%%?%!%?%!%!%%!!%!?%!%!?%%%%%!%!%%!%!%%?%%?%%?!!%!?%%?%%!?%!%?%%!!!!!!%%!!%%!!!%!%!?!%!%??%%!!!%?%!%%%!%!?%%!!??%%%?!%?%!!?!!?%%?%%%??%?%%%%???%%%!!%!%!%%%%!!%%!!%!%?%?!?%%!!%%%?%%!??!!%?!!!!%!!!%%!?%%%%%!%!!%!???%%%!%!??%%%!?%?!%%!!%%!!%!%?%%%%!!%%%%%%%%!%?%%%!%%%%%!%%%!?%%!!%%%?!?%%!??!!!!%%%%?%%%!%%%%%%%%?%?!!%!%??%!!!%%!%!!%%%!%%%%??!?%%%!?%!?!?!!%!!%?%%%%%%%!%!?%?!%%!!?%%%?%?%!?%%%?!%!%%!%%%%%%?%%?%!!!%%!%!!%%!%!?!!!%%?%!!!??%!%%%!%%!%!?!%%!!?!%!?%%!!!?%%!%!%?!!!%%!%!%!!!%%?%%!!%%!%!!??%%%%!!!!%!!%?%%?%%!?%%?!%%%%%?%?!!%?%%%%%?%?%!!%?!?%%%?!!!%?%!!!%!!?%%!%%!!%%!%%?!!%%%%!!%!%?%%!%!!%%%!%%!?%!%%!?%%%%?!?%?%%%!!?!!!%!%%!%!!!%!%%%%?!?%%%%%%%!!%!!?%!%%%%%!%!%?%%%?!!%?!!!!?%%%!%!%%?!!!?%%!!%%%%!%%%?%%%?!%!%%!?!%%%!?%%!%%%%%%!!!!%!?%%!!%!%!!!%%%%%%%!%%!!?%!%%%%?!!%%%%!%!!!?!%!%!?%%!!!%%?%%!%?%%%%?!!%%!!%!!!!!%!!%%%%%%!!%!!??!%%!!%?%!%%%!?!!?%%!%%%%!!%%%!?%!!??!%!%?!%!%%%!!?%%%!%?%%%!%%%!%!!%!!%?%%%!?!%!%!%%!??%%??%%%!?!?!%%%!%%!%%?%!%%!%!?%?%?%??!!!%%%?!!!%%?!%?%!%!%?%?!%%%!!!!!!%%%!!%%%%%?%!?!!%!!%%%%%?%%%%%%!!?%??%%%%%%%!%!%!!%!%%!?!%%%?%%!!%?!%!%?!%%??!%%%!!%!%%%%!%%!%%%!%%?%%%!!!?!!!!!%??!%%%!?!%%!?%%%%!%%!!%?%%%??%%%%??!?%!?%%%!!%%%%!%!!%!!!%%!%?%%!??!%!%%!%?%!%%!!!%?!%%%%!?!%?!??%%?%%!%!!!??%%%%%%!%!%?%??%?!!%!%?%%!%%?!%?!%!%%?%%%%%?%!!%!%?!!%%?%%!?%?!%%!%%!%%!%!?%%!!?%!%!%?%%!%%%!%%!%?%!%%%%%%%%%%%%!!%%%!??!%%!%!!?!!!?%%%%%%%?%%!!%??%%%%!%???!!%%!!%%?%%%??%?!%%%%!%%%%%%%?%%!!%%?%?%?%%?!!%%!%!%!!!?!!!%!%%?%?%%!!!%?%!%!%%?!!!?!!!%%!!!!!?!!%%%%!%%?%!?!!%%%!!%?!%%%%!%%%?%?%!%!%?!?%!%??%?%!!!%%!?!!%?!%%%%!!%!%%%!!!!%??!%%!%%%!!!!%%!!%!%???!%%?!!!%%!!?!%%%!%!!%%%!?!%%!%%!%!!%!?%!%%%%%?%%!%%%!%%!!%!%%%?%%!!%!%?!%?%%?!!?!?!!%%%%!!%!?%!%!%!%!!%%?%%?%%??%!%?!%!%%!!!!%!??%%%!!!%!%%!!!!!!%!%%?%%?!?%%%!!%!!?!%!!%?%!!!!!%!%?%!%%?%%!%%%%?!%%%%!!?%?!%%!!%%%!?!%!%!!!!%!%%!!?%%%!!?!%%!%!%!%?%?%!%!%%%?!%!!%?!%%%%!!!%%!%%%?%!!!%%%?%%!!!!!%!%%%%%%?%!?%%%%!?!!%!!!!!???!%!!!%%%%%!%!?%%!!%?%!!%?!%%%!%!?!!%!%%?%%%%??!%?%!!?%!!?%%%%!%%!!!%%%%?%?%!%%!%%!%!!!?%%?!!!!?%%%%%!%?!!%!!!%!%%%!!%!!%%%%%%?!!%%!!!!??%%%%%%?%?!%?%?%?!%?!?!%%!%%?%%%%!?%%%%?%%%!%?!%!%%!!!?%!%%!%?!!%?%%!%%?!%!%%?%%%?%?%%?!?%?%%%!%%%!%!%!%%!%!%%!%?%%%%?!!?%%%!%%!%%!!%%!?%!%%?%%?%%%?%%%!%%!!!%!%???%?%!!?!%?!%%%%?!?%%!%%!%%%!!%!!%?%%!%!!%!?%?!!%%?%!%!%!?!?!%%%!!!?%!!%%!%%%%?!%%%%%?%?%!!!%??%%%!%!%%%%%%%?%!!?!!?%%?%!%%?%%?!?%%?!!!%!%!!%%!%!%!%%!!!%%???%!!%!%!!?%?%!%%%!%%%!%%%!!!!%??%??%?!%%%?%%%!!!%%!!!%?%%!!%!%!%?%%%%?%%!%!?%%%%%%!%!%!??%!%?%%!!%%%%!!?%?%%!%?%%?%!!%???%%!!%?%%?!!?!%%%%!%?!!%?%?%!%!%%!???!!%%!?%!%!%%!%!!!%!!%%%%%!%%?!??%%%?%!%?!!%!%!%%%?%!!!%?%%!!%?%%%%?%!?!!%%!!!!%%%!%!!%%%!%!!%%%??%%!%!%%%%%!!%%%!%?%?%?%?%%%%!!%%!!%%%%%!%!%%!%%!!!%!%%?%%!%%%%%?%?%%?%%!%%%%%!!%!?!?%%%%!????!%%%%%!%%%%%%%%%!%%!?%!!?%%!%%%%%%?%?!%%%%!%!%%!%!%%?%!?%!%?%%!%!%!%?%%%%!!!%%%%%%!!%?!%!!!?%%!%!?%%?!!?%?%!?%!?%!%!%!!%!?!?!%%!%%%%!??%?%?%%!!?%%!!%%!!%!%%%?%!%???!?%%!%?!!%???%?%!!%!%?!%!?!%?%!%?%!!%%%!!%?%!!?%!!!%%%!%!%?%?!%%%%?!%%?%%?!!??!?%?!%%?!?%!%%%!!%%%%%%!!%!%%%!%!%%!!!!!%?!%%?%%!?%!%?%?%%!!%?%%!?%%!?!%?!%%?%%??%!!!!%!%%%!%%!?%%!%!%%%%%%!?!%%!!??%?%?%%!!%%%%!%?!?%!!%%!?!!%%%%?%%??%%!%%%!!%!%%!?%%?!!%!%%%!%!!?%%!%!!!!%%%%%!%%%%??%!!%!%!%%%?!%%%!?!?%%!%%%%%?!??%%!?!!!!!!!%!%??%%?!!%%%!?%??!?%%%%!!?!%%%%!%!!!%?!!%%!?!%%%%!?%%!%%!%%!%%%!%?%!!%%!!%!%%%!%?%%!%??%!%%!%?%%%!!%%%!%!%!?%%%?!?!!%!%%%%%!!%%%%%%%?!%?%!!%%%%%?%????!%!%!!!%%!%!%%!?!!?%%%!%%%%%?!!?%!%%?%?%!?%!%%%%!%!!?%%!!%!%??%%???%!%?!%%%!?!!?!%!%!!!%%%!!!!!%%!%?!%%??%!?%%!!!??%!%%%%%!??%%!!!!%?%%%!%%?!??%%%!!!??%%%!%?%?%!%!%%!!!!?%!%%%%!%%%%!%%%%!!!!?!%!%%?!!?%%%!%%!%!!%!%%%%%%!!?!%?!!%%!%!!?%!%!%!!!!!%%!%%?%%%?!!?%%!%%!%%!%!%%!%%!%%%%?!?%%%!%!?%!!%!%!?%%!!%!%%%%!%%!!???%!%%%???%!%!?%%??%%!?!%%!!!%%%!%?%!!?%!!!%!%!%%%%?%%%!%%%%%%?%%?%!%%!?!?%?%?%!?!%%%%%!!!%!?%?!%%%%!%%!%?%%!%%%?!%!!%%%%%!?!!%??!%%?!%%?!%!!%?!?!%%%!%%!?%?%%%%%%!%!?%!?!!%!%%?%%%!%!%!%%?!%%?%!%%%%%?!%%!%%%!!%!%!!%?%%!!!%%%?%%!%%%!%%%!!%!!%%%%%%%%%!%%%%!%%!%?!%?!%!%%%%%!!%!?%%!%%%%%%%%!!%%!%%%??!?!!%%%%!!%!%!?%?%!!%?%!!?!!!%!%!%%!?%%!%%%?%%!?%!%%!%%!???!%!%?%!%?%!!!!?%%%!%%??!%??!!%!%!!%!%%!%%?%%%??!!???%%!?!%%%?!??%%!!?%?%!!!%%!%%!%!?!!?%%?!!?%!!?%!!%%!%%!!!!%%!!?%?%%!!%?%%?%!%%%%%%%%%?%%?!%%%%%%!%!!??%?%%%!%!!%!%%%!!%%%?%!%?!!%%!%?%%!!!%??%!!%!!!%%%%%!!!%%%%!??%?%!?!%?!?%!!??!%!%!!!!%!%%%!%!%!?%%!%!%%?%??%!!%?!!%%%!%%%?%!%%!%%!%!!%!%%%%!%!?!%%%%%%%%%!!%!%!%?%!%!%?!??!%!!!%%!%!!%!?!%%?!%%!%%!%!%?!?%?%?!%?!%!?%%%!?!?%%%%%?!!?!?%?%%??!%%?%%%%!!%!%!%!?%%!%!!%?%!!%?%!?!?%%%!!!%!?%!!%!%!!!%%!?%%???%!%!%%!%!?%%!!%%!%%?!%%%!%?%!!%%!?%%%%!?!!!!%?!!%!%%?%?%!%!%%?!?!%%!%!??!%!%?!%%!!%!%!?!!!!!?%!?%!!!!?!%!%!%%?%?!!!%%!??%%!!%??%!%!?%!!!!%??%!%%!!%%%?!%%%!%%%%%??%%!%%!%%%?!?%%?%!!%????!%%%%%%!%!!!%?%!?%!!!%!!!????%?!%%!?!!!!!?!%%?%?%!%!!%%%%!%!%?%?!%%%%!%!?!%!!!%!%!?!%%%%!?%%!%%!%%%!%%%!!!%!!?!!%%%!!%!%%%%!?!%%!!!!%!!%%!%%!%%%%%!!?%?%!%%%%%%?%?%!!%%%%%!?%%!?%!!?%%%?%!%?!!%%?%!%?!%%%!%%%?!!%%!?%!!%%%%%%%%%%!!?%!!!!%!!%!%%%!%!%!%?%!%!%!!!%%!%%%%%!!%?!%%!%?!!??!!?!!?!%%%%%%??!%%?%%%%%%%%%!??%%!%!%%?!%!!%!%??%%!%%?%%%%%%!!!%?!%%%%%%%%?%%!??%!%!?%!%?!%%%?%?%?%%!???%!%%!%%?%??%!!%%!??%!!?!?%!!!%!!?!!?%%!%%%?!%?!%???%!%%%!?%%!%%!?%!%!%!%!%!%%??!%?%!%!%!!%%%?!%%%!%!%!%%?!%%!!%!??%??%!!%%%%!??%!%?!%?!%%!%%!%?!%%!!!%?%%%%!!?!?%%%%!!%%!%!?!%!!!!!%%%!!!%%%!%??!?!!%%%?!!!%%%!%!%%?!?%!%!%?%!%%!?%?!?%%%%??%?%!?%!!!%?%%!%!!?!!!!%%!%?!%!%?%%!??%!???%!?!%%??%!%!?!?%%%%%!!!?!%%%%%!!??!%%!?%!%!%%!!!!%!?%%!!!?%%%!%!%%?%%?%!!%%!%%!!%%%!%!!!?%%!?%?%%!?%%%?%!%!!%!%!%%%!!%!%?%!!%!!!%!!%%%%%?%%?%??%!%!?%%%%?!!%!%?!!?%%!!?%%!%%%%!%%!?%%%?%%%!%?%?!%%!?%%%%%?!%%%%%%%!%%%%?!%%!!!?!?!%%!?%%%?%!!%!??!?%%!%%%%%%%%!!%!!??%!!!%!!%%!%???%%?%?!!?%!%!%%!%?%??!%!%??%%%%%!%?%!%!%!!%%?!%%%!%%%%%!!%%%%%!?%%%?%%%%!%%!%%!%%%???!?!%%%%!%%%!%%%?%%!%?!?%!!%!?%%!!!!!??!%!??%%%?%%%!%?%%!%%%?%%?%?!%%!!??%??!!%!%!!?!!%%!%%!%%!%%!?%%!%??%!!%%!%!!%%%?%!!%%??%!!!%!%?%!!!%%!?%%?%!%%%!!!%%%%?!!?!%?%%?%%!?!%?%%%!?%%%?%%?!%%!!!!?!%!%%!?%%%%!!%%%!!!!%%!%%%!!%!%!!!!%%%%%%%%%%!%!??%!?%!%%!?!%%!!??!!%%%%%%!!%?!%??%%%?%%%!!%!?!!%!!%%%%?%!!%%%?%%%?!%%%?!!%!??%%%%!%!%!%%%!!%?!%%%%%!?%!%%%?!!!??!%%%??%%?%??!%!!?%!%%%!!%%?%!%%%?%!!%!!%?%??%?!%??%!!!%%%%!%!%?%!%%%%%%!!?%%%%!!!%!%?%!!!!%?%%%%!%??!%!%!%?!!?%%!!%!!?%!%%%%!!%?%%!!!%!%%%?!?!%%%!%%!!?%!%!!!?!!!%%%%!?%%?!!!%!%%%%!!%!%%%!%!!?%!?!%!!!?!%!!!%%%%?!!?!%%%%!%%!%%%?!!!!%!%%%%%%?%%%??!%%?%!%%???%%!%?!!%%??!%!!??%!%%%%?%%!%!!%%%%?%%%!!%%%%!%!%%%%!!%!%!%??%??%%!%!?%%!!%!?%!!!%!%%%!%%%?%!%!?%!?%%!!%?!!%??%!%!??%%!%!!!%%!%!?%%%%!!%??!!%!%%!%!!%!%%%??!!%!%%!!?%??!%!?!?%!%?%%?%%!%%%%%!!%!!!%!?!%!%%!%%!%%!%%!??%%%!%!%!??%!?%%%%!??%!!!!!!%!!%!%!%!%%%%!!%%!%%%!%%%%%!%!%!?%!!!!?%%%?!?%!%!%?!?%!!!!%!!%?!!?!?%%%%!????%%?!!!%%%!%?%%??%!!?%?!%!%%%%%?!?!?%%%%%!%%%!!!%%%??!!%!?!?!%%%%%%%%%%!%?!??!!?%?!!?!!%!%!%%?!%%?%%%!!?!?!%%!!!?%%?%?!%%??%%!!!%%!%%%%?%%!!%%%%?!%!!%!!!%?%%%?%%%!!!%%%!!%!%?!!%!!!?%!!?%%?%!%!%!?%?!!%!!%%%%%%!%%?!!%%%!%?%!%%!%!%%%%?????%%%!?!?!!!%!%!!%!%?!!%!%%%?%?!!%%?%%%!?%!%%!%%%!!%!!%?!???%!?%%!?!!?%!!%?!%!%%%%%!?!!!!!!%!!!!!?!!!!%%?%%%!%!%?%%%%%!!!!%!%!%%!%!!!?%?!%?%!%%%!%%%!!%!%!%!%%!!%?%%%%?%%%%!%%!?!!%???!%%??!??%!!!%?%?%%%%%%!!%!%%%!?!%%!%%%!%%!%%??%%%%!%!!!%%%%!%%?%!!!%%%!%%%%%!%%%!??%%!%!?!%!!%!%!%?!?!%%!%%!!??%!%%!?%%!%!!!!%!%%%!%%%!!!%!%?%%?%%%!%?%%%??%%!?%%%%%%!%?%%%%!%%%?%%?!!%!%%%%%?%%%%%%%!%!!%%%%!%!??!%%?%?%%%%%%%%!%!%%%%!%%%%%%!!%%!%%%!%?%?!%!%!%!%%!%%%%%%%!!!%??!!!%%!%!?%!!?%%?!?%!%%%?!%??!!%%!?%%!%%%%!!%?!?%!!!%%?!!!%%%%%!!%%!%%%!?!?%%??%%%?%%?%??%!!!!%%!!%%?%%%!!?%%%%%!!%?%??!?%!%?%?!%!??!?%%%%!%%%!%?!%?%!%?!!!%%??!%%!!%%%!%%%%!%!%%?!?%?%%%%%%%!%?%%%!%%%!%%!%!%!%!%!!%?!%%?%%%?%??%???%!%?%%!%%!!%%%!!!??!?!%!?%%%??!!%!!%??%%%%%!!%!?%!%!%??!!%!!%!%!%!%%!%%?%%%!%%%!?%%!!!%%%%!!!%!%%!!?!!%%!%%?%?!!%%?!%%!%%%!%!!%??%%?!%!!!!%?!%%%%%%%!?!%?!?%%%%?!%!%%%%%%!%!?!%%%%!?%?%%%!?%!%%?%%%%%?%!%%!!%?%%%!!%?!%%%%%!%%?%!%%%%%?%!%%%!%!!%!!!?%%%?%%%?%%%?!%%!!?!%!?%!%?%%%?%!?%%%?%!!?%%?%%%!?!%%!%!%%!%??!%!%?%%!%!!%!?!!!%%!!!??%!%!!%%?%!%!??%?%?!%?!%%?%%%%%%%%!%%%%%!%!!?!?!%%!%???!%!%?!%!??%%!!?!%%!%%!!%%%%%?%%!?!%%%!!!%%!!!%%%!%!?%%%%!!%%!!%!!!%%%!!%%!%!%%!!!?%%%!%!!%%%%%?%!?%!%%!!!?%%%%!%%!??!!%!?%?!???%!?!?!%?%%!???%?!?!!%%%%!?%!?%?!?%%%%%%?!??!?%!!!!%%%??%!!%%!%%?%!%%%%!!!%%??%%!!%%%?%!?!!!%!%%%?%%%?%%??%!!!!%!%!!%%?!%!%%!%??%!%?%%%?%!!%?!%%%!%%!%%!?%??%!!%??!!%%!!!?!%%%%!!!!?%?!!%%%%?!!!%%!%?!?%%?%%%%%%!%%%%%?%%%?%%%!%!!???%!!%!?!!!%!%!%!?!%?!%%%!!!%%??!%?!?%%%?!?!?%!%!?%!?%!%!%!?!?!!!!!%?%%%!!?%!%?!?%%%%%!!!%?%%!%%%%!%!%!?!%!!%!%!!?%%%!%%%%%!!?%???%!?%!!%!%%%?%!%%?!%%!%?%%%%%%%!!!!%!%%%!%!%%!%?%%%%%??%!%!!!%!%!%%%?%%!!%%?%!!%%%%!!%?!!%?%?%!!%%!%!!%!%%!!%?!!%?!?%!%%%?%%?!%%??%?%%%!%%!%?%%%!%%%!!%%%!%%%!!!!%?!!?%%!!%!!%?!%!!!?!%%!%!???!!!%?%%%%?%?%!!!!%%%%!%%%?%%%%%?!!!?!?%%!%!%??!%%%!!%!%%!?%?!%%%!%%%??!%?%%!!%?%%!%!%!%%%!?!!???!%%%!!%%!%%!%%!%%%%?!%%%!%%!!?%?%!%%?%%!!%%%%%!!%!%!??!??%%%?%%%!%!%!%?%!%?%%!!?%?%?!!%?!%?!%!%%%?%!!!?%%%?%!%!?!%!%%!%%!%%!??%%?!!!%!!??!!!%%%%!!!%%?!!%?!!!!%?%?%?!%?%!%!???%!!!!%%%%%%%!!!%%!!!!%!%%?!?%%?%%%!%!%?%%%%%%%%%%!!%?!%?%%%?%!!%%?%?%%%!!??%%!!!?%%!%%!!?%%%%!%!%%%%%%!?%%?!%%%!%!!%?%!!%?%?%%%!%%!%?%%%%!%%!%%?!%!!%%%%%%!?%!%?!!%%%?!%!%%!%?%!???%%!?%%%%%%!%%%%%%%!%!!!%%%%!%%??%%!!!%%!!!%!?%%%!?%%%%%%%%!%!!?%%%!%!?%%%!!%!%!!%%!!??%?%!%?%?!!%!%!%!%%?%%%!!%%%%!%?%%%!%%%!%!%!!%!%?%?!%%%%!!?%%%%%!%!%%%?%?!!%%%%!%%!%%!%!!%!!%%%%%!!%!!%%!%%%?%?%??!!?%%!?!%??%?!%%!%%%%%!!%!?!%%?!?!!?%!!!%%!?%!%%!%%%%?%%%%!%%%%%%%%%!!!?!%!%?%%!%!!!%%%!%%!?%%!!%!!%%%%%%?%!%!%%!!%!!!!?!?%!%%%%!?!?%!?!?!%?!%%%%!!!?%!!%%!!%%!!!%???!%!!!!?!%!?%!?%!%!!!%%%%!%%!?%%!%?%!??%%!!!%?%%%%!!!!%!%%%!?!!!!%?!??%?%%!%%%?%%%!!%%%%%%!!!%!%!%%!!%%%%!?!%?!!!?!!%%%%!?!%%!%%!?!!%!%%!%%!!%!%!!!%%?%%%!%%%!!?!%%!!??%%?%!%%!!%!!??%??%!!!!!%!%!%!%!%%%%%?!?!%!%%%!?!%!%%!?!!%%%%!%%!%?%%%%!!%%%!%%!!%!?%!%%?!%!%!?!%!??!?!!!!!?%!!!!!%%?%?!%%%?%!!!%!%%?%?%!%%?%%%?!%!!!!%!!!%!!%!!%%?%%%%!!?%!%!!%%%%!???!%!%?!%%%%?%%%%!%!!%!!!%%%!%%?%!%!!%!!%!%?%%!?%!%!%!%?%!%!%%%%?!!%%%%%%%!!!%!?!!%%!%!!%!%%%!!!%!%?%%%%%%%%%?%%!%%!%?%%!%!%?!%?!%%%!%%%!!%!%!%?%?%%%!%!?!%%!!!%!!!%%!%%%?%%%?%?!%!%%?%!!%!%?%%?%!%%%!%%%!%!%!%!!!!!?%!%!?%!!!%%%%%%%%!!%%??%???!!%?!!?%?!%%%!!?%!?%%!!%%%%?%!!!%!!%%%%%%?%?!!%%!%%%!!?%%%%!!!%!%%%%%%!!!?!!%%%?%!!%%%?%?!%%!??%%%%%!!!%!%%!??!%%%!%%!%!%%!??!!%!%!?!%!?%%!!%!%%%!%%?%%%%%!%!%%%%!%%?%%%!!!?%!%?%??%?!%%%!!%?%%?!%%!!%!%%%!%!%%!%%%%%!!!%?!?%%%!!%%%%%%?%!?!!!%!%?%%%!%!!!!%%%??%?%%%%%%!%%???!%%%%%%%%!!?!%%%%!%?%!%!?%??%%!?!%!!%%!??!%!?%%%%%%!%!%%!!%!%!!%??%%%%%?!%%%?!%%%%%?!!??!?%%%!%%%%!%!?%!?%!%!%%?%!%%??!!%?%%!!?%%?!%?%!!!?%!%%?%%%%!%%!?%%%?%?!%%!%!!%!!!%%?%!%!??%?!!%%!!%%!!%!%!!%%!%!%%???%!%!%%?%?%!%!!?%%%%!%%!!!%!%%%!%!%%%!%?!%%%!%%%%%%%?!!!!%%%%!!%%!%!!%?%%!!%%!?%%!%%%%%%%%%%!%!%%!%%!?%!!!!?!%%?%%%?%%%!!%??!?!%%!%%!%!%!%!%%!?%?%!%?!!%%%%!!%??!!!!%%%!%%?%!%!!%!!!%!!%?!%!%?!%!?%!%!%?%%!!!%?!!!%%%!%!%!%%!%!!%%%?%?%%!%!?%%%!%%%%!!%%%%!!%%%!%!!!?%!?%%%!%!?%%!?%!%%!%%!%%?!?%!%%%%!%%!!?!%?%!?%!%%%%%?!%%!%??%!%!%%%!?%!%%%!?%%%%?!%??!%%%%%%?!%!%!?%!%%?!%%%%!%%%%%%?%%?%!???!%%%%%?%%%??!%%!?!%%%!!%%%%%%?!%?!!????%??%%%%%%?%%!%%%%!!%!!%%%%%!!!%!!%%!%%?!%%%%%%?%!!!!!%?%!%?!%!!!!%!%%!??%%%%?%?%%%%%%?%!%!!??!!%?%%?%%%!%!?%%%%!!%%!%?%!!!%%%!%!%?!%%!!!%%%!%?!?%?%%!!%%%!?!?%!!?%!%%!%%%?!?%!%%%%%!%!%%%%%!!%!!%%!%?%!%%?%!%%!!%%?%!%?!%%!%%?!%!!%!?%%%?%%%%%%%%%!!%!%%?%!?!%%%!%?%??%%%%%?!!!?%!?%%%%%%?!!!!%%%%%%?%!!!%%???!%?%%!%?%%?%!?%!!%%%!!%!!%%?!!%%!!%??%%%%%%%!%%%%%%%%!?%%?!?%!%%?!!!!!%!?%!!%!!!%!?!!%%%%%??%%???%?!!?%!%?%!%%?!%!%%!%!%!!%!%!!%%%!?%%?%!%%?%?%!!%%%%%%!!%%%!!!!?!?%!!%%%%%%!!!!%%%!?%%%!%?%%!?!?%!!%%!%?%!%?%!!!?%%!!?!%%?%%%%%%%%%?%!!%%!!?%%?!%%!!?%???%%?!%!%%%?!!%%%%?%!%%%!%%%??%%%!!?%%!%%%%%!!%%!!?!?%!%?%!%!!%%%%??!!?%%?!!!?%%%%?%!%%?!!%!?%?%?%%?%??!!!!%?%!%!?%!%%%!?%?!%!!!%?!!%?!%??%%?!%!?%!%!!!!!%%%?%!%!!?%!?%?%!%%!%%!%!!%%%%!!%!!?%?%%%?!%!!%%%!!???%!%??!!%!%!?!%%?!%%%!?%%?%?!%%%?!%!!!%%?!%%%%!!?%%?!?%%%%?!%%%??%%%!%%?!%!!%?!!!%?%%%%%!!?%???%%%%!%!?%%?!%%?!%!!?%%!!?!!!%%?%%!?!%?!%!%!%%!!?%%%%??%!%!%%%%!!%?%!%!?%!!?%%%!%%!%%!%%!%%!!%%?!%?!%%!!%%?%!%%%%!%!%!%%%%%!!?!%%%%!%%%%%%%!%??%!%%!%%%?%!%%?%?!!!%%%%!%!?%%%%%?%!!?%?%!%%!?%%%%!%!%!%!?!!?!!%!?!%%%%?%!%%?!%!%%%%%%%%%!?%%!?!%!!%%%%?!!!%%%!%??%%%??!%!!!%%%!%%%%%%%%%%%%?%!!?!!%%%!%%?!?!%!!!!?%%%%%%?%!%%!%%%!?%%!%!!%??!!!?%??!?!?%!%!??!%%!???%!%!%?%%!%%!!!%!!%%!%%%%%!%%!!!!%?%%%!%!!%%!%%%?%!%%%%!%!%?%%?%!!?!!%%?!%!?!%%%%%%%%%%%!%!!%?!!!%%!?%%%!%%??%%%%!!%%%%%!%!?!!%!!%%%%!%%%!!!???!%%%%%%??%!???!!!!%!%%!!%!!?!?%!!!%!!!!?%%%?%!??%%!!!%%?!%!?%%%!%%!%!%!%??%!!!!%?%!!%%%!!%?%!!%%!%?%!!!%?!%%!!!%%%?%%%%%%%!?%!!!%?!!%%%%!%%%!!!%?%%!%%%%%%%!!!%%!!%!!!?%!?%!%%?!%!!%!%?!?%!%%!%%?%%!!%!??%?%?!!!%%?!?%%!!%%%%!%%%%%!%!%%%%%%?%?%?%!%%%!%?%%%!!!?!?!!?!?%%!!!%?!!?!%!%%%%!!%?%!!!%%!%%%%%%%!?%%%%!!!!%!??%!!!%?%%%?%?!!?%?!?%%!!%%?!%!!%%%%%%%%%%!%%%!%!?%%%%%?!!%!!!!%%?!!%%!%!%?%%%%%%%?%!%!%!%%!%?%?%!!?!%%%!%?%!??%%!?%!%!!%!!?%!!%%%%%%%!%!?%!!!?%!%%%?%!%!%!%!!!%%%!%?!%?%!%%%?%?%%!%%%!!?%?!!?%?%!?%?%%!?%!!!%?%!!!%?%!?%?!!%%?!%%??%?%%%%?%%!%!!!!%%!!%%%!%!%!%%!%?%!????%!%%!!%!??%!%%??!%!%%?!!%!!?%%?!?%!%%!%%%%%%%%!??%%!%!%?!%%%!%?%!!?%%!??%!%!%!%%!!!!%%!%!!!%%?%?!%!%%!!%?!!%??%%%%%%%%!%%%?!!!%%!%%%%%%!%?!?%!!%?!%!%%%?%!?!%!%!%!!%%%!?!!?%?%!%%!!!%%?%%!%!%%!%!%%?!!!?!%?!%?%%??%%!!?%?%!??%%%%%!%%!%%%?%%!%%%%?%?%%!%%%!%%%%%!%%%?%!!%!?!!?%%%%%??!%%?!!%!!%%?%%??%!!%!%?!%!%!?%%%%!%%?%!%!!%!%?!%%%?!%%!%%%!!!%!%%%?%!!?!!!%%!%?%!!!!?!%%%!!!%%!%%%%!?!?%%%%%%?%!!%?!!%%!%!%?!%?%!?!!!%!!!!%!?%!!!!??%!!!%%?%%!%%%!?%%!?%%!?!!%!%!?%%!%%%%%?%!%%!?!%%!???%%!%!??!%%!%!%!%!%!%!%%!!!!?%%%!%%%%%%%!%!!%!%!!?!%%!%%%!%!!?%%!!%%%%!?!%%%!?%?%%%!%%!!!%!?%%!%?%%!!%%?!?%!??!!%!!!%%!%!?!!%%%?%?!%%!%?!%?%!!!?!%%!%!%!?%?!!?!!%!%?%!!%?%%??!!%%%%%%%?%!!?%%%%!%!%%?%%!%!%%%?%?%%%%??!%!%%!%%%!%!!?!%!%?%%%!?%%%?%%!%!!%%%%!%%?!%%?%%%!%!%%!!?!!!%!?%%%!!%%!??%!%!?%%!?!!%?%%!??!%!%!!%!!?!%!!?%%%!%%!%%%?!?%%!%%%!!?%?!%%%%!%%?!%%!%%!%!%%!%!%!%%%%%%%!%%%!?!%%%?%!!!?!%??%!?%%!?%%!%%!%!%%!%?%!?%!?!%?%!?%%!%%%?!%?!%!!%!!!%?%!%%%!!%?%!%%?!?%??!!!%!%%%!%%%?!%%!%?!?%?%?!%!?%?%!%!%%?!%!%%%%%%!?!%%%%%!%%%%%?!%!!!%%!%%!%?!%%?%%!%!%%!%%%!?%%!!!%%!?!%!!%!!!%%?%%!!!%!%%%!%!!!!?!!?!%!%!!?%%%%%!%%%!?!%!!%!%%?%!%%!%!!?%%%!!?!%%%%??%!%%%%!%?%%!!!%%%!!%%%%!!!!!%!%%?!%%!!!%!!?!%!!??!!?!?%!%!!%%%?!%?!%%??%!%%?!!%%%!!%?%%%!%!??%!%!%%%%?!?%%%?!!%!%!%!%%%!%!%%%%%%%%!%?%??%!%!?%%!!%%?%!!!%%%?!%!%%%!%!!%%%!!%?!!?%!%%!?%%??%%%%%%%!!%%?%!?!?%%%!!%?!!!%%%%!%!%!?!%%!!??!!!%%%!%?!%?!!%!%?%?%%?!!%!%%!??%?!!!!??%%%!%!%%%?%%%!%%!!?!!%?%%!%!!!%%%?!%%%%?%?%!%!?!!!!%%%%%?!?%!%%%%%%!??%!!%!%%%?!??!%!%?%??!%%!%!%%%%!!?%%%?!!%!%%?%%%!!%?!!!!!!?!!%!!%?!!%%!%%!!!!!!%%%%%?%!?%%?%%%?!%%%?!!?%?%?!%!?%!?%%!%%!!!?!%!?%%!%!?!!?!%!??%%??%!%%?%!%%!?%!?%%%!!!?!!%%%%%!??!!%%!%%%%!%?%!??!!??!%%%%%?%%!!%%!!%!?%!?!%%!!%!?%%%%%?!!%!%%%!%%%%%!%?%?!%%?!!%?!%!%!%!%%%%%%%%%!??%%%%!%%!%??%!%%?%%?!!%!?%!%%%!!%%%%%%?%!?%?%!%!?!%!%%%%%%!?%!%%?!!!%%!%?%?%%??%%%!!!!%%?%!%!%%!%%?%!%!%%%??!!!!!%!!%%!!%%%?!%?%!%%%!?%%%%!%%%%%%%%?!%%%?!?!%!%?%%?%%%?!?%?!?%%%?%!!!???%!?%%?%%%!!?!?!!!?!!?!!!?%!%%!?!%!!!??%%!?%%%?%%?!!%%%!%%%%%!!!%%?%!%%%?%?%!%%!!%%%?!!%!%?%??%!!!%?%?!%?!%%%%!%%%%!!!%!!??%!??%!!%%!?!%%?%%%%%!%!?%!%%%?%?!%!?%%%?%%%%!?!%!%%!!%%%%?%%%!?%!!?%?%%%%%%%!!!%%?%?!?%!?%!%!%!%%%%?%!?!!%?!%%%%%%%%%!%%%%?!%%%%%!!%!%!%!!%%%!??%%!?%%%%?%!??!!%%!!!%%%?!!?!!!!%!%!?%%?%%%%?%??!!!!?%??%!%!!%%%%%!%%%%%%!%%%%%%%!%%%?!?%%!%??!!!%%%%!%%%!%%%%??%%%%%!!%?%!%??!!%?!?!%??%%%%%%!?%%??%%%!!%!%%!%!%%%!!!!!%?%!%!!?%%??%%?%!%?%!?!!%!!%%!%%!%%%???%%%%!!!%%%!!%%?%!!!%%%%!%%!!!!%%!?%!%?%%!!%%%%%???%%%!%%!!!!?!!?%%!%%%!!%!%?%!?!%%!%%%%%%%%!%%!%%!!%!%!!!%!%%!?!%%%!%%!%!?%%?%%!!%%%!%%?!!%??!!%!%!!!%%%!%%%%!%!!!%!%?!!!!??%%?!%%?!??%%!%%%%%!!!!!?%%%%%!%%%%%%!%%%%???!!%!%!!%%%%!%%%%%?!?%%!%!%%%%!%!!%?!%!%!??!%%!%!!!%!!%!!?%!%%%%!%%!%?%?!?%%%%?%%%?!%!%%%??!%?%%!%?!%%!%%?!!!%%!!!!!%!%%?%?!!%!!!!!%!%%?%?!!%%?!%%?!%!%%%%%?!%%%!%%%%%?!!!!!!!%???%?!%!%!?!?%?!%!%?%%!%!?%%%%?!%!?%%%!%%!%%!%%!%%%!%%!!%%!%%?%%!%?%%%!!!!?!?%%%??%?%%??!%!%%%%%%%!!%?%%%!%!!%!%!?%?!!%?%%!%!!%!!%%%%%%!%?%!??!%!%%!%!?!!%%!!!!!%%%!%!!%!!%%%%%!%?%%%!%!%!!%!%!!!!%!!%%!%%%%%!!%?!%?%!!!!!%%!%%%!%!!%!%!%%%??%%?!!%%%%%?%!!?%!%?!%?%!%!%%%%%%!?!%%??%%%%%!!!%%!%!?%?!%?!%%%%?%%?%%%%%%!!%!?%!!!%%%%%%%!%%!%%%!%?!%%%%%!%%!%?%%%%!!%!!%!!%?%!%!!%??!?%!?%%!?%!!!!!!?%!%%%!%?%!?%?%?%!%!!??!!??!%%!%!%%!%%%%%!?!!%%?!?%?!%!%!!!?%!%!!%%%%%%%?!%!!!%!%%%%?%!%%%!%!%%?!!%%!%!?!%%%!%!!%?!!!%%!!%!!%%?%??%?!?!??!%!%%%??%!!!%%%!!%%?!%!!%?!%?!!%%??!%%!!!%%!!?!%!!!%%%?%???!!%%%%%%%%?!%%%!?!%%!!%%!?%?%!%!%%%%%%!!?%?%!%%%?%!%??!%!!%!%!!%%!!%!!%?%%?!?%!%!%%!%%%%?!%?!%!?%%%!%!%%!%!%%!%%%!%%%%%%%!%!%%%?%%%%%%%%?%%%!!?%%?!!%!%!%!?!%!%%?%%%?!%%%%%?%!!%%!%!%!%!!!%%!!?%%!%%?!%%?%%%%%%!%!%%!%!%%%?!%%%%%!!!%?%%%!!!!%%!%%!%%%%%%%%!%%%?!?!%%?!!%%%%%%%%%!!%%!%%%!%!!%%??!!!%%%%!?%!%??!?!?!%!?!%!%!!?!?%%%!!%%%?!%%!?!?!%!%?%%!%!%?%!%!!%!?%%?!%%%%%!!?!!?%?%%??%?!%%!?%%%%%!%?!!%!%!!!%%%!!%!%!!%?!%?%!%!?%?!!!%%%?!!%%?!??%%%!%%??!%%%!%!%%?%!%%?!%!?%!%?%%?!%%%%%!?!?!!?%%%%%%%%!%???!!?!%%%??%?%?!!%%%%%!%!%%?%%%%%!%!%%%%%%%?%%!%%?!?!!!!!!%!!!?%!!??!?%%?!%%%!%!?%!%%%!%%?%%?%%?!%%!%!%?!???!%%%%%%%%%%%!%?%!!%!?!!%%!?%%!!%%!!??!%%%!?!%?%%!%%!!!%%!?%!%?%?%%!%%?%%!!!!%%?!?!!!%%%!!!%?!%!%!%?!!%!!%?%%!?!!?%?%!?%?!%%!%!%%%?%%??%?%!!!!!%!?%%!%!%!??!!?%!%%%%%%%%%!%%%%!!%%%!%%%%%?!%!??!%%%%%%?%%%?%!%%?%!!%!%%%%%??%?!?!!%!!%%?%%%%%%!!!!??!!!%?%?!%%%%%!%!%?%!!%!%%%!!!%!!?%%?%!%%!%!!%?%?%!!?%%%%!??%!!?%!%%?!%%%!%!!!%!%??!%%%%?%?!!%!%!?%%%!%?%%!?!%%!?%%%%%%%%?%!!%!%%!%?%%?!!%%!%%?!??%%%%%%?%%%!%!!!%%!!%?%!?!%?%?%%%!?%?!%%%!!%%??%?%!%%%%%%%%%?%%!!%?%!%%!?%!!%%%?%!?%%!?!%!%%!%!!?!%%%%?%!?%!%%!%!?!!%%!!%!%?%%%%?%%?%!?%?!!?%!!%!?%!%%%%!?!!!%%%%%%?%%!%%%%%%%?!%%???!%%!%%!%%!!?%!%!!!!%%%!%%!%%!!%?!%?!%!%%!%%!!!?%?%!!%%%!?!!!%!!%!!%!%%%!?%%!!%!%%%%!!%!%!!%%!%%!?!?%?%%??!!%%%%%!!%%%?%%!!!%!!%%?!%!?%%%%%!!%!?%!%%!%!?!!%%!%!%?!%%!%!%%!%%!%??!?%?%%%%%%%%?%?%!%%?%%%%!%%??%%%%!!%?%!!%!%!%!%%%??!?!%%%!%%!!%%%%!%!%!!!!%!?%!%%%!?%%%%!%!?%%%%%%%!?%%%%!%!%!%%!!%%!%!!%%%!!%?%%%%%%%%%!!%%%%!!!!!%%%?%?%!?!!!%!?%!!%!%%%%!%!%%!%?!%%%!%!!%!%%!%!!%?%!%!%!!%!!?%!!%%!%%!!?%!?%!!%!!!!%%!%!!%%!%!%?!!%??%%%!!?%%%%?%!%!?%%%%!!%?!??!%%!!%?%??!%%%%!!%?!?%!!%%%?!%%%%!%??!!%?%%%%%?!%%%%%!%!!?%%%???!%??!%!%?%%!%!%%%!%!%%%%!!!%!%?!!!%%???%%!?!!%!?!!%!!%?!!!?%!%??%!%%%%%%!%%!%%!%!%??%%?%?!!?!!?%!!?%?!%?!!%%!?%%%?%%?!?%%!%%!??%!%%%!?%%%%!!!?!!?%???!%%%!?%?%%%%?%%!!%%!!%%!%!!%%%!%!%?%%%!%!!?!!!!%?%%!%%?%%%!!%%%??!!%!?!!!%%?!!%!%%%?!!%?!!%!!!!?!??%!%%!!!%!%!!%??%%!%%%!%%!%!%%%!?%!!!%!%%!??%??%!%%%??%%!%!%!!!?%%!%%%%?%?%?!%!%!!!%%%%%!%%%!!%%?!%%!?!%%!%!%?!??%%%%?%!%???%!?%!%%%%?!%%!!!?%!?!%!!!%!%!%%%%%!%%%?!!!%%%?%%!!!%%%?%?!%%%!?!??%%%!?%?!%%??!%%?!%%%%!%?!!%%%!%!??%%!!?%%!???%%%!?%?%%%?%%!!%%?%%!%%%??%%%!%%%%%?%!%%%%!%!%?%%%%!!!%%%?%!%%!?!%!%%!%%%%?%??!%%!%!%%%%!!??!%%?%%!?%!!!%%!%?!%??%%!!%%%!%%%!%!!%%%%?%!%!%!!!!%%%!%%!%!%%!!!%!!!%%??!?%%%!%%??%??%?%!!!?!%!?!%!?????%%%%!%?%!!!%%%!!%!!%%!%%%!%!%%!???!??%!!!%%%!%%!%%??%%%%!!%%%%%?%!?!%%%%??%!%?%%?%%?!%!!!!%%%%?!??%!%%%%%%%%%?%%%%%?%!?%%?%%!!%%%%!%%!!!??%%%!!!?%%%!%!?%%%%%%%!%?%?!!!%??%!?%%%?!%%!%%!%%!%!%?!?!!!!!?%%%!?%%?!?!%%%!%%%!!%%!!%!%%%%?!!?%%%%!%%!%!%!!!????!%!%!!?%!%!?%?!%%%?%!%!%?!%?!!%!%%%!%!!%??!%!?!%!%%%%!!%%%!?!%%!%!%!%!!%%%?%%!%%!%%%!?%%!?%!%!!!%%!%%%%%%%%%%!%%!%!!%%!%!%%%!%%%%!%%?%%%!??%!!!?%%%!!!%?!%!!%?%%!!%!%%%%%!!%!%%!!!!%%%%!%%??%??%!??%?%!%%%!!!%%!%!?!!?%%!!%%%%???!??%%!%%!!%%?%%%%%!%%!%!%!%%!%!!%%!%%%!%%%%??!%%?!%!?%!?%!%%%%%%%%!!%!%%%%??%!?%!!!!!!%!%%!%!!%%%!%!%%?%%??%???!?%%%%%!?%!%%%%!%%%!!!?%%%%%!!%%!?%!!%?!!%!%%!!!%!?!!!!?%!!%%%%!%%%??%%!!%%%%%%%%!%!%!!!%%?%%%!%%?!!!%%!%!?%%%%%%%??!%!%%%%!%!%%%%!??%%%%?%!!%?%!%%%%%!!%%!!%?!!!%!%%%%%%!%%?!%%!%!%%%%!??!%?!!%?%!%%!??%!%%%!%!%%%?%%!%!!%!!!%!!!%%%%!!%%%%?%!!%!!%%%!%%!?%%%!!!!%!!%!%%%%??%%!??!%%%%?%%%!!?%%%!%%%!?%%%?%%%%%%!%?!!%%%%!%%!%%%!%!%!!%?!!%%!%!!%?%!!%%%!!?!?!%%!!!!%%?%%%%!%%!?%!%%%?%?!%%%!%%?!!%!%?%?%?%?!!!?%%%!%%%?!%%%!%%!!!?%?%%%!!??%%%%%%!!%%!!%!!!%!!!!%%?%%%%?%%!%!!!%%?!!!!!?!!?!%%%%?!%?!%!???!!!!!%%%%!?%%%!!%!!?%%!%%%%%!?!!%!%?%!%%!%%%%?!%!%!%!%!!?%??%!%?%!%%!%?%!%%%%?%%!%%%%?!%?%?!%%%!%?%%!?%%!%!%%!?%!!%%%%!!?!%%!?!!%?!!%%!?!!?!?%!%%%?!%!%!%%%%?%%%!?%%%?%%%!%!!!%%%%%%!?!%!?%!%%?%%!%!!??%%%%%!!%%?%!%%%?%?!%%%%%?%!!%%%!?!!%?!!%%%!%%%!!?!%%!%!%%!!%!!%%%!%!!%?%!!!%%!%%%!!!%!??!?%%%%%%!!!%%%%%?%!?%!!?%%!!!?%%!%!%?%?%%%%%!!!!%%?!!!!?!%%%%!%%%!?%!%?%%%!!!%?%?!%?!!%%!%%!!?!%!%?!!!!%%%?%%?%?%!%!!%!!%%!!%%!%!!!!??!%!!%%%%%%%%?!%?%!?%!%?%?!!%%?%%%%!!!!!%!%%?!?%?!?%!??%?%%%%%?!?%%!%%?!%???%!?!%%%%!%?%%%%??%!?%%%!%%?%!%!%!%%!%?!!?%%!%?%%!!%?%!!%?%!%%!!%%?%?!!%!%%!!!!!%%!%%%?%%%%%!?!!?%%%?%!%%?!%!%!!!?%%!?%%?!!%!!?!%%%%%%%%%%!%%!%%%!%%!!?!?%%%!%?%?%%?%%!?%%!??!%%!%%!!!%%!%!!!??%%!!%%!!!!%!%!?%%%%!%%!%%%!!%!!??%%%%?!%%%%%!?!%!%?!!?%!!???%%!!%!?%!%%%?!%!%%!!%?!%!!%%???!!%!!?!%%%%%!??%!%%%?%%%?%!%%%!%?%!!%!%!%???!%?%%!%%!%%%%??%!!!%%!?%!%?!%?%!%%!%!!?!?!%!%%%!%!?!!%%!%?!%%?!%%?%!!%!%?%?!%!!!%?%!!!%?%%!%???%?!%%!%!%%?!!%!%!!!!!%%%!!%!?%%!!%%?%!%%?%%%%!%%%%!%?%%%!%!!%%!%!%!!?%!%?%%!%%%%!!%!!%!!!!!%%%%%%%%?%%%!?%?%!%!?!%?%!%!%!!!!?%??!!!!!%!!!%%%!!!%%%%??%%!%%!%%!%!%%%?!%%!!%%?%%?%!%?!?!!%%%!%??!%!?%%?%!%%!%%%%%??%%%%?????%%%!!%?%%!!?%%!%%%%%!%%?!!%!?!!!!%!%!%%%!?!%%%%%?%!!?%!!%%%%!%%!!%%!%%?%?%?%!!!%!!??%%%%%%!!%!!!%%?%%%%%!%%%%%%!!%?%%?%%?!?%%%%%%!%!?!%!!%%%!%?!?!!?!%%%%!%%%%?!%?!%%!%%%%?!%%!%%!?%!%%%!%%!%%!!!!!%?%?%!!!%%!%!!!%!%?%%?!%?%!!!!!%%%%!?%%%!%?!%%%%%%!!%%%%%!%?!%%%%%%!%%%%!%%%%%??!!!!??%!!%?%%%%%%%%!%!!%%!%%%?!%!!%!?%!?!%%!%!%%%!%?!%%?%%%!!!%%%!?%!?!?!!!%!??%%!%!!%!%!?%?!!%?!!%%%?!!!!?%!%??%%%%!%%%%!?%?%?%!%!%%%!?%!%?!!%!?%%%!!%?%?%?!%?!%!!%%%!%!%%!%?%!%%!%%%!%!%%!!!%!?!!!!%??%?!%%%%%%%?%%%?!%%!!%!%%%!?!%?!?%%%%%??!!%%!%%!%%%!!!??%%?%!!%!%!!!%%!?%!!!!!!%!%%!%%%!!!%%%?%%%!%%%%%?!%!%%!%%!!!!!!??!!%%%!!!%%%%%?!%!%%%%%!%!%%!%%!?!%!?%%!%%%%%!%%%%!%%!!%?%%%%%%%?!%!%!%%%?%%%?%%!??%%%?%!%!%%!%%%%%!?!%?!!%%%%!?!!%?%?%!%!%!?!%%!!%%%!!%!!!?%!!%%%!!%%%!%%%?!?%%!%%!%%%!!??%%%%!!%!%?%%%%%?!%?%%%!!?!!!?%%!%%!%%!%!%!%%?%!%%!%%?!!!%%??%!?%!%%%%?%!%%%%?!?!%!?!!%%!%%%!!!?!%%%%!!?%%%%%?%%!%%!%!%%!?%!%!!!%?%%?!!%%?%%%%!%?%!%%!%!%%!%%!!%%%%!!%?%?!??!%!?!?!%!%%%!%?%%%!%!%%%!%!!??!!?%%%%?!%!!%!?%?%%%%!%%!%%%%%!!%?????%%%!%?%%%?!%%!%?%!%!%%%!!!??%%%!?%?%%!%%%%!%%%%%!!%%%!%!%?%%%!!%%!??%%%%%%!%%!!!!??%!%!!%%!%!%%!!%%%%!%!%%%%!?%!!!%%%%!!%!%%?!!!?!?%%%!!???%!%!%%!%%%?%!!!!%%!%%%?%?%%!!%!%%%!%!?!!%!%!!%!!??%%%?%%!%!!%%!?!?%%%!!%%!!%%%%!!%%?%!!!!!%!!!?%!!?%!?!%%%!?%!!%%%!!?%!??!!!%!%%!?!?%!!!?!!%%%!!%?%%?%!%%?%%?%%%!%!!?!!%%?!!!!%!?%%!%???%%??%?!!!??%!!%%!%?!%!%%%!!%%%?%%%%%!?%%?!%!%%!%%!!???!!!%!%%!%!??!!!%%%%%?!!!%!%%!!!%!?%%?%%!??%?%!?%%!!!%!!%%%!%!%!%!%%!%!?%?%%?!%%%%?%%?!!%%!%!%%!!%!%!?!?%!?!!?%%!!??!!?%!%!%%!%%!!%!!!!?%%!!%%%?%?!%%!!?%!!%!%??%!!%!?!%%%%%%?%%!%%?%!!%!%?!%!%%!%?!%!!!?!%%!!!%%!?%!!%?%!%%!%?!%%%?%%??%%!%?%?%!%??%%!!%!!%!!?%%!?%?%!!?!%!?%%%%%!%%!!%%!!!!!?!?%%%%?!!!%?%%%%%!!%!??%?!!!%!%!%!!%%%%!%!%%!%%!%!%!%%%%%%!%%%%%%%!%!??!%!%?%%!?!%?%??%%!%!%?!!%?!%!%%??!!%!%!!!%!%!!%%!%!?%%%!!%?!%%%?%?!!!%%%%%%!!!!%!%%%%%!??%%%!%%!!!%%!%%!?%!?%%!!%!%!%!!%%%%%%??%%!!%??%%%%??%%!%%%!%%?%!%?%!%!%!!%%%!%%!%%%!%!!%!%!%%??%!?!%%%!?%!%!%?!%%!%%?!%%!%%???%%%%%%!!!%%%!%!%???%!%%!%?!!%%!?%%%!?!!%!!!!%!%?%%%?!%?%%?%%%%?%%!?%?%!%%!%!%?%!%%%?%?!!!??%!%%!%!%!%%%%!%!!?!%%!?%%!%!%!%%?%!?%!%!?%%%%%%%?!%?!%%!%?!!%!%%!?%?%!?%?!!!%%!%%%!?!?!!!%%%%%%?%%%!%!%%?!!!!!%%%%%?%%!?%!%%?%?%%?!?%?%?%!!!!%!%%%!%%!!!%!%%%!?%%%!!%!?!%%%%%!!%?!%%?%!%%%!!%!%!!%?%%!%?!%!%!?!%%%!!%%?%!?%%!!%%%%%%!!%%!!%%!%%!!!%%?%%%!%!!%?%?%%%%!%!?!?%?%%!!??%?!%!%%??!!!%%%!%%%%%?%?!!%!!%???%?!%?!!%!%%%!!%%!%?%!?%%%!?%%%?%!!%!%%%%!?%%??!!?!%??!!!!%?%!!%%?!%!!%%!%!!%%%?!%%%?%!!!!!!%!%%%!%%?!%!%%!!%!!!!%!%!%!!??%!%%!!??%?!!%!?%%%!%!!!??%?%!%!!%%?!!%!!%!?%%!?%%%%%!%?%%%!!?%!!%%%?!%%!?!%!%%!%?%%%!!??%!?!%!%!!%%%!%%%!%%!!!%%%%%%?!!!%?%!%?%!!!%%?%!%%%?%%!!!?%?%!?%%?%%?%!%!!%!%!%!%%%%!%%?%%!%!%%?!!!!!%%?!?%%!?!%%!??!!%%%?%%%!!%?%!!%%%?!?%?%?%%%%?!%!?!%%!%!%%!!%%%!%?%?%%!%??!!%??%!!%%?!!%%?%%%%%%%%?%%%%%!%%%!!%%%%!!!!%?%!?%!%!%!%%%%!?%%!!%%?!??%?!!!%%?%%%%%??%?%%!!!%!%!!%%!%%!!!!%?!!!%%%!%%%%%!!!?!!?!%%!%%?%?%!?!%%%%%%!%%!%!%%!!!%!%%!!?%%%??%%?!!%%!!?%!!?%!%%!%!%%!!!%%%%!!!!!%%?%%???%%%!%?%%%!!!!%?!??%%%%%!??%?!%!!!?!%!??!!%%!%?%%!%!!%!%%%?!%%%%?!%%?%!??!%%!%%!!%%!?%!%!!%%!!!!!%%!!?%%%%!%!!%%?%%%%?%%!!%!!?%!?!!??!?%%%%!%%%%?!!!!%!%?%%%!!!%?!%%%%!%%!!!?%!%%?%%!!?%%!%!!%%%%!!%!!%!%?%!!%!?%%%%!%!%??%?%!!%%!!!!%%%%%%%!!!%%!%%%%?!%??%!%!!%!%%?%?????!?!!%%?!!%%%%%%%%%%%!%!?%?!%%??%!?%%?%%%%!%%!!?%%%?!!!!%!%%%!!%?%%?!!!%!%%!%%%!%%%%!%!%%%%!??%!!%%!?%%%%%?!!%!%%!!!!!%%%?%%%%%%%%%!%?%!?!!!!!%???%%%%%!%%!%!%%?!!%%%?%!!%!!%!%%!%%%!?%%%%%%!%?%!!!!?%%!%%?%%%?!%%%%%%!%!%%%%%!?%%%!!!!%%%!%!%!!%%!!%%%%?!!!%%%%!?!%?%%?%%%!?%!?%%?%%%!?!%!!!??%!%!!%??%%?%!!%?!%?!%!?!!!%?!!%!!%!!%%%%!%!??%!%?%%?%%%!!!!!%!%%!%%!%?%?!!!?%!!%%%?!%%%%!%?%%!%%%%%%?%!!%!?!!%!??%?%?!%!%%%%%!%!?%%%!!?%%%%%!!?!%%!%?%?!%?%!%%%?!!??%%!?!!%%%%!%%!%?!?!!!!!!%!%!%?%!%%%?%!%%?!%?%!%!%%??%%?!%%%%%%%%%!%!%%%!?!%?%!!?%!!!%?!!!!?%!%%%%%%!!!!!!!%!?!%%%!!%%%!!?%!!!?!%!!!!???%!%%%!%!!%%?%%%?!%%!%!?!!?%%%%!?%!!!%%!%%%?%?%%%?!!!!%%!?!%!%%?!!!%%!!%%!%!!??!!%!%%!?!!%??%%?%%%!?%!!%%!!?%?%%?!%?%?%?!?%%?!%!!??%%%!!%!!%!?!%%%%%?%!?!?!%??!%!!!%!?!!%%?%%!%%%%!%?%!?%??%%!!!!%?%%??%%%!!%?%%%%%%%%?%%%%!??%!!!%%%%!!%!%?%%!%!%%!%!!!%!%%%%%?!!?!?!%!%%%!!!!!%%!%%?!!%!%%!!??%??!%?%%%%!!%%!?%!%!%!?!%!%%%%!%!%!%%!%!!!%%!%!%%%%%??%%%%%!!%?!?????%!?!!?!%!!%?%%%!?!??!?%!%!!!%%!?%%!%%%!!%%%?!%?!??%?%?!!%%!%!%?!!!?!!!!!%??%%%!!%%%!%!%?!!!!!??%!%!%%!!%%%!%??%!%%?%%%%?!!!%%%!!!%!!!%?%!%%!%?%%%!%%!%%!!%%%%!?!%!%!%%!%%%?%!!%%!%%%??%!!!%?%!%!?%%%%%?!%%!%%!%!%%!%%%%%%%%?%%!!!??%%%%%!%!%%%?%%%%?%!?%%??!!?%!%%%%?!!%!!?%!%%!%%%%%%!!%?%??%!%%!!!%?%!%!!?%!%%!!!!!%%!%%!!%%%%!%%%!!%%!%!%!%??%?%!!!%!!%%??!%%%??%!?%%%?!!!%??%%%%%%!!!?%!!!??!?%!%%?%!!!!!?%!!%?%!%??!%?!!%%??%%!??%?%%!!%!!%%!!%!%%%%%??%%%!%??%?%%??!%!?!!%%!!!!%%%!%!!!?!!%%!%!%%%?%!%!!%%%!!%%%%!!!%%%?!%%%!%%?%?%?%%%%???%%%!??!%!%??%!%?!%?!%!%?%??%%!%%%!%%%!%%%%%!%%%!!%%?!%!!%%%?!?%!!%!%%%%%!%%?%%!%!!%%!!%?!%%!!%%%!!%%%!!%??!%?%!?%%%!!!%%%%!%%%!?!?%%%%!!%%!!%%%%%%?%%%%%%%%%!?!!!%!%!?!%%%%%!%%%%%?!%%%!?%!%%!??!%%?%%%!?!%!????!%%!!!%!!%%%%%%%!%%?%%%%%!!%?%!?!%?!%%!%?!%%%!%!!%%%%!%%%!%%!?!%?!!%%%!?%%%%%%!%?!!%%%%%%!%%??%%%%!!!!%!%?!%%!!%!%!%??%!!%?%!!%%!%!%%?!%?%%%%!??!?%!!%!%%!!%!%!!%%%!!?%%!!!?!!!%%?!%%!%%!?!!!!!!!!%%%!!!??%???%!%?%%?%%!!%!%%?%%!!%!%%%!!%%%%%%%!%??%%%%%%!!?%?!!%!!%?%!%?%%%%%?%?!%??!%%?%?%!%!%!!!%%!%?%??!!%%!%%??%%?%%!%!??!%%%%!%%?%?!%!%%%!!?!%%!!%!???%%!%%%?!%!!%%%%%?!!%%!?!??!%?%%%%%%?%%?%%%%%%%%%%%%%?%%%?!!?%%!!??%%%?!?%???!!!%%%%%!%!??!!??%%%?%!%%!?%!!?!?%?!%%%%%!???!??%!%%%!!%?%%%%%%?%%!%?%!%%%%!!%%%?%%?!%%%%!%!%?%%?%%!%!!%%?%%?%%%%%!?%%!?%!%%!%%?!%%!%!?!?%?%%?%%!%!?%%%!%?%!?%%!%%%!!!!!!%%!%?%!!%%%%!%%!%%?!??!!%?!!!?%!!%%!%?%?%!?%??%%?%%%%%!%!%?!!%%%%!?!!??%!??%!%!!%%%?%?!%!%?!%%!%%%!%!!!%!!!!%??%%%%?%?%%%!%!%%%!%%!?%?%!%%!!%%!%%!!%%!%?!%!%!!?%!%%!%!%!!!%!%%%%!!?!?%%%!%%??%%!%%!%%!%!!%?%%!%!!!%?%%%?!%%?%%%%!%!!!?%%%%%!%%%!?%%%!!%!!!!%?!!%%%!!!!%!%??!!%?%!!%%%%%%?!?%!%%??!%??%!!%%!?!?%?%%??!!%!??!%!!?%%!%%!%%%%!!!!%?%%!?!%%%%!?%%!!%!!%?%?%%!!?%%!%%!!%%!!%%%%%%%?%%!!%!!%%%%%%%%%%%%%%%!%%%?%%?%%?%?%!%???!!?%%?!%??!!%%%%%%!%%?%!?%?!%%!?!%%!!!%%!??!%!?%!%%!%!%%%!!%!%%%???%?!!%%%!%!?!%!%!%%%?!!!%%%!!%%%%?!%%!%%%%!!!!%!%?%%!!??%%??%??!%%!%?!!%??%%??!%?!!!%%%?%!%!!!?%%!%?%!%!%!%!%!?%%%!%%?%%%%%%%!%!?%!!!%%%%%%!%!!!%!%!??%%%?!!?%!%%%%?!%%%%%%%%%%%?%%?%!!%%!!%!!??!%%%%!%!?%!%%?%!!%?%?%%%%%%!%!!!%?!!%!%%!!?%%%%%%?%!!!!%!%%%!!%%%!!%%%%%??%!!%%?!%!%%%?%%%%%%%!%%?!%?!%%%%%?%?%?!%??!!%%%?%?%%?!%%%!!%%%!?!?!!%!%%!%%%%%!%%%?!!%%!%%%!%!%%???%%%%%!%%?%?%!%?%!?%%?%!%%%%!%?!%%?!?!?!%!!??!!!%%%!!?!%%!%%%!?!?%%%%!%!?%%%%!%!?!%??%!?!%?!?%!%%%??%!!%%%%!%!%%?!%%%!%%!%?%%%%!!%%%%?%%?!!!!%%!%%!!!%%?%?%!?!%%%%%%%!%%%%%!?!?%%!?%!!!%%?!%?%!!%%%!%!%%?!!%%%!!!?%%!%%%%!%%!%%%%!?!!!!%!!%%?%%%%??!%!%%%%%%!%!%%?%%%!%?%%??!%%?%%%!%!%%??%!%%!%%!%%!%%!%%%!%!!%!%%%%!%?%!!%?%%%?%%?!%%%?%?%!%%?%!?!%%??!%??%!%%!?%!%%%%!!%%!!%!!%%%!%?!%?%%!!!%!!%?!%!!%?!%!!?%?%??%!%%%%%!!!%%%%%?!!%!?!%%?%%%??%%%%%%%??%!!!!%%%!%!%%?%!%!%%%%%!???!%!??!%!%%!%!??!??!??%%%%!%%?%?%?%%%!%%!%%%%%%!%%!%!%%?%?%?!%%%!!%%?%%%%!????!!!%%?%!!%%!!!!!%!%?!?%!??%!?%%!!%%?!%!!%%%%%%%%%%%%!%!!%%!%!!%?!!?!%%%%?!!%?!!%?!?%!?%%%%%%!!!!?!%!%%%%%!%%!%%?%%%!%%%%%!%!!?%%!%!%%%?!!!%??%!!?%!%?%%%%?%?%?%%?!?!%!%!?!%??%!%?!!?%%?!%%!!%?!%%%%!!?!%%!%%!!%?!%%!!!%%%%%%%!!%!%%%%%%%!?!!?%%??%%?%!!%!%%!!%%%%!%%%!?!%%%?%%%%%%%%!%%?%%%?%!!%?%%!!%%%?!%!%!!!%!%%!%?%%!!?%!%%%!%!!%!%%%!!!%%??!!!!!?%!%%?!%!?%%!!%!!%?%%!!%?!!!!%%%!!!?%%%%?%!!%%??%?%!!!!!%%%%!%%!!%!!%%%!!%%!!!%%%!!%!!??%!%%%!!%!%!%%%%?!!%%!?%%??!%%??!!%!!%%%%%?%%%!!!!!?!!!%%!!?%!?!%%?????%%%%?%%%!%%%%!!!!?!%%!%!?%?!??%%%%%%!!!%!!%%!?%!?%%!%!!???%!?%??!?%!%!!%?!%%%?!%%!%?!!!%%%%?!%%!%%!%%!?!%!!!!%%!%%%?%!%!%%%!%!%%!%!!%!%%%%?!!!%%!!%%!%%%!!!%!%%?%%?%!%%%%!%%%!?!%%!%%%?%%%%!!%%%%?%?!?%!%%!%%%!%%%!?!%!?%??%!%%%%%?%%%!%%%!!!%%?!%%!%%%%%!%!%%%!!!?!!%%%!??!!?%?%%%!!%!%!%!%!!?!!?%%%%!%!%%%%?!%!%!?!!!%%!%?!?!%%%!?!%%%?!%%%!!%%%%!%!!??!%%%!%%?%!!!?!!!%%!%!%%?%%%!!!%%%!!%!!!??%?%%%%%%!?%!%%%!%!!!!!?%%%%%%%!%!!%%!%!!?%!!%%!!%%%%%!%?%%%%%%%!!!??%%!%%!!?!!!%%%!?%%?%?!%!!%%%!!%%!%%??%%%!!%?!%%!%%%?%!%%!!!?%%?!%?!%!%??%!%!!%%!%!%%%%??%!!%!!!%%%%!!?!%!%!%%!?%%!%?!%!!?%%!%%!!%%%%%%?%%?!%!!%%%%?%%%??%%%%%%%!!%?%%!%?%%!?%%%!!!?%!%?!!%%!?!!!?%!!!%?!?%%%%%!%%%%!?!%%!%%%??%%%%%%%%!%%%!%%%%%!?!%%%%%!!!%%!%%%%!%%%?%!!????%?!%?%!?%!!%!%!!?!??!%!!!%%!%%%!!%%%!%%%%?!%!!%%%!?%%%???!!%%!%%!??!!?!%%%!!%?!!?!!%%!%%%?%%!?%%%?%%!%%%%?!?!%!%!!%%!!%!!?%!%%%%!%!?%%!%%!%??%?%%%!%%!!?!%%%?%%!%%?!!?%%%%%!%!!?%%!%!%%%?!!%?!??%%!!%?%%%%%??!%!%%%%!!!??!%?!%?!!%!%%%!?%!?%%%!!!%%%%%!!%%!!??%?!%!%%!!%%%!%?%%%?%!%!%%!%%%!?%!!?%%%!?%%%%!!!%%?!%%!!%?%!!!!%!?%%!?%?!!!!!%!!!%!!!!!%%%%%!%%?!%!%??%%!!%!?%%!?!!?%%%!!%!?!%!!?%%%?%!%?!%%?%%%!!!%%%!?!?!%?!%%!!%??!%?!%!?!%%%!%%%%!%%!!%!!%%%%%!!!!%?%%%!?%%!!!%!!%!!%%%?%!%!%!%%%?%?!%!!!!!%%%!%!!%%?%%%%!%!%%!%!%!?!!!!?!%%%%??%%!!%%??!%%%!?%%%%?%?!!?!%!!%!!%!%!!%!?%%%%%%%!?%%%%!%%!?%!%%%!%%%!!??!%?%%?%?!?%%?%!?%!?!%!%%!!%!!%%!%!%%%!!%%%%?%%%%!%????!?%!%%!%%!%!%%!%!!%!!%??%%!%?%%!%?!%%!!!!!!!!%??!%%%%%!?%!!!%!?!%!%%!%%!%!%%%!%!%!%!?!%%?%%?%%%!!!!%%!!!%!!?!%!%%?%%%!%!%%?%%?%!!!?!!%%?!?%%%%!%%%%!%%!%!??!!!%%%%%%!%%!%!!!%?%%!!%%!%!%%!!%!!%!%%%?!%%!?%%%?%%!!%%%%!%%!%!?!%%%!?!!%%!!!%%%%!%!%?!%%%?%?!!!%!%?%%!!??%!?%?!%!!%?%%??%%%%%!%?!%!?%!!%??!!%%!%%!??!%?!!!!%!!%?!%?%!?!%%%%!%%%!%!%%?%%%!%!%?%?!%%!!%?!?!%!%?!%%%!!!!!!!%!!?!!!%!!?%!!?%%%%%!%!%!!%%!%!%?%!%%!?%%???%%!%!%%!?!%%?!?!%%%%%?%%%%!!%!!!?!%!!?!%%%!%?!%!%%%%%%!!!%?!!%!%%%%%%?%!!%%!%!!%?%%%%%!%!%?!%!%%!%%%%%%!%?!!%%!%%%??!!%%%%%%!?%?!%%%?!%%%!!!!!?!?!%%!!?%%%%%?%%?!!%%!%??%%%%%!%%?%%%%%!?%%!%%!?%?%!!!%%%!!%?!?!?%%!!%%!?%%?!!?!!%%%?!%%%%!?!%%!%?%?%?!%%%%%??%%!%!!!!%!%?%%!%%%%%??%%%!%%%%?%?%%%%!?%!%%%!%!%%!%?%%!%%%!%!%?%!%!??%!!!!!???%?!!!!?%!%%%%!%%?%!!?!%!%%%%!%%%!!!%%!!%%%%!%%!?%!%??%?!%!!?!?%!!!!!%!!!!!!%%!??%%?%!?!%!%%!!%!!!??%?%%%%%!%%%!!%!%%%?%%%!!%%!!!%%%!%%%?!%!%%!?%!%!%??%%!%??!%??%!!%!%!!%!%!%%!%!%!%%?%!!!%%!%?!%?%!?%!%%%%?%!%!%%%%!!%%%!!%%%%!!%?!%????%%!!!%%%%%%!%%%%%?!%!!%?%!%%%!%?!!!%%!%%%!!!!%!!?!!!%%!%%%!%%%!?!%%%%!%!?%?%!%!!%!%!%%%?!!!%!%!!!!%!!!%%!%!%?!??%%%%!%%%!%%%%%%%!?%?!!!?%!?!%?%%%%%%%??!%%!%%!?%%?%%?!%%!%%!?!!?%!?%??%%%!!!%%!!!!!!%%!%%!%%%!%%!%???%%%%%%!!%%%%%!%%%??!%%!%!!!!%%!?%?!%?!%%!?!??%%%!%!%%!%!!%!%?!!?!!!!!!!%!%!%!!%!%!%!!!!!!%!!??%%!%!!!?%!%!%%!??%%%%%%%!!%!%!!?!%!%!%%!?%%!!%%??!!%!%%?%!?%%!%%%?!%%%%!!%?!%!?%%?!%?%%!%!%%!%!%?%%%%%!!??!!!!%!?%?%%%%%%%!??%%%%!%%!!!%%%!%!!?%!!?%!!?%!!%%!?!!!!!%%%!?!!!?%?!!%!!!%%%%%%%?!?!!%%%!%?%%?%%?????%%?!%%!%%%!%!%!%!?%%%?!!?!!%%!!!%%%?!%!!%%%%!%%?!%!!%%!%%!%%%!!!%%!?!!%%%?%!%!%!%!%%%!%%%!%%%%%?%!%%%%!?%!!??%?%%%%%%%%!?!%%???!!?%%??%%!!!!%%!!%!%?%!?%%!!%%!!%%?!!%%%!???!!%%%%%%??%%!??!%%%?%%!!!%%%!?!%%!%?%%?%!%!!?%%!??%!!%??%?%??!?%!!%%%%??????%%!?!!!!%!!%!%%%%%!%?!?%%!?!%!?%%?%%%!%%%%!%!!%%?!%!%%%%%!?%!!!%?!%!?%%?!%!%%!!%!%%!!!!%%!!?!%!%?%!?!%%%%?!?!!!!%!%%!%??%%%%!%%%?%?!%%!!!%!?!!%?%!?!%!!!?!%!%%!%%?!?%?!%?!%%%?!!!!?%?!!!!!?%%?%?%!%%%%%%%!!%!?%!!!??%%!%%%?%?!%?!%!??%%???!!?!??%%?%%%%!!!%%??!%%%%!?%%%%?%!%%!%%??%!%!!%%%!%%%%%?!!!%%%!?!!%%!%%!%!%%%%!%%%%%!!%?%%!%%?!!%!%%%%??!?!%!?%%%%!!?%%!?%%%!%%%!!%!%%!!?%%?%%%%!!?!?%!%%!!%%!%!?%%?%%?!?%%?%%%!%?!?%%!%!%!!%!%?%???%%??%!%!!!!%?!%!!!?%?!!!!!?%!%!%!!%%!!!%%!!!!!%%!%%%?%!!%%?!%%%%!%%!%!%%!%!%%?%%%!%%?%%!!%?%%%%%?%%%!!!??%?%?!??%??%!?%%?%!!%%?!%!!%%%%%?!?!%%%!!%%%!%%!%???%%!%%!%?!?%%%%!%!%!!!!%%!!?%!%!%%!%!%%%%%?%%%%%?!!?%!?%%!%%!%?%!%!!%%!%!%%?%%?!%%!%?%!%!!!%%%?!!%%!!!!%%%%%!%!%!?!%!!?!!%%%!%!?!!!!%%%!%%!%%%%?%!!%!?!!???%%%%?!%!%%!%%%!%!?%%?%%%!%%%?!%%%%%!%?!!!%%!!!?%!!%%!!%%!%!%!!%!%%!!%%!%?%!!?%%%%!!%%?%!!%!%?%%!!???!!?%%!%!!%%%%?!%%%?!%!%%!%!!%%??!%!%%%?!?!%%%%!%?%%%%%%?!%!%%!!%%!!!%%%!???!!%!%%%!!%!?%!?!!!?!!!!!%!?!%!%%%!%%!%!!%%%%%!%???%!?!!%%%%%!?%?!%%%??!%!!?%%?%%%%%!!%%!!?%%%%!%%%??%!!?%%%!%%!%%!%!!!!%%!!??%?%!%?!%!%!%??%!?%%!%!!??%%%%%%%?!%!?%!!%!%%?%!!??%!!?!%%%!!%?!?!%%?%!%!%!%!%?%%%!%%%!!%?%!!?%!%!%%?%%?!%!%%!%%%%%%!?!!%!%%!!%!%!?!%??%?!%!%%???!!!%%%%!%%%%!?!!%%!!%%%%!!%!!%!%?!!%%%!?%%%%!%!%%!%%%!%!%?%!!!%!%%!!%%!!%?%!?%%%%%?%%!?!%?%%?%%%%!%%!%!%%%%%%!%?%%%!%%%!%%?%!%!%?!!!%%!?!?%!%%!%?%!?%!!!%%%?%%%!%%??%%%%%!!!%%!!!%%!!%!!!%?!!!%?!!%?%%!%%?%?%?%!?!!%%%%!%%!%%!!?%%?%%%!!!!%%%?%?!?%%!%%!?!!%%%?%%!!%!%%!%!%%?%!?%!%!%%%%!!?%!%%%?!?!???%?!!!%%!!%!%!!%%%!%!%!!!!!!!%%!%%%!%%%%%!?!%%%%%?!%!!%%%??%%%??%%%%!%%!%%!!%%%%%%!%!!%%?!?!??%%!!!!!!!%%?%%%%?!!??%!??%%?%!%%!%%%!%%?%%!!!%%%%%???!%?!!??!?%%%!%%!%%!%%?!!!%!!%!!!?!!!%%?!!!%!!!!?%%!!%%%!??!?%%!!%!!%!???!%%!!%%?!%!%!?%%%%!%%!%%??%%%%%%?%!!!%%%%%!!%%!?%!%!!%?%!!%!%%%%%%%!!!!%%%%%?%%%?!!?%%%?%!!%%%!%!%?%?%!!!!%!!!!!???%?%%!%?!!%??!%%%%%!%?%%%!%!!?!!%%?!!!%%%%%%!?!!%?!!%!%!%!%%!?%!?%%%%%%!?!??%%!!?%%?%%!%!?%!!%?%!%%!%?%%?!!!%%!!%%!!!?!!?%??%!!%%%?!%??%?%%%!!!!%%%?%%!!!??%%%!?%!!!!%!?!!!!%%!?!%%%%%%?!%!%!%%%?%??%?%!%!!%%%%!!?!%?!%??%!?%%!%%!%??!%%%!!?%?%?!!!?%!??!!%%%!?%!%!?%%%!%%%?%?%%%%!%?!%?!%%!!!%?!!?!%%%!?%!%?%%%%%%%%%%%?%!%%!%%!%?!%!%%%!%!%%%?%!?!%!!!%%%%%???%%?%%!!%!%?%%%%%%%%!!!%!%%%!!%!%%%%!%%?%%!%%%%?%%%%%%!?!!%!!?%%%%%?%?!?%!??%%%%%%??!!%%!!%%?!%%?%?%%%!%%!%%?!%%??%!!?%?!!!%%%%!%!%!?!%%%%!!!%%!%%!!%!?!%%!%%!!%!%?%%!!!%!!!!%%%!%!%%%%%!?%%%!%%!!?!%!%!%%%!%?!%%%!!%!?%!?%!%%%%%%!!!%%?!!%!%!%%%%!?!%%?%%%%%!?!??!!%%!%%%%%%!?%%!%!%!!%%%!%%%%%%%%%%%%!!?%?%%!!?!?%!%%%%%%!%!!!!!%%%%%!!!!%?!%%%%%!%!%%%%%%!%?%??!?%%%!!%%??%!!%!!!?%!??%?!%%?%%%!?!!!?%%%%!!?!?%%%!!%?%!%%%%%!%!!%%%%!?%%%%%%!!%!?!!!?%%%%!%%!%!%!%%%?!%%!!%%!%%!%%?%!!%?%!%%%!!%!%%%?!%%!!?%!%!%!%!!!%%?!!%%%%%!!%?%%%%!%%?!??%?!%%%%!%%%%!%%!!%?%%?%??%%!!?!%?%%!%%%%!!?%!!!%!%!%%!%%%?!%!!!!%?%!%%!!%%%%!%!!!%%%%!!!!%%%!%%%%!?%%%!%!!!!%%!!!%%!!%%!!!!%!%%?!?!!?%!%!!!!?%%!%!%!?%%%!%?%!%%?%?!!%!!%???!%!?%!?%!%?!%?%!?%%!!%%%%%?!!%%!?!%%!%!!!%!!%!%%%%%%%%!!?%%!%!?%?%!!%?%??%%!!!%!!%%?!%!!!%!%!%??%%%?%%%?%%!!!%!%!%?!!%!?%?!!!!%?!!%?!%%!%!?!?%%?%!%!%%%%?%%?%!!?%%!%!%%%%?!?%%%?!%%%%!%%!?!%%!!%!%%%%%%!%%%?!%%%!?%!%?%?%%%%%?%%%%?%%%%!!%%?%!%!!%%%%!%?!!%%!!%%%?%!!%%%!%%!!%%?!%%%?!%?%??!!!%!%%?%%!?!%%%%?!%%!?%%??%%!%!!%%!%!!%%%!%%!%!%%!%%!!?%%!!?%%!!%!%???%!%!!%%?%!%%%%?%%!!!!%%?!%!%%%?!%%?%?!%!%!!%!%%??!%???!%?!%%%!%%?%?%!!?%%!%??%!%%?%%%%%!%!!%%!%??!%!%%%%!!%!%%?!%!!%%?!?!%%%!%%?!!!!%!%!!%%!!%!%%%%%!?!%%%!%%!%%?%!!?%??%%%%%%!?%%%%?%%%%%?!!?!%!!!!!%%%?%!!%%!!%!%%%!!!!?%%%!%%%?!%%%?%?%!%???%%%!??!?!%%!?%%%%!?%?%?!!??%%%%!%%%%!%%!%!%!%?%%%%%%!!%%?!%%!%%!!%%!%!%!!!!%!%%%?!!!%!%!%%%%!%?%!!%%%!!%!?%%%!%%%%!%??!!?!%%%%!?%%!%%%?!?!%%!%%!?%!%?%%%%%?%%!??%??!?%%%%!!%!!!%%!%%%?!!%!?%!?!%!!%?%!!%!%?!!%!%?%%%!%!%!%%!!%!%%%%!!%%!%%!%%?%%%%!%??!!%%?%%?%%%%%%!%??%!?%!?%%!%%?%%!?%!!%?!%!?!%%!%%?!??!?%%!!%%?%?%%%%!%?%!%%%!!%!%%%%!%%%??%!%!%%!!%???!?%%%%%%%!%%%!%%%%!%!?%%?!?%!%%!??!%%%%!%?%!%%%!???%%!%!%%%!!%%!%%%!%%%!!?!!!!!%%!!%?!!%!?%%%%!%%%!%!%%%!!!%%?!%!!%%!%%%!?%%%!%!!%%%%%!?%!!%%%%%%!!?%!!%!%%%?!%%%%%%!?!%?%%%!!%!!?%%%%%%%%!%%!!%!!?%??!?%%%?!!??%??!!!!%%!!?%!%%!!%%!!!%!%%!?!!?%?%!!%%%%%%!%!!?%%?!?!%%?%!!%%%%%!%%%!%!%!%?%!%?!%!??%%??!%!%%%!%%!%!?!%%%!%%%%%!?%%%!%%!?!%%??%!!!?%%!%!!%!?%%!%!?!??!!%%!%%!!!?!!%!%%!!!!%??!%%%%!%?%%!%??%!?%!!%%%?%%%%%%%?%%%?!!%!?%%!!!%%?%%%%!%?!%!?!%?%%%%%!!%?%%%%?%%%?%%?%%?!%%!!%%%!!%%!!!%%%%?!%%?%%%%%?%!%%%%?%%%!!!!%%??!!!%%%%%%!?%!%??%!%%!%?%!%%%%%%%!%%%%%%?%%?%!!?%?%?%?%%%!?!%%%??!%%???%?%%!?%!%%%?!!??!!?%%!%%!%%%!%%!%%?%%?%%%%!?%%?%%!!%%%!%%%??!!%!%%%%%%%!?%?!!!!%!!?%%?!!!%%%!?!%%%!!%%?!%?!?!%?%%%%%!%?%?%!%!!%%%!%!%%%!!%%%!!!!%%?%%!%%?!!!!?%!%%%%?%!!?%??%%%%?%!%%!%%%%!??%%!%%?!!%!!!!!%%%!!!%%!%!%?%?%!!%?!%%%%!?!?!%?!%%%%%!%%!%!!!!?!%!%%%!!%%%%%%!!%!!?%?%%%!%%%%!!??%!%!%%?%?!!!!%%%!%!?%%%%%??%%!%?%?!!!?!%%%!!?!!!!!%%!%!%???!%%!?!?!?%?%!%!!%%%!!!!%!!%%%?%!%%!!%%!%%!?!!%%%%%%%%%!!!?!%%%??%%!!%!!%%%?%!?%%?!!?!?!%?%%?%!?!!!?%%!!%!?%!?!!!!??!%%!!??!%!!!!%%!?!!%!%?%%!%%%%!%!%%?%%%?!!%%!?%!?!?!%!%%!!?%%%%%%%!!%%%%!!%%%%!%%!?%!!%!%?%%%?!!?!!?!?!%!%!%%%?!%!!!!%%%%%!!!%!%%%!%?%!!?!%!!%%!?!%%!%%%!!%?%!!!!%%%!!%?%?!!%%%%!%!%%!!!!%%?!!%!!%%?%?%%%!??%??%%?%!%?%?!!?%!!!!%!%?!%%!!?%!%%%!%%%?%!!%%%!%%?%??!%%%!!?%%%%????%?%?%%?!!!!%!%%!!?%??%?%?%%!%!!?%%?%!%!!%%%!%?%?%!%!%%!%%!%%%!?!?%%?!%%?%??%%%%%??!%%%%%?%%?%%%%!%!?%%!%%%%!%!!??%%%%!!%!%!??%%%%%?%%%!%!%??%%%%!!!!%%!%%!%%!!?%%?%%!!!!%%%!%%%!!%%%!%?!%%%!%%?!!!!?!!!?%!%%?%!%%!!%???%%%%%!!%%%%!%%?!%%%%!!%!!%!%?!%!%%%??%%??!%?%%%?!%?%%%%!%%?!%%%?%!%!!?%%%%%?%!??%%!!%%%?!%%%?!?!?%?%!%%!!%%!?!%!?!%%%%!%%!!%?%!!!!!!%!?%%%!%!%!%?!!%?!%%%!%%%!%!%%%%%?!?!!?%!%?!!?!%?%%!!!!%%!!!%%%!%%%??%%%%!!?%%?!%?%%!%!!%!%!%%%%!!?%%!?%!%!!!!?!%!%!%%%!?%?!%%%!%!%%%??!?%?!!!?%%%!%?%!?%??%%%!%%!!!%!%%!?!?%!??!%%??%%!!%!%?!?!%%%%%%%!%!!!!?!!%!%??%%!%%%%!%!!!?!!%%%%!%!%!!%%?%%%?!!!%?!%%%%%%!!%!?%!!%%%%%!%%!?%!!%!%!!?%%?%%?%%%!!%!!%!!!%!!%%%%?%%?%?%!%!%%!!%%!?%%!!!?!!%?!%!!%!!%%?%!?%%??%?!%%!%%%%!?!%!%%%%%?!%?%!??%%!!%%!?!?%!!%%!!?%%!?%%%?%!%!%%?%%%%%%!%?!%%?!%?%%%!!%%%!!!!!?!!!%!!%%%!%%%?!%!!!!!!!%%!%%%%!%?%!?%!!%?!!!%%!!!!?%?%%?!%%%%???%!???!%!!%!%%%%!%%%%?%%%%%%%?!%?%!!%%!%%!?%?%!!%!?%%!!?%?%%%!!!!%!!%!%%%%!?%%!%!!%%%%!%!%%!!%%%%%?!%%%??%%%%%%%!%%%!??%?!?!%?%%!%%%%%%!%%%%!?%%!%%!%?!%!%?%?!?!%%%%?!??!!?%%!?%!%!%%%%?!%%%%?!%%!?!%%?%%%%%!%%%%%!!!%!!?!%%!!?%!?!%%%!%?%%%%?%?%!%?!%?%%!%?%??%%!?!?%%!!?%?%!!%%%%??%!%?%%!!%%?%!%%%%%!%!%?!?%%%%!%%%!?!%!!?%%%?!?%%?!%!%!%%!!!!!!%%%!%!%!?!%?%?%%%%%!%%?%!!!%%!%?!%%?%!???!%%%!%%!!!%!%%!%!!%%!%!%%?%!%!?%!%%!!?%%!!%!%%%!!%%?%%!%%%%%%%??%?!%!%%?%%?%?%%%!%!!%!!%%!?!%!%%%%!!!%!?!?!?%!??!?%??%%!%%?!!%%!!%%!%?!!?%!??%!?%!%%??!!%!%%%?!%!!%%%?!%%%%%%!!?%?%%%?%%!%%!%%%%!%!!!!!!%%%?%%!%!%%%!%%!%%!%%?%%%!?!!%?%!%?%%%!!%?%%!%!%?!??!%??%!%?!!!%%!!!!%%!%%%?%!??%!!%!%%?%%??%%%%%%!%?!%?%!%%!?%?%%!%!!%!%?%%?%%%%%%?%%!!!%??!!!!!%%%%%!!%!%%%?%!%%%%?!%%%!%??!%%?%??%!!%%%?!!?!%?!%%!?%%%!!%??%!%!%!!%?!%?%%??!?%?!!%%!!%%%!?%%%!!%!%%%%%%%%%!!!%%?%?!??!?%!?!%%!%%%!%%%%!?!%!!!%?%%!!!%??%%%!!!?!!%%%!%!!%!%!?%!%!%!%%%%?%%%!%%%%%!%!!!%%?%!?!!?%%!%?%%!!!!%%?%?!%%%%%!%%%%?!%%!%%!%?!!%%!%%%!?!!!%!?%!!%%!!!?!%%!!!%%!%!?%%%!!%%?!%%!%%%!?%%%!?!!!?!?!%!!%!!%%?!%%%%%%??%!%!%!%%%!%%%!!!?%%?%?%!?%!%%?%%%%???!%!%%%%%%%%!%!!!%?%%!!!%?!%!?!%%%%%!%!%%%%!%!%?%%???%!?!%?%!%?!%?%%!!%%%?%!!?%!!!?!%%?%%%!%%%%%!!!%!!%%%!!%?!!%%%%%%!%!%???!!!?!%%%?%!%%%?%!?%%!!%%%!%!%%!%%?!%%%!%!%%!%??!%!%!%?!!%%!%???!!%%%?!?!!!!%!?!%%??!%%%%%%!!%!%!?!%%!%%!!!?!%?!!%!%?!%??!%%%!%?%%%!?!%%%%%!!%?%?%?!??!?!%!!%%!%%!%?%!!%%!%?%%%%%?%!!%%!!!%%!%!?%%%%%%%!%!%%%!?%%%%?!!%%%%%!%%%%!%%%?!%%??%%?%%?!!%?%!!%%!???%%%!%%%%!!!%%%!%!%%%%!!%!?%!?%%!!%!%!!%!?%%%%%%%!!!%%%!%%!%%%%!%!%!!%!%%%?%%%!%%%%!!!!%%!!%%?%??!!%%!!!%!%?%?!!%%!%%%!%%%?%!%%!?!%!%%%%%%?%!%%!!!%!%%!%%!%!%%?%!!%%%!?%%!?!%?%!?%!!%!!%?!%!?%%!?%?!%%?!?%%!!%!!!%?!!?%!%!!%!%%%!%?%!?!?!?%!!!!%%%!%!%%%!!!?!!%!!%%!%%%%%!%%%%%!%%?%%!%!%%%%%%!!%%%%%%!%!??!?!%%%!!%!%%!%%?%%??%%!%!%!!??%!?!%?!?%?%!?%!!%??!%?!?!!?!!%%!%?%!%%!!?!?%!!%%%%?!?!?%!?%?!%!%%%%%%!!!!%%%%!%!?!%%!%!%%%%?!%???%?%!%%%?%%!%!!%!?!?!%%!!!%!%%!?!?%?!?%!!%!%%!?%%!!!?%!!!??!%!?%%%?%!%%%%%??%%!%!%!%!%?!%!!%!%%%%%?!%!%!%%%%!%%?%%%%?!!%!!%!!??!!!%!!%?!?!!?%%?%%?!!!!%!!!%%!!%!%!!%%?%!%!!?%%%%%!%%?%!!%?!??%%%%%%!!%!%%%!?%!%%%?%!%?%%?%?%?%!%!!%!%%?%?!%?!!%%%%!%%%%!%?%%!%!!%!%%%!%%%%%?!%%!!%?%%!?!%%%!!%!%%!?%%%?!%%%%!!!!%%!!?!%%%%?%%?!%%%%!!!%!%%!!%%%%!%!%%?%%%%%!?!?%!!%!??!%?%??!?!%%%%!%%%?%%%%?!%!!%!?%!%%%%%!!%!%!%%?%!!%?%??!%%%%%!?%??%!%%!%!%%%!%%?!%!%%?%!!!?%!!%!%?%!?!%!!%%??!%%?!%!?%%%%?!%!%?%!!%!%%%?%%%%!!%%%%?!!!%%%!%%!%%%%%!%%%%?!!%%%?!%!%!!%%%%%%!%!%?!%%%!!?%%!%!%?%?%!!%%!?%%!!%%?!%!!%%?!%%?!%%!%%%!?%!?!!%?!?%%?%%!%!!%?!?%??%%!%%!%%%!?%?%?!%%%!!%%!!%!%!%%!?%!!!%%%!?%!%%!!!%?%!!%!%%%%%!%?%%%!%?!?!%%%%!!%%!?!??%%!%!??%!!%%???%%%!???%!%!%!!!?%!!%%?%?%%?!!!%%??%%%!%!%!%!!!%!%!%!%!%!%%!%?%%!%!!%!!?!??!%!!???%??!!!!%%%??%!%%!!!?%%%%%!??!%%%!?%%%?%?%!%!%%%%%%!??!!?!!%%!!%%?%!%%%%%%%?%?%%!%?%?!%!%?!!%%%!%%!%?!?!??%!%!%!!%%!%%!%%!!%!!?%!!%?%!?%%!%!%%%?%%%%?!!%?%%%!%%?%!%%%%?%!?%?%%?!!?!%%?%?%!!%!%%%?%%!%%??!?%!!?%?!%!%!%%%%!!%?!%??!%%!%%!!%!%??!?%%%!%!!%%%?%%!%!!!!!?%!??!?!!%%%%?%%%%%%%%!%!%!!!%%?%?!!%%!%!%!%%!%%%%%%%!!?%%%?%%!%!%%!!!%?!%%!?!%%%%??%%%!!!?%%!!%!%?!!?%%?!%!!%!?!!!%%%%%?%%%!%%%?!!!?!%%!%!?%!%%!%!!!?%?!?%!%?%%!%%%!%%%%!%%!%%!%!?!%!?%!!!%?%%!!!!!%!!!!%%!%!???%%%%%%?!!?%%!!!!?!?%%%%%%%!!?!%%%%%!?%!?%?!%%!!?!%%%%?%%??%%?%%%!?%%?%??!!%%%%!%!!?%!!!??!?%?%!%%%%%%%%!!!%%%%%!!!%%?%%!!%!%%%!!%%?%%%%%!?!?%!%!%%%!?!%?%!%!%%!%!%?!%%%!%%%!!%?%!!%%%??%%%!%%%?!?%?%!%%!%%??%%!%!?!%!%?%?%%%%!%%%!%%%%%!%%%%!%%%????!%?!?%!%?!%%%%%!%%!%!%?!?%%???%%%%%!!%%!!%%%%!!%!%!!?%%%??%%%?%!%?!!%%%%%%%%%!%%?%!%%!%%!!!%%%%%!?%%%!%!%!?%%%!%%!%%%%%%%%?%?%?!!%?!!%%!!%!!!%%%??%%??%!%??%%%?!%!!%%%%!%%%!!!!%%%?%!%%!!!%%%%%!%??%%!%%!%?!!%!!%%?%%%%!%%?!?%%%%%!?%!?%!%!!!%??!!??!%?!%?%!%%%%?!%!?!%%%%!%%%!%%!!!%!!!?!!%%!%%%!!%%??!!%!?!%!!%%?!%?%!!%%%%?%??%?%?%%%!%%%!%!%!%%!%!?%%%%%!%?%%%!%%%%!%%!%%%%!?!!!??%%!%%%?%!%%%!%?!!%%!!%!%!%!%!%%!%?!%%%!%?%%%!%%!%%!%!!!!%%%%!!!!%!%!!%!?%%!!%%?%%%%%%%??!%!!!%%!!!!%%!%%%?%%?%%%%!!?!!?%%?%%%!%???!!%!%!!%?!?%%!!?!%%?!%?!%?%%?%!!%!%!!%!!%%%!%%!%!?%%!%?%%%%%!%%!%%!%!%%!%%%???!?!!%!!%%%?%!%!!!!?!%!%?!%%!%%%%%%%%!!!%!?%%%%%%%%!%%%%%!?%%%?%!?%!!?%%!%%!!!%%%%!%%?%%%!%?%!%?!%%?%%%%%%%%!!!%%!!%!%%!?%!%?!!%%%%%!%%%!!%%??!?!%%%!!%%!!%%??%%%%!%!?%%%%%%%!!%!%%!!!%!%!%%!!%!%%!%!%!%?%!!%%!%%!!?%%!%?%%!!%!%??%%%?!?!%%%%!%%??%!!%!%%%%!!%!?!!%!%!%%!%%%!!!!%%%!%!!!%%%!?%?%%!%!!%%?%?!!!%!%?!%%%??%?%?%!?%!?!?%??%%%%!%%??%%%%%!%%!?!%%%!!%??%!!!%!?!!%%%%%%?%%%?!%!!!??%%!!%%%!!%!%!!%%%!!!%?%%!%!%!%!!!?%%%!%%%?%??%%!%%!%%%%%!?%!%%?%!!?%%%!!%%?%!?!%%?%!!?!%%%%!%!!%!!!%?%?%!%%?!%??!?!%%%%%%%!%%%%!!%!!?%%%!!!%!%%%??%%%%?!%?%!!!%%!%%%%?%!!!!%%?%!%?!!%%%!%%%!%%%%!?!?!%!!%!%!!?%%!%?%%%!%?%!!%?!%%?%%!!!%!!%!!!%%%%%!%?!!??%%!?%%%%%!%?!!%?%!??!?%%%%%!%%%%!!?!%%%%%??%!!%%%!?%%?%!!%!%?%%!!%!!?%%%%%%?!%!%!%?!%%!%!%!??%??%%%!%!%%%%%%?%%??!!!%?!!!!!!!%!%%%!%%!!%!%%%%!%%%?%%?%%!%!%%%!?%!!%%%%%!!!!!%?%!?%!%!?%%%!?!!%%%%?!%?!!%%!%!%%?%%%!!%????!%%%!%%!%%%%%!%!%%!!%%%???%%%%%%!!%!!%%!!%!??!!%!!%%%?!!%!%%?%%?%!!!%!?%%!!%?%%%%!?%????!%!%!%??!!%!%%!%?!!!%%!%!%!!!!!!%%%%%%?!!?!!%%?%%%%!!!!%!%!%%!?!%%%%!?%%?!%?%?!%??%%!!!%%!%%?%!%?%%?%?%%!!!??%?%%%!%?!!%?!!%!?!%%%?%?%!%%!%%?%!!%%!!!%!%?%%%%%!%%!%?!%%?!!!%?%%%%%%!%!%%%?%%?%%!?%!!%!!%%%?!!%?%%%!?!?%?!%!?%???!%!?!!!!?%%?%!!%!?%%?%%!!??%!%!%!!%!%??%%%%??!!!!!!!%!?!%!!!%%!!%%!%%%?!!%!%%?%!?!%%%?%%%!%!?%%!!%!%!?!!!%!%%!%??!%%??!%%%!%!%%?!?!!?!!%?%%%!!%%?!!%!%%%!!!?%??%%%%%?!%%%!?!!?!%%??%?%%?%?%%%!%%%%!!%%%?!%%!%?%%%%!!!!%%%%%%%%?%%!%!!?!!!%%%!%%%!!%!!%%%!%?%%%!!%%!!!%%%%!%%!%??!%%%%%!%!%%%%%%?%%!!!!?%%!%?%?%%%!%%%%?!%!%!%?!%!%??%%%!!!%?%%!?!%?!%%%!!?%?!?!!!?%!!!?%!!!%%??%%%?%%%?!?%?!?%%!%%%!%%%?%?%?%%%%?%%%%!%%%%%!%!!%%%!%%%%?!!?!%!%!%!!%?%%%!!%!?!!%%!%%%!%%!!!%%!%%%%%%!!?%%!!%%%%?!%!!!%%?!?!?!!%!%!%?!!%%!!!!!!?%%!%!%%%!%!?%!%?%%%?%%!!%%%?%??%!!%%%%!%%%%!?!?!%%!?%%!%%%%%%%%!!?%%%%%%!%!?%?!%?%%%%?!%?%!%?!!!!?!?!?!%!?%%?%%%%%?!%%!%%?%%!?!%%!%?!!%%?%!%!%%%%%%!%%!?%%?%%%!?%%%!!%!!!!!%?%%?!%!!%%%%!!%!!?%%%%%%!!?%?%!%%!%?!!?%!%%%?!%?!%!!!%%!%%%%%?!!!%%?%%%!!!!!?%%!?%?%?!%%!%%!%%?%!!%?%??%%!!?%%%?%!%%%?%%!!!!??%%?%%%!!%??%!%%%!?%?%??%%!%%!%!!%%%!%%%!!!??%%?%!%!%!!%!%%%%!%!%!??%%!?!!?!!!%%??!%!!??%%%!%%%%%%%?%%!%%!?%!%%!!%!%!!%!%!!%%%%%%%?!?%%!%!!%%!%%%!%%?%%%?!%!%%%?!?%?%!%%!?!?%%%%?%!%!%%!%%%!%!!%?!%%%%%!%%%%!!?%!%%?!!%?!%%?%%%%%%%?%%!?%?!%!%%!%%!!!!!%!%%%%%?%!!%!!%%%!!???%??%%!%%%!%%%%?!?%%%%%%!%%%??%%!%?!!!!%!%!%%!%?!???!%?%%%%!%?%%!!%%!%%!%?!%%%!?!!??%%%!%%%%%%%%%!%%!%!%%!%%!!%!%%!%%%%?!!%%!!!%%?%%!!%%!%%%%%%!%%?!!!??%!!!!!!%%!!!?%%!%?!%!%?%?!%%!!!%%%!%%%???%%!%!?%!%??!!!!%!%%!%!%%%%!!!%%?!?%%??%?!?!%%??!!%?!!%%%%!%!%?%!%?%?!%%!%%!!%%!%%%%%!?%%%?%%!%!!%?%!%%%%!!!%?%%!%!!%!%%!%%%?!%%%!%%%!?!!%!%!?!!!!?%!%!?%%%?%!!!%%%%!!?%!?!!%%!%!!!%!?%%?!%%%%!%%%%!%?%%?%%%%%%%%%%!%!?%%!!%!!%!!%!?%!%%!!!%!%%?%%!!!%%%%%?!??%!?%!%?!%!!?!%!?!%%!?!%%!!!!%%%%!!?%%?%!?%!!!%!%?%!%!!?!%!%!%%!!%%!%!%!%%???%%%%%!%%?%!?%?%??%?%!!%%%!%!!%%%%%%!!!???!%?%%!%!%%!%%%%!!%%%%???!%!!!??!%%%?!%!!%!!!!%%%??!%%%%%!%!?!%??!%?%%%%%%!%%%%%%?%%!?%%?%%?!?!!%!!?!!!!%%%?%?%?!%%%%??%%!?%!!%%%%%%%?%!%?%%!!!%%!!?%%!!%%!%!?%%%%%%!%!!!%??!%!%!%!!?!!%!%!!!!!%%?%%%?!??!%!!??%!?!!!%!?%??%%?!%?%!%?%%!%!%%???!%!%!%%!%!%%%%!%!?%!!%%!%!%%%%%%?%%!%!!%!%!?%?!!?%%!!%!!!%%%%!?!%!!%%!%??%?%?!%%%??%!??%!%!!?%?%%%%??%?%%!%%?%%%%%?%?!%!%%%!%%%%%!%!%!%?!!!??!%%??!??%%!%%!!%%%%%?%??%?%%!!!%??!!!%%%!%%%!??%!%%%%!%!%%%%%%?%!!%%%%%?%%?!!?%%!!%!!!%!%!?%%%!!%%!?%%??%!%%%!%?%%%?%%%%%%%%?%!?%!!%%%%?%!%!!!!!!?!%%%?!%%!?!%!%?%%!%!!%%!!%?!?%!!%?!%!%!%!?!???%??%!!%%??%%!!!%!!%?%?%!?!%%!%?%?!!!!%%%!%%!%!!%%!%!?!?%!%%!!%?!%!!!!%!%?%!%%!!%%%%!!%!??%!!?%%%%!!%!!!%%!%%%%!%!%!?%!??!%%%%%!%!%%%%!%%%%??!?%!%%%!%%%%%%!%%%!%!%%%%!%!?%!%%!%!!%!%%?%?%%!%?!%?!%%%%??!?%!%%%%?%%%!%%%%%!!?!!%!%%%!!?!!%!!!??%!%%!!??%%?%!!%%!?%%%?%%!%%%%%!?!?%!%!%??!?%%%?%!%!?%?%%!%?%%%%!?%%%%!%%%!?%!!!%%!?!%!%%%!%!%%!!!%!!?!?%%%%%?!%!%%%!%%!%%%!%%!%!!%!%!!!%%?!!%!!%%%%!%%?%%%%%%?%%?!%%%!%%??!%??%%%%??%!!!!%%??!!%%%%!%!%!%%%%?!%%!%%%!%!!%%!!!!%%?!!%%%!%!%%%?%%!%!!!%!!!!%!!!%?%%??!%!%!!?!!%%!%%?%?!!%%!%%!?%!?%?!!%!!%!%%?%%%?%%%?!%%%?%?!!%!!%!%%!%!%?!%?%??%%%!%?%?%??%%!?%!%%%%!%?!!%%!!!%?%%%%!?%?%%%?%!%%%%!!!!!%?!?!%%!!!%%%?%!!%%!%!%!%!%!%!?!%%%?!%!!!!%!%%!?%%?!?!?!!%!?!%%?!%%%%!!!!!?%?%?!??!!?!!%%!%!%!?!!?!%%!?%%%?%%!%%!!%!?%!!%?%!!?%!%%!?%?%%%??%!?%!%?%%!%%!!%!!%!%?!!%!!%%!!?%!%!!%%%%%!!%%%!%!%!%?!!%!!!%%%%!%!??!%%!!%%%%%!%%%%%%%!!%%!!?!%%%%!!%%%%%!%!!%!!!%%%!%!!!%%%?%??!!!?%!!%!?%!%%!%!%!?!%??%%%?%!?!%??%!%!%?!??!?%%!%%!?!!%%%!!?%%!%!%%%%%%%!!%%%%%?%!?%%!%!!%!%%!%%?%?!%!%%!!%!?!!%%%%%%%%?!!!?%!%%!?%???%%%!!%%?!%%%%%%%!%%%%!%!?%%%%%%!%!%?%?%?%%!%%!%!%?%%?!??!%%%!!!%!%?%%%%!!!!!%%%%%!%!??%!%%!!%!%!!!%%!%%%!!%!!?!%%%!?!%!%!%!%%?!!%?%!%?!!%!%%!!!!%%!!!!?!!%???%!!%?!!%%!%!%%%???!!?!%!%!!!??%!%%%!%!%%%?%%%!%%%!!%!%??%%!?!!!!%?!%%%%!!!%%!!!!!!%%%%!%?%%%%%!?%!!?%%%%!!!!%%!%%!%%%%%!%!%!%??!%?!%?%%%%!%!%?%!!!!%%!?!%%?%!%!?!%!!!%?%%%%%%?%!!!%!!??%!%!!!!!!%%?%!?%!%%?%%%?!!?!%%%??%!!!%?!%%!!!!%%%?%%%!?!%%%%?!%%%%%%!%!%?!!!%%!?!!%!?%!%!%!%%?!!%%%%%!!!!%?!!%!!?%!!%!?%%!?!%%%?%!?%%?%%?%!%!%%%%%!!%%%?!?%!?%%%!??!!!!%%!%%!!!%!!!!%!%?%%!%!!%!!?!%??%?!%%%%%%!???%!!!?!%%%?%!???%%%!!%%!!!%?%!%%%%!%!?%%%%%!!!%%%%!!%?%?%%!?!!%%%!!%!?!!?%!?%%%!%!!?%%?%%!!%!%?%?%%!%%%!!?%??%%!!!%%%!%!!!%%%%!!!%%%!!%%!%!!!!?%%!%%%%%!%%?!!?%%?%%!%%!!!!??%?%%%??!!%%%!%%%!%%%!%!%!!?!%?%!!%%%%!!%%!%!%%%!!%?!%?!?%!%%!?%%%%%%%%!!%%%!?%%!!?%!!?%%?!??%!?%%%?%%!!%!!!%%%?!!%%!?%%!!%%%%%%?%!%?%?!!!%%?%?%%%!?%!%!!%!%!??%%!!%?%!%?%!!%?!!?!!?%%!%?!%%?%?!%!!!!%%!!%%%%%%%%%!!!%!!!!!!!%??!!!!!!?!%!%%%%%?%?!!!%%%!!%!%%!?%??%%?%%%%!?%!!%!%%!%%??%!!%?%!??%!!%%!!!!?%??!!%!!!%%!??%!!%%?%%%%%!%%!!!?%!?%?!%%!!%?%%%%%%%%%?!%%%%%!!%!%!%?!!%%%%%?!%%!%!!!!%%?%%!?!!%!%!!%%%?%!!!%??%!%%?!?%??!?%?!!?%!!%!?%!?!%%%%!%??%%?!?%%%!?%!!%?%%!%%!!%!?%%?%!!%!%!%%%%%%!%%?%!!!%?!!!?%?%!!?!!%!%%?%%!%%%?!%?%%!!%%%%%%!%!!%%!%%?%?%%!!?%%!!%%%%!%%!?%?!%?!%?!%%%%!?%?!?!?!%%?%!?%!%?!!%%!!?%%%!%!%%?!%%!!?!%%%%!!!!!%?!%!%%!%!%%%?%%?%%%?!!%!%%%?%%!!!%%?!?!%?%%%!!%?!%%%!?%%%%%%%?!!%!!!%%%%%%%!!%%?%?!!%!!!?%%!!%%%%?%!%!%!%!%%%!%!%?!%!!%%!%!!%??!%!%!?%!!%%?!!!?%!%%!!%%!%%?%%!!%%%%%!!!!!!%!%!!%%?%%!!!?!%%?%!%!%%!%%?!!%!!%?%%%??%!%%%?!%%%%?!%!%%%%%%%!%%!%!!%%%%?%%%!%!%!%%?%%??!%!%?%%%!!%%!%%!!!%%%!%!%??%??%!??!!%%%!%%?%%??%!?!%%%!%%?!%%?!!??%%%!%%%%%%?%%!!%%!?!%%%!%!%%%!%%%%?%??!!%%%%%%%!%%?!???!!%%!!!!%!!%%!?%%%?!%?!?!%!%%%!%%!?!%%?%%?!?%%!%?!!%%%%%?%%%!!%!?!%%%%%??%%%!%%%%??!%%!?!%%%%%%%%?!%!%%%%!%%?!%!?%!!?%%!%!?!%%%??!%%%%?%%%%!%?%%?%?!%??%%!!?!!%!?!!%%%%??%!%%!%?%!%%!%%%!!%%%?%!%????!%!%!%!%%!%%%!%%%%!%%?!?!%!%!!!%%??%%%?%%!%%%!%%!%%!%%!%?%%!%?%?!??!!%??%%!%!?!%??%%%!?%!!%!%%!!%%%?%%%?%!%%!%!%%%%%!%!%!%%!%%!!%%%%%?%%%%%%!?%%!%%!%?%?%?!!!!!?%!%%!%?%!%%%%?!!%%?!%!%?%!%??%%%%!?%%%%%??%!%?%%!?!?!%%%%%???%!%%%!%%!%?%?%%%!!%!?!%%?!%!%%!!!!%%!!%%?%%%?%!!%%!%??%!%%%%!!!%!?%%!%%%%%?!?%?%%?!?!!??%%%%%!%%%%!%%!%%%%!!%%?%!?%!%!%!??%%%!%?%%!%%!%%!!!!%%%!?!??!%!%%!!%%%!%?!%!?!%!%?!!!%?%%!!!%?%!%%!%!%!!!%%%%%?!%%!!%?!!%!?%%%%%!%%!?%!!%?!%%%%%!!%!!%%%%?%%%%%%!!?!%%!?!%?!?%!!%%%%!%!%?%!%%?%!%!?%%%%%?%%%?!%%!%?%%%!!%?%%%?%%%%!%%?%%!%!??%%?!!!!%%!?%%%%%%%%!%?!!!%%%%%%%%%?%%%%%!!!%!???%!%%%!!?!?%??%%%!?!%!%?!!!!?!%%%%!!%%?%?!!%%!?!%!?%%!%?!%??%%%!%?%%??%%!%%!!?%?%!%!%!%!%!??%%%%%!%!%!!?!%%%%%%%%%!?%%??!%!%!%%%%%?%%!?%%!!%!%?!%%%?!?%%?%%%!!?%%?!!!%!?!?%!%?%?%!%!?!%!%%?!%%%%%?%%!%!?!%%%?%!!%%%!%%%?!!%%%%!!!?%%?%%!?%%??%??%!%%%!!!!%%%!!?!!!%?!%%!!%?!%%!!?%?%%?%?!%%%%%%?%%!%!%%%!?%?%%%%?%?!%!!%%!!!%%!?%!!%%%%?%!?%!%%!%%!!%%%?!?%?!!%%%%%?%!!%!?!?%!!%?%%?%%!%%%??!!!???!???!!%?%%!%%?%!?!?%!?!%?%%%!%?!??%!?%?%?%%?!%%%%%!%%!!%!%%%?%?%!?%!%%%%!%!?%!???%!?%?%%!%%%?%??!%%%?%!%!%%?%%%%%!?%%%?%?%!!!!%%???%!?!!!!!?%%!!!!?%%%!%!?!!%%%%!!%%!%!?%?%!?!!%?%??%?!?%%!%%!!!%%%%?%?!?!%!!?!!%%%!%!???%!!%%%?!%%!%%%!%!%%?%!%%%%!%%%!!!%?!!!!?%!%!%%!%%%%%%!%!%%?%?%%!?%%!?!!!%!%%%%?%!?!%%!!%?!%!!!%%%%?%%!%%%!%%!!%!!!%%%!!%?%?%%?%%%!%%%%?%%%!?!%%%!%%%!!%?%%!!??!%%%???!%%!!%?!%%%%%!?%!%!%!!%!%?%!?%%%%%%%?!%!?!%!%!%!%!%??%%!%%%%!!?%%%!%%!%!!%%?%%%%%!%%%!%!!%!!?!%!?%%!%%!!!!%%!!%?!?!?%!%%!%!?!%?%%%!!!??%%!%!%%%%%%%?%%%?%!%??%!%?!%?%!!!!%%!!%%!!%%%!%%%%%%%%%!!!!!?!%%%%?%!%%!%!?!?!%%%!!%%??!!%!!!%!!!!%%!%%%%!%%%!%%%%%!%?!%%%??%%?!%%%%%%%!!?!!?%!%%!!%%%%!%!%%!!%!%%%%%%!?!%%?%!?%%%%%%%%?!%%!?%!!%?!!%%!!%%%?%%%%%%!!?%!%%%%%!%%?%?!!%!?%%!!!%?!%%!!!%!!!%%%%!?%%%%%%%%!!%!!?!%!!!%!%?%!%!%!!!?%!%%%!%%%!??!%%%!%!!!!!!!%?%%!!???%!?!!!?%!!!%!%!%!!?!!%?%%!??%?%%!%!%!?%%!!!!%%!%%%!!!!%?%%?!%%!%%%%%!!!!%%!%%%?!%!%!%!%%%%%?%!%%%?%!%!%!%%!%!!!!%?!?!%%!%%%!%!%%%?%%%%%%!%!%%??%!?!!!%?!?!!%%?!%%?%?%%%?%!!!!?!%%!%%?%%%!%%!?!!%!??!%!!!%!!?%%%%!%%%!%%%%?%%!%%%?!%%!!?%%%%%%%%!%!%%%%%!!%%%!%%%!!%%%%%!%!?!%!?!%!?%%!!%!%%%%!%%!!%%!!!%%!!%%%%?%%%?%!%%?%%%%?!%?%%!%%!!??!%!%?!%%%!??!%%!!!%%%%%!!!!?!?%!%%!!%?!??%!!%%%!?%?!?%?%?%%!!!%!%%%!%!%%%!%!%%!?%!!%!?%!%%%%?%%!%%%%!%!?!!%%%%%%%!%?%%??!!!?%%!%%!%%%%??%??!!??!!%%%!!!??%!!??!!%%!%%%%!!%%%!%%%%?!%%%%%?%%%%!!!!!%!%?%%?!%!?!%!!%!?!!!%!!!%?!%%!%!%?%%!?%%%%%??%???%?!%%%!%%?%%?%%!%?%%!!???%??!%?%!?!%%!?%?!!??!%!??%!%%%%!%%%?%!%%%!%%%%%!%!?!!!!??!%?%%%!%%??%%!%%%?!!%?!%%%!!%!?!!!?!%%?!!?!!?%!%%!%!%%%!%!%!%?!?%%%%%?%%%%%%?!%!%!!%%%!%!!%%!%%%!!!%!!%!%!%%?%%%?%%%%!%!!%!%%%!%!%%%%!?%?%!%?%%!!?%?%?!%%%%!!?%?%?%?!?%%%!?%!?!?%%!!%!%%?%!?%?%!?%%?%!%%%%%?%??!!?!%?%?%!%?!%!%!!%%??!%!!!%!%?!%!!?%?!%%%%%!!%%%!??!!%!!??%%%%!%%%%?!?%??!%%%!%%%%?%%?!?!!!%!?!!!!%%!%!%!?%%%%%!%!!%!!?!!?!?%!%%!%%!%%!%?%!%??!?!%?%?%%?!!?!!!!?%%!%?!!%!!!!!!%?!%!!!%%?%?%%%%!%%?%?%?%%%?!%?!%%%!!%!%?%?!%?%%%%!%%%%%%?%%!%!%%%%%%?!!!!!%%!!!%%%?%%?%%%!%?%!!?!!%!%!?%%%%!%%!!%%!%%%?%!%?%!%!!!!%!%%%?%!!%!!!%!%!%!!%%!%???%%?%?%!!!%!%%%?%!%%%!%?%?!?!%!%%%!?%%%%%!%!!!%%%%%!!?%!?%%!%%?!%!?%!!!%!!?%%%%%%!%?%!?%%!%!%?%!???!%%%%?%%!%%%%%%%?%?%!?%!??!??!!?%%?!?!!?!!!%!%%%?!%%?%?!!?!%??!!%!%%!%%%?!%?%?%!!!%!%%%%?%!?!%%!%!!?!%??%%%%%!!!!%%%!%%%!!!%%%!?!!?%%?!%!?%%%%!%!!!%%!%?%%?%%!!%?!%!?!%!%!%!%%!%%???!!!!!??!%%%%%%!%?%!%%%%%!!%!!%!%!!%%%!!!!!!!%?!!%%!!%%!%%%!!%?!%%%!!?%?!%?%%?%?%%%!?!%??%!!%%%!?%!?%%?%!%!???%%%!%?!!%?%!???%??%?!%!?!%%%%!!%!%!%!%%!%%%%!!%%?%!%%!!!%%%!!%%%%%?%?%?%!%!%!?!%%%%%!!%%!!!!%!?!?%!!%%!%%!!??%?%%%%%%%%!%%!%!??%%?!%%?%?%!%%!!!%%!!%%%%%%%!%!?%%!?%%?!!!?%%%!%%%%!!!%?%%!%!%!!%%!%%%!%%%?%!%?%?%?!?!!%%!!!!?%?%%?!?%%!!!%!!!!%!%%%%!%!!?%%!%?!%%%%%!!?%%?!%?%!!%%!%???!??%!!!!?%%!%%%%%!!!!%%??!%??%?!%%%!!%!??!?!%%!!!!?%!??!?!%!%!%!%%?!!%?%%%?%!%%!%!?!%???!%%!%!??%%?!!!%%%?%??%!%%!???!%%!!%??%!?!%%?%?!!!!??%%%%%%%!!!!%%!?%%!%%%%%?!?%%%%%%%!%!%?!%%%%%%%??!%!%%!%%%!!?!%%!?%%!?%!?!%?!?%!!%%%!%%%?%?%!%%%?!%!!??!%%?%?????!!%?!%%!%!!?%??!!%!!!!?!%!%?!%%%%??!%%?!!!%%?%%!%%?!!%%!%!!!%!%?%?!!!!!?%%!%%!?%%%%?%%?%%!!%%!%!!%!%?!%!?%?%?%!%%%%%!%?%%!!%!?!%%%?!?%%?%%!!?%%!%?%!!%?!%?%%!!!!?%%%%%!%%!%%!%%!!!%%%%!%%?!%?%?%%?%?!%%%%?%?%%%!%?!!!%%%%?%%!%%!%%!?!!!!%%%?%%%!%%%?!%%%%?%%!%!%!!!!!!!?%%!%%%%!%!!!!%!!%!%!!!!?%%!%%%%!%%?!?%%!!%!!!?!!!%%%%%!?%%%%!%%%%%!%?!%%%%!%!!?%%?%?%!%%%!!%%??%%%%%!!?!%!!%%%%%%!?!?%!!%%!%!%!!?%!!%%%%!?!%%%?%!%!??%!!!!%%%%%!?%?!%%!?%%!?%%%!%?%?!%?%?!%?%!?%%%%%?%!!!?!?!%???!!%!%%%!%?%%%%!?!!%!%%!!!%!%%%%!?!!%%%!%%%!%!%!%%%?%%%%%?!!%!%%?%?!%!%%?%%!%%!!%%!!%???%?%%??%%%?!%%%!!!!!%%%%%%!!%!!!%!%?%?%%%%%!%%!%!%!!%%%?!!!%!%?%%%%?%%!%%??%%?%%%!!%%%?!??!%!!%!?%!%%??%%%!!!%!?!?%!!%!!%%!?!!%!!?%?%%%!!?%?!%%%%%!?!?!%!%!%%?!!?!!??%%!?%?%!%%!???!%!!!!!?%%%!%%%%%!%%!%%!!!?!!%%!%?%?!%!%%%!?%%%!%?!!%%%%%%%%%%%%%!!!!%%!!?!%%%!?!%!?%%%%%!%??!%%%%%?%!%!%!%%%!%%!!!!%!%%!!%%%!!%%%!%%%%!%%!??%!!?!!?!!!!?%%%??%%%?%%%?!%%%!%%%!%!%!%!!!?%!%%!%!%%!%?!%%%?%?%%%?!!%!%!!%%!%?!?%!%!%!%?%!%!%!????!%%!!%%!??!?!!?%%%%%!%%%!?%%??%!?!%!%!%?%%?%?%%!?!%!!!!%%!!!%!!!!%!??%%!!?%!!??%!!!%!%!%!!%!%%%%!?%%!%!!?%?%%!%%%!!!?!%%%%%%!!!%!!?%!%%%%%??!?%%%!%!%%?%%!!%!%!%!!%!?!%%%%!?%%%%!!%!%!?%%??%%!?%?%!!!%%?!!!%!!!!%%%%??%!?%%!?!%!%%%??!?%!%%%%%%!%%?%!%!%%%!%?%!!!???%?%%%%!!%%%%!?%%?%!%%!%%!%!%%%!!!!!!!!%%!!?%!?!%%!%?%%%%!!!%!!%%%!?%%!%!!!!%!%%?!!?%!%!%!!%?%?!%!!?%!%%%?%%??!?!??%!?!!!?!%!!?%%%?%!??%!!!%!!%!?%%?!%?%%?%%%!%!%!%%%!!??%!%!!%!%%!!%%%!%!!%!%!%??%??%%%%!!!?%%%%?!%%!?%%!!%!!?%%%%?!!%%%%%!%%?%%?!?!!%%!%?!!?!!?!%%%?%%!%%%%%!%!%!?!?!!%%%!%%?%?!?%%%%%%%%?%%!%%%!?!!%%%?!!%?%?%?%%%!??!%%%!!?%!%%?%!!!!%%?!%%!%!?%?%!%%%%!!!%%%%%%%!!%%!%%%???%%%?%??%!%!%!%!?%!%?%?%?%!!%%!!!%!%%%%!%%%%!%%%%%!%%%!%%?%??%%!%?%!%%%%%%%%%%%?!!%%!!?%!!!%!!%?%!!%%?%%%%%%?%!!!%!%!!%%?%%!!!!%!%%!!!!!!%%%!%%%!%%!%%%?%!?%%?%!%%%?!%%%!%%%%?%!!%!%%!%%%?!%%!%!!%%%!%%%!%%!!%%%!%!!%%!?!%??%%%!!%%?!%%?!%!!%!!?%?!%%!%%%!%?!%%!!!?!%!%!%%%?!%!!!??%%%!%%%%?%!%%%?%%!!%%!?!%%!%%%!?%%!%?%!!%?%!!%!%%%!!%!%%%!!?%!%%%%!%!%??%%!!?!!%!%??%%%!!!!!?!%%%%%%?%%!%!%%!???%%!%%!?%%!%!%!!%!%!%%%%%!%!%%!!%?!!!!%%!!!%!!%%!!%?%%%!%?%?%%!%?%%%!%%?!%%%%%!%!!%!?%!??!%%%%%%!%%!%!!%!!%%%%!?%%?%%%?!%?%!%!%!%%!%%?%?!??!%%%!!?%!%%%!%%%!%%%??!?!%%%%?!%?!?%%%%!%%!%?!%%!?!%%?%%%!?%%!%%%!!!!%%??%%%??!%?!?!?%!?%%!%%!%!%!?%!??%%!%%!%!!%%%?%?!?!%%!?%!!??%%%!%?!!!%?%!!!?%%%!%%%%%!%%?%%!%%%%%?%%%%!%%!%!%!%!%%%%!!!%!?!!!?%%?%!%%!?!??%%%?%!!??%!!%%!%!%%!%!%%!!%!?!!%%?%%?%!!?%%%%?%%!%!?%!!%!?%%!!!!!%%%%?!!%?!!?%!%!!!%!!%%!!%!!%%!!%!%%!?%%!%!%!%!%%!??%!%!%?!%!%!%%%%!!%!?!!%%?!%!?!%!%%!!!?%?%%!?%!?%?%%%%%%%%!%??!%!!!?!%!%!!%%!??!%!!%?%!?!!!%%%%!%?!%%%!?%?%%!%%!%%!%%%%!?!!!%?%%%????%%!%%%!%?!!?!!!%!!?%!??%!!%!%%%?%!%%%%?%%!%%%%!?%!!!%?%%%!?%%!%%!!??!%!?!?%%%%%!!%%%%!%!!!%?!?%!!%%%%?!!!?!!%%!?%!%!%%!!!%!%!%!?%%%!?%%%!%?%!??%!%???%%!%%%!%!%!!??%!!%!!!!%!%?!%%%?%%%%!%!%???%%?%%%!%%%%%?%%%%!%%%%!?!!?%%!%?%?!!?%%%%%!!!?%!%%%?%!?%%?%%?!!!!%%%!%%!?%?%!%%%!?%%%%!%!!?!!!!!%%!?!%%%%!?%%%!%%!!!%!!!!%%%!!%%%%!%??%?%!!?%?%%!%%!%%?%%?%?%!!%!%%%!??!%%%!%%!%%%?%!%!%%%%%%%%?!??%?!%?!!!?%%!%%%!%%%!%%!%!%%?%!%%%%%%?!?%!?!%%%%!!%??%%!!!%%?%?%??!%%%?%%%%%%?%?%!?!!%%!!!%%%%%%!?%?!%%%%!%?%!!%!?!%%%%%%%%%!%%!%%!!!%%%%?%%??%?!%??!?%?%%%%?%%!!%!?%%%%?%%!!!!%%!%!%!?%%!!!%%%!%%!!?%!!%?%!%??%%%%!%?%?%?%?%%!!!?%!%?%!?!?%!?%!!?%!!?%!%%!!%?%!%!%%%%%%%%!%%%!%!!%!?%!!!%%!?!%!%?!?%%%%%?!%%??%?!%!%!?%%?%!%!!?%%!!!!!!%!%?%%%?%%%?%?%!!%?!?%%!%?%%%%!%!!%!!!%?!%%%!!!?%%%?!%%?%%?%!!!%!%%!!!%!!?%?%!!%%%!?%?%%%%!%!%%?!%%!%%%%?%!%?!%%!?!%%!??!!%%?!%??%%?!!!!%%%%?!!?%?%%%%%%%?!!%%%%!%%!%??%?!!%%%!?%%!???!?%%!%%!%?%%%!?!%??%%%%??%!!%?!%!%%!%%%?!%!!%%!%%!!%%%!!%%%!%?%!!%?!%!!?%!!%%%!%?!?!!%%%!!%????%%%!%?%%?%!%%!%?%%!%%%?!%%!!?!%%?%%%!%%%%%!%%!!%%%!%%%%%?%%%!?%%%!?%%!%?!%!!?!%%%???%!%%%!%%%%%%!%%!!?%?%!?%?!%??%%!?%!%%?%%!??%!!!!!?%?%%!%%?%!%?%%?!%!%%%!%!%!!??!%%%?%!%!%%?!%!%!%%%%!%%?!%%!??!%%!%!%!%!%!%?%%%%%!%%%%!!!?%?!!%%!%%%??%???!%%?%!!?%%%!!%%%!%%%%???%!!!%%!%!%%?%%%!%%?%?%%!?%?!%!%%%!!!%%?%%%!%!%!?%?!%%?%!!?!%%!%!%!%!?%!%%%!%!!%%!%%??!!%%%%!%%%%%%?!??!?%!%%!%!%%!?!!%!!!!%!%%%%!!!%!!!%%!%!%!%%%%%%!?%%!?%%%%!%!%%%!!!!?!%%%%%!%%%%?!!%%!%!%%!!%%%%%??!!?%%!%!%?%!!?!!!%?%!%%!!!%?%!?%%!!!!!?%%?%!%?%!!!!?!%%%%%!?%%%%!?%%??!!?!!%%?!!%%!?%!%%!!%%%%%!!!!%!!%%!%%%%%%%!%%%%%!%%%%%!!?%?!!!%?!!!!!?%?!!%%?%%%%!!!!%%!!%%!!!%%!%!%!?%%!!%!!?%?!?%!!%!?%%%!?%!%!???%%!?!%%%?%!?%!!?%%!%?%%!%%!?%?%!!%%%?%%%%%%%%%?!!%?!%!%%?!%!?%%%???%%%?%!?!%!%!%?%!%%%%%%?%!!?%!%%?!?!%!!??%?%%%?%%!!!?!!%?%?!?%!!!%!%!%!%%!%%!!?!%!!%%!%?%!%%%!%%?%%!!!%%%%%!!??%!?%!!?%%%!%!!?%??%%!%!%!%!%%%?%!!!!%%%%!!%!%%!%%%!%??!%?%?!%%!!%!!%!!!%!!?!%!!!!%%!%%!?%!?!%!%?%%%%%%%?%?%!!!!?%%!??%!%!?%%!!%!!???%%!!!%!%!!%?%%!%%%!%%!!!!!!?%!%%!!!%?!%%%%?!%%?%!!%!%!%%?!!%%%!?%!%%!%%!%!!%!%!!%!!%?%%!?%%%!!%%!%!!%!!!%??!!%!!%%%%!%%!!%!!%!!?!%%%%?%%!!!%!!?%!%%%!!!?!!%!%%%!%%!??!!%%!!!?%%%%?%!%!%?%!!!??%?!!?%!%%%?%%?%!!?!%?!%%!%?!%%?%?%%%%%%%?%!?%%!%!!!!%!!%!%?%%%!%!?%%%?%!!%?!%%?!%!%%!??%%!%%!%%?!%%%%%%%%!%%!%%%%!%??%%?%??%!%!%??!!?!%!%%?!!%%%!!!%?%!!%!!%?%!%!%%%%!%!%!%%!%?%?%!?%!%%??!!!%!%%!%!!!!!%%%!%!%!%%!!!??%%??!!%%?%?%%%?%!!%%%?!?%%%!!!%!!!!%!%%!!%!%%?%!%!%!%%%%?%!?%%%!!!%%%?!%%?!?%!!%%%%%%!%!!%%?!%!%%!%??%!%!%!!!!!%%%%?%!?!!!%!!%!?%!!%!%%%!!%%!!!%!?%?!!%?!%!!%%%!!!%%%%!!%%?%%!!%%!%%?%%%?!!%?%??!%%%%!!%%%!?!!?%%!%%!!%%%!!%!%?!%%!%??!!!!%!!!%!%!%%%%%%%!?%%%%%!%%%%%%%%%%%%!%%%%!!%%!?%!!?%!!?!%%%%???%!?%!%%!!!%%!!!%%%!!%%%%%%?!!!!%?!%%%%!!%?%!%%%!%%!%%%!??!%%%%!%??!!!!?%?!%!%!?!%!?%!!%!%%?!!%%?!?%%!?!?!%!!%%!!??%%%%!%%!!%%!!!!%%%%!%%%%%%?!?%%%%!!%!%%%%!!%%%%%!%%!%!!!!?%%%!%!!%%?%%?!%!!!%%?%!?!%!%!%%%??%%%%%?%%!%%%!?%!%%%??!%%%!%!!%%?%%!!?!!?%%%!%%!%!!%!?!?%!!%!!!!!%?!!?%?%!!%!!!!?!%?!!!!%%%!?%%%%%?%%?!!%!!%??!%!!%%%!!!!%%?%%%!!%%!!!%%!%%!!%!%!?%%!!??!%%!!%?%%%?%%%%%!?!!%!!%!!!?!!!!?%!?%%!?%!!!!%%!!%%%?!?%%%?%!!%%%%!%%!?!!%%?!%?%%!?!%%%%%%!%%%??!%!%?%%%?%%%!???%?%%!%%%!%%%!!%%%%!?%%%%!!!%!?%%!%!!%%%%!%?!%!!?!!!!?%%%?%!!!!%%!!%?%!%?%?!%!!%%!?%?%!!?%!%!!%!%%!!!%!%!?!!?%!%%?%?%!%%!%!%%%?%%!?%%%%%%%!?%?!%%%%%%?%%!%!%??!%%?!!?%!%%%%%%%%%?%?!!%%%?%%!%%?!%!?!!?%%?%%!%%!!%%!!%!?!?%%!?!!%!%!!!?!%!!%%%?!!?%%%%!!?%!?!?!?%!%%?%%!%%%?%?%%!?%!!?%??%!!!!??!%%!%!%!!%!%!?%%%%%%%!%%!!!%!%?!?%!%!!%!%%!%%%!!%!!%%%!%!!%%?%%?%%%!?!!%%%%!!!!?%%!%!%!%!!!?!!!%!%!%%??!!?%?%%!%?%%!%%!!%%?%%%!%!!%%%%%!?%!%!%%%?%!!%%%!%%?%!%%!%!???!%?%%!%!%%?%%!!%%!%%%!%%%!!%!???!!!%!!%%%%%%%!!!%!%!??%?!?%%??!!%%?%!%%?!%?!%%!%%!%%%%%%!!!?%%%%%!!%%%?!%%%%!%!%!%?!?%!%%%%!!?%!!?!!%%?%%%%%!!!%%!!?!%%!!!%%!%%%%?!!!!%!%!!!!!%?!%!!%%!%%!!%%!%%%%%!%?%%%?%!%%%?!!%%%!!!%%%!%%?!!%!!!%!%%%%%%%!!%!!!%?!??!%!%!?!!%!%%?!!!!??!?%?!%??%!%%%%!!%!!!%!!!%?!%!%%!??!%!%!!%?!%!!%%!%?!%%!?%!!?%!!%?!%?!%%!!%!%%!!?!!!%%%!%!!!?%!!%!!%!%%!!%%%%%??%%!?!?%%!%%!!!!%!?!%%%%%%%!!%!%%!%!!%!%!?!!%%%!%%%!!%?%!%!%%!%%%%%!?%%!?%!!!%%!%%%?%%?%?%!!?!%%%!%%%%%?%%%%?%????%%%%!!!!!%!%%%%!?!?%%!%!!!%%?!!!%%%!!%%%%%%%%%%%!%%%!%!!!!%%%!%%%%!!%!!%%%%%%!%%!%?!%%!%!%%%!%%%!%!?!%%!%!!?!%%??!%%!!%?%!?%!!%?%%%%?%%%%%%%!%%!!%%%%!?!%!!%%%!!%%!%!!%!%??%%%?%?%%??!!%%!?%%%!%%!?%%%??%%%%!%%%!!??%?%%!%%!%%?!!%!!???!?%%%%%!%!!%?%?%%%!%%%%%%?!!%%?%?!%!%%%%!%%%%%!%!!?!!%?%%%!%?!!?%%!???%%!%%%?%%!%!%%%%%%%!!!!%?%%%%%%!!?%!!!!%%%!%!?%%%?%%%!!%!%?%%!?!?%!!%%!%%%%?%?!%!!?%%!%!%%!!%?%!%%%%%%%%%%%?%!!%!!?%%%?%%%!%!!%%!!%%%%%!%%!!!!%%!!!%%%%%?%%%%%??%?%?!!?%%%%!%!%?!!?!%%%!!%!?%?!!%?!!%%%%%%!%!!%!!!!??%?!!%!??%??!%!%%!%%%%%%!!%!%!%??%!%%%!?!?%!%%!?%%%?%%!?!!!!!%!!?%!!%%%%%%%%%%!!%!!!%!%%%!!!%!?%%%!!%%%!%!%%%!?%?!!%%%%!%?%%%!%%%!%%?!!!%!%?%?!!!%!%%%!%?%%%!%%%!!%%!%!%?!%%!!?%%%?!!!?%%%!%%%!!!!%!!%!%%%?%%??!%%%!?!!!%%!!!!??!%!%?%%%%%!!%%!!!!%%?!%!%%%!%!%%%%!%%!%%!%!%%%%%%%%%?%!?!!!%%!!%?%?%!!!%!%%%!!%!!%%%%%%%%??%%%!%?!%%%%??%!??!%%!!%%!%%!?%%%%!!!%%!!!%%!%%%%%?!!!%%!%!!%%%%%!%!!!!??%%!!?%!!!!!?!%%!!%?%!!!%%!??%!?!%!%!?%%%!?%%%!%%%!?!%%%%%%%?!?%!??%!%%%!%%%%?%%%%?!!%%!!%%%!%%!%!%%!!%%!%?%!!%?%%%%!!?!!%%!%!%%?%!%!%!!??!%!%!%!%%%!!%%?!!%%?!?!%!??!%%!%%!!%?%!%?%%%%!%!?%%%?%%%!?!%%!%!%%?!%!!%?!!?%%!!!%%%!%%%??%%%%%%%%?%!%!!!%!%%!%!%!!%%%!!%%%%%%?%%%!!?%!%!%?%%!%%%%!%?%%%?!%%%!%%%?!?%!!?%!%%?!!!!%!%%%%!%%?!?%!%%%?%%%!??%!!!%%%??%%%%???!!%%!%%%%%%%%??!%!%%!?%!%?!!%?!!!%!??%?!%%!%!%!!!!%%!!!!%!%?!%?!%!!%%%!!%%%%%!!%!?!??!%%%?!%!!!%%!%!!%!%!!%!!%%%%?!??!!%%!?!%!%%!%!%%!%!%!%%!!?%!%!%!!!?%%%%%!?%?%!!%!%!?%?%%!%%%!%%!%%%%%%!!%!%???%!%!%%!!%!%!%%%%%%?!%%%%%%!!!!!!!%%!%?%!?%!%%!%%%%!?!%%??!%!%%%%%%%!%%%!%%%%%??%%%%!%%!!!?%%??%!%%!?%%!%?!!!%%!!%%!!!%%?%!%!!????%!!%%%!?%!%%%%%?%%%%%%?%!%!!%!%%??!%!!!%!%%%%%%!%%%%%%%%!!%!%!%%%%!%%%%!%%%!%!!%%!!?%?%%%%?%%?!%%%%%!%%!?%%!!%!!%!%!??!%!%%%!%%?!%?%%??%%%%%%!%!!%!%!!%!!%%?!??%?%!%%!?!!%%%%%%?%%%!%%?!%?%!!??!%%?!!?%!%!%%%%?%!!%!?%??%%%%???!!%!!%!%%%!%%%%%?%%%%%%%%!%%?%%!%!%?%%!%!%%%%%!??!%%!%!%%!%%!!?%%!%!%%!%%%%!?!%!%!??%?%!%!!!!!%?%?%%%%%%!!%!%%%!%?%%!%%!?!!!!!?%%!%%%%%!!?%?%!%?%%!%!%?%!%??!!!%!%%%!%!%!!%?!%!%?!%%!%%%%!!%?%%%!!?!%!%!?!?!%?%!%!%!!!!%??%!??!!!%%%??%!??!!%???%!%!%!!!?%!%?!%%%%?%%%%?!!?%!%%%!%%%!!%%!!%!!%%!!!%??%!?!!!%!%%!%!?!!%%?%%!%!%!?%%%%%%!?%!?%!!%!?%!!!%!%!%%%!?!!%%?!!%!%!%%%!%?!%!%!!%!!%!%%%%????%%!?!%%%%%!%%????%?%%!%%!!!%%%???%!%%!%!%?!!!?!!!!!%!!%%?!%??%%%!!!%%%%%%!%!?!%%%%%!%%!!!%%%%%%!%?%!!%??!%!%%!!??!%!?!%%%%%%!%!??!%%!%%?%%%%%%%%?!?%%!!%!%%!!%!!%%!%%%?%!?!%%%?%%?%!!%%?%!!??%?%%%%!%!?%?%!%!%?%!!%!%!!!!%??%%%!%%%%%%?%%!%%?%!!?%%%!!%%%?!%!??%%%!!%?!%%%!%?%!?!!?%!%!?%?!%%%!%%!%?%%!%!%!%%%!%!%?%?!!%?!%%%%%?%!%!%!%!!%!!%%%!%%%%?%?%%%!%%%%%%%%!!%%??%!?%!%??!!%%!%!%%%%%!%%??%!%!?%!%%!%!?!!%!?!%!?%?!%%!!!%%%!!%!%!%%!%%%!?%?%%!%%%%!%%%%%%?%%!?!!%?%?!%%?!!?%!!%%%!?!%?!%%!?%%!!%%%?!!%!!!!%!%!??%!!?%!!?%%%%!%!%%%%!?%?%%!%?%!!!!!?!%?!??%%%%!%?!%%%%%%%%!%%%%!!%%?!%%?!%%!!!!??!!?!%%%!%%!?%%!!?%!%%%%!%!%?!!%!?!%%?%%%%%!%%!%!??!%!?!%!!?%!%%%!%!%!%!!!?%%%?!%!%!%%!%?!?!!%??%%!%%%%!!!!?%%!!?%%!!?%!!%!!%%!%%!%%%%%?%?!!%!!%%??!%!%!%?%%!%!?!%%%%%%%%%%?!!?!%!%?!%??%!?%%!%!?%!%%%%?%?%%%%!!%!?!%%!%%%%%%!%?%!%?%%?!%?%!%?!%%%!%%%%%?%!%%%%%%%!??!%%!%%%?!?%%!?%?%%??!%!!%!%!!%!!%%%%%!%!!%%!%!%!%%!?%%%%?%!??!%!!?!!?%!%%!!!!!!!?!??!%%%?!?%!!%!?!%?!?%!%!!%!%!!%%?%%!%%%!!%%%%?%%%!?%%%!%%%?%?!!%%%??%%!!!%%?!%%%!%%%?!!!%!%%%!!%!!!!!!%!%%!?!%!?%?%%%!%!%?%??%!!%%!?!%%%!?%!%%%!%?%%%%!?!!%!%!%%!!%%!?%%?%?%!!?%!?%?%!%!?!?!%!!?!!!%???!%%?!!%!!%%??!%%!%!!%%%!!%%%!%!!?%%%?%%%%!?%?%?%%!%!!?!?%%?%!%%!%%%%!%!%%%%%!?!%!!?%!!?%%!%%!%%%!!!%%?%%%?%%%?%%!?%%%!%!?%!!%%!%!%%?%!!%%%?%!%%???%%%%!!%!!!!%%?%%%%%%%%%!%?%!?!%!%%!?!?%!!!%!!??%%%%!!?%%!%?!%!%%%%?%%?%%??!%%%%?%?!!!%!?%!%%?%?!!!%!%!!%!%?%%?!%%!%!%!%!%??%%%!%!%%%!??%%!!!%%%?%%%%!?!%?%?%%!%?%!!?%?!%%%?%%!%!%!!%!!%%?%%%!!!!%!%!%!%%?!!%%%?!%%%%!?%!%!%%%%%%%!!%!%%%!!%!%%!%%%??!%%??%%?!?%?%!??%!??%!%!%%!!%!%!%?!%%%!!!%!%!!%!!!%%!%!!!%%?!!!!!%!?!?!%%%%!!%?!!!%%%!%!!%%?%!%!!!%%?!%%!%!!%?!%%?%%%%%!!!?%%!!%%!!%!%!!%%!%?%!?%%!?%%%%%%%%%!???%%!%?%%?%%%%!!%%%%!!%%!%!!%!!!?%?%?%?%%!%!%%%!%%!!?%!%%!?%%!?!!%%%%%?!%!?!%%%!!!%!%%?%!!%%%%!!?%!%%%?%%?!?!%%%?!%!?%!!!%!?%!%%%%%!%%%%?!%%!%%%!%?!%!%%!%!?%!?%%%%%!?%%%!!?!!?%%?%!%!%%!%!%?%?%%%?%!!!!%%!%?%?%%%!!!%%!%?%!%?%!%%!?%%!!!?%%!%%%%%??%!%%%%%!%%?%?!?%??%%!%!%%%!%%!%%%!!!%!%!%!%?!%?!%%!?!?!%??!%!%%%!%%?%!?!!%!!!?%%%%!!%%%?%%%%!!!?!%!?%!!%!?!!!!%%%%%!?%%?%%%???%%!%!!%?%!%!!%!!?%%%%!!?!?!%?%%!%!%%%!?!!!!%%!%??%%!%%!%?%!%!?!%!?%%!%%%%%!%%!!!?!!%!%!%!!!%%??!%??!!%!%!%%%!!%%?!%%?!??%%%?%%!!!%%!%!%?%%%!!?%%%%%!?%!%?%%%!%??!?!?%!%!%%%%!%%?!!%!!%?!?%%??%%%%%?%!!!%!???!!%!!%%?%?%%%%%!?!!%%!%%!%%%%%?%%%??%!%!?%%%%!%!%%%%?%%%??%!%%?!???%!%%%%%!%%%?!%%!!!!?!?%?!%%!?%%%!%%%%%?!!%%!!?!?!%!?!!!!%!??%!!?%%!!?%%!!%!%%?%%%%!!%?!?!%?!%??%?!%!%%!%!!!!%!!!!%??%!%!!%%!?!%%?%!!!!!!!!?!%!%!!%%%%?%%!%!?!??%%?%%%%%%%%%!%%%%%%%%!??%%%%??%!%%!%?!?%%!%%?%%!%%%%%%!!%%?%?%%!%%?%%%%?!!?%%%%%%!?%!%%!%!??%%%!%?%!%!%!%?%%?!%%%%!%!%%%?!!!%%!?!?!?%!!%!!%!%%!%%%?%!?%!%!%%%%!!%%%!?%%?%!??%%!%!%%%!%%?!%?%%?%?%%%%%%!!%!?%%%!%!!%%!!%%%%?!%!%%!?%?%!%%!%%%%?%%?!!%%!??!%!%!!%??%!!%!!??%%?%%?!%%!??%%?%!!!%%????!?%%!%!!?!!!%%%?%?%%!%%%!%%?%%?%%%%%??%%?!%!%!?%%?%%!!!%!%%%!%%!!!%!%?%!!%%%?%%!%!?!!!!!!!!!%!?!%!!%!%?!%!!!??!%??!%!%!!%!%!!!!%?%%%%!!!%%?%%!%%%%!!%%%%!?!?%%!!%!%!!%!%%%%!%!%!%!?%%%%?%?%!%?!?%!!%%%%%%!%?%!%??%%?!!%%!!%!%?%%%%!%?%!%%%%%%%!%!%!%%!!%%!%!!%!%%!%!?%!%?!%!%%%?%%?%!%?%%%!%%%%%!%!%%!%%%!%!%!%%!%%!!!?%%?!?%%%?%%??%%!%!%%%%%%%%%!%%??%!!!?!%%%!%!%?%!!!%!%!%%!!%!!???%%!?%!!%%%!!!!%%%!%!%!%%?%%%?!%%%!!%%?%%%%!!%%%!%?!%%%!!!!!!?!%!%!!!%?%%?!!%!!!%!%?%%?!%%!?%%%!%!?!!!%?%%!%%!!!!%%!%%%%%?%?!!%%!?%!!%?!%??%%?%?!%%%!%?%%%!!?!%!!?%!?%??!?!!%%?!!%?!%%?!%%%!!!!!%??%?%%%%!%%%%%%!!!?%!!%%!?%%%%?!%!%%%?%%!!%%?%?%?%!!!%?%%!?%%!!!%!%!?%%%!%!%%!%!%?%%%%%%!%!?!%!??!?%!!%%!!!!%!!%??%%%%?%%?%%!%?!?!!%!??%!!%%?!%!?%!?%%%!?%%!!%!?%%%!%!%!!%!%%!%%%!!%%!%!%!%%%%?%!%%!%%%?!?%%!!%%!?%%!%%%!%%?%%?%%!%%!%%!%%%%%%%!?%%!%%%!?!%%%?%!?%!%%?!!?!%!%!!%%??%%!%!%??%%!%!%%%%!!%%!%?%%!%?%%?!%!%!!!%%%%?!!!%?%%%%%!%?%%?%%??!!%!!!?%%!!!%!%?!?%%!%!!?%????%%%%!?!%%!??!%?!!?%!!!!!%%%%%?%?%?!!?%!!!!!%%?!!%!!%%?%%!%!!?%%!!?%%%!!%%!!%??%!%%%!!!%!%%??%?!!%!!%!!%%%%!%%?!!%%%!!%%?%%%%!!%%%%!!!%!%%?%!!%%%%!%%%?%%?%?%!%%%!?!%%!%%%%!!%!!!!%%%!%%%%%%?!%%!%%!%%%%%??%?!%%!%?!!!!!!?%?%?%!%!%%??!%%??%!%?!!!?%!%!%%!?!%%%!!%?!!%?%!%%!!!!%!%%%?!!%%%?!%%%!?%!%%%?!!%!?!!%??%%?%?!%!%!%%%%!%?%%?%%?!%?!%!!%%%!%!%!!?!??!!%!%!%!%?%!%%!%!%%!??!%%%%!%!%!%!!!!%!?!?%%%?!!!!!!!!%!%%!%%%%!%%!%?%%!%%%!%%%!%%%%?%!%!%%!!!%%%%%?%%%%%%?%%%%!%%!?%??%%?%!?%%%!%?!%!!%!%!%?%%!%?%%!%%?%%!%?%%!?%%!%%!?%!?%?!%?%%!!!%?%!!!!%%%!%%%%%?!!%%!%%!%!%%!!%%%!%%%?%%%?%%!%!!%!!%%%!%%!!%%%%!%%??%%?%?%%%?%%?!?!%%!%%?!%%%%%%%?%!?%!%?%%%?%!%%%!?%!!?!?!%!!%%!%%%%%!%%%!%?!!!%?%!??%?%%%%!%!?!?!?!??!%%%%%!%%%!!?!%!%?!!!%!%%%%%!!!%!!?%%%!%?!%%%%%%%?%%%!?!%%%!!?%%%!%!?!!%%%%!??%%!?!%!%%!!!!!%%%??%!%?!??!%%%%%%%%%%!%??%%%%%!!%!%%!!%%%!%!!%!%%%?%%%???%!%?%!%%?!%%!?%?%%%!%!%??%!%%!???!%%%%%%%%!!?%%%%!%!?%%!!!?!%?!%%%%!%!%!%%!!?%%%%?!!!?!!%%%%%%!%%%!%%%%%!!?!!!!%?!!?!%%!%%%%%%%!%!%%%%?!!%????%!?%?%?%!!%!%!!!%?!%!!%!??!%%!%%%!%?!?%%%!%%%%%?%%??!?!!%%??!%%%!?%!%!!%%%%??%%%!%%!%%?%%!%!!?%!%%%!%!!%%!!!%!%%!%?%!%%%%%%!%!%!!%!!?%%%!!?!!!%%%%!!!%??!%?%%!!%%?!%%?%%!%%%?!%%%%%%%%!!!%!%%!!!%?%%!%%!!%?!%%?%%!%%%!%%%?%!%!%%!%!%?%%?%%?%?%!%!%%%%%!!!!!!!%?!!?%!%!!%?%%%%?!%??%%!?%%%?%%%%!%%?%!!!%%!%%%%%%%%%?%!%%!!%!?%?!%!!!!%%%!!%%%!%!%?%!?%%%%!!%?%?%%%%?%%??%%?%!%!?%%!%!!%!%%!%%%!!??%?%%!%!%%!%%!%!%!?!%!%!!!%%%!?%%%%!%%%???%%!%%%!%!?%!%%%%%%!!?%%!!%%?%%%?!!!?%!!!%%%?%%%!%%%?%!%?!?%!?%??%%??%!?%%%%!%!!!?!%%%%%?%?%!%%%!%%%!%%?%%%%%%!!!!%%!!%%!!%%!!!!%!%%%%%!%%%!?%!%!!!!?%?%!%!%!%!%%!%!%?!?!!%%%%?%!!%?!!!?!!!%!%%%%!%!%!%%%!!%!??%?!?%!%%!?%!!%%%%%!%%%%!!!!!%%?%%!?%?%%%%%!!!%!%?!!%%%?%!?!%%!?!!!%!%!!%%!%?!%!?%!%?%?%?%?!??!!%?!%%%%?!!!%!??!%%!%??!?%!!!!!%%%%?%%!?%?!%%%!!!!%!%%!%%%%!!!%%%%!%%%!!%?%!!!!?%?!!!%%?%%%!%!!%?!!!!%!!!%%%%%?%!%!!!?%!!%%%%%!%?%?!!!%?!?!!?%!?!?!%!%!%%?%%!!%!?%!!!!%%%?%%??%%?!!%%!!%??!??!?%!!?%!%!!!!?!!%%%%?%%%!%??%%%%%?%!%%%??%!%?%%%?%!!??!??%%?%%%!%%?%%%!%!%%%!?!!!!%%!?%%%!%%?%%%!%?%%?!!?%!!!%%!%%%?%?%!%?????!!%!!%%%!!!??%%%%?!%!!?%%!%!?%!?!!%!%%%!%!!%%!!!%%%%!%%!%!%%?!%%?%!%!!%%!%%!%%%%%%%!%%?!%%?!%!!%%%?%%%!%!%%%%%!%%%%?%?!!!!?%%!!??%!!%?!%?%%!!%!%!!%!%!!%%?%!%?%%!%%%%%?%%???!%!%%%%?%!!%?!%!!%?%!%%%%%?!?%%%%%!%%!!!!!!%?%%!%%!%%%!!%!?%%!!%%!!?!!?%!!?!!%?%!%%!%%%?%!!!%%%!?%?%!%!%%%%%%?%%!%%%%!!!%%%!%!!?%!??%!!%%!!%%%!%?%?!!?%%%%%?%%!!%?%%?%!?%%%%!?!%?!%%?%%?%!%%%?%!%%!!%????!!?!%%%!%?%%%%%%%%%%?%!%!!%!%??%?!%?%%%%!%%%%!!?!%?%?%?!%?%%%%!!%!%%?%?!%!!!%?%!?%%?!%%!!%%%!?!%!!!?%%!%!%%!!!%%?%%!?%!?%%%%!!%%!%!!%%%!!%?!%?!?%!!!%%%!!%!!!!%%!!?%!!?%%%?!!%%%!%?%!??%%!%!?%%%!%!%?%%!%%?!%?%%!%%?%?!?!!%!?%!?%%%%!?%!%%!%%%!!%???!%%!!%%%!!!?%%!%!!%?%!%!%??!!%!?%%%%%%%%?%%!%%%%%%!%%%?!?!?%!%%!?%?!?%%%%%%!%!!%??%%?%%??!%%!%!%!%%%%%%?%!%%%!?%!%!!!%%!%!%%%!!%?!%!%%!?!!!%!?%?!?!%?%%%%%!%%!!!!?%%%?%%%?%?%!%%%!%!%%!!%!!!!!%%!%%%%!%%%%?%!??!%!%!%%%%!!!%%%!%?!!%%?%%%!%%!%%%!%%%!%!!!%%%%!!%%%!%!!%!%!%!%!%!%!?!!?%!?!%%?!?!!%!%?%%%!!%!!%?!!%%%!%%%%??%?%!%%?%?%%!?!%%%%!!!%%%!%!?!?!!%%%%%!!?%%?%!%!%?%!!%%!%!%%?!!!%?%!%!!?!%%%!%%%%?%!%%!%!%%%!%%%?!!!%%!!?!%%!%%%!!?%%%!%%%??%%!%!!%%!!?%%!%%%%!!!!??%!?!?%%?%%!%%%%?%%%%%%%!%%!%%%!%!!!?!%%!!%?%!%?!?%%%%??%!?!%?%%!!!?%?!!%%%%??!?%%%%%%?%!???%!!%!%%%?!!%%!!%!%%?!!%%!%%!!?%%!%%%%%!!!!?%%!%?!!!%!%%!%%%?%?%!%%!!?%%%%!%!%%%%!%%!%%?%?%%!%%%%%?%!%!%%!%%??!!!!%!%%%!%%?%%%!%?!?%?%%%!%!!!!%!!%%%%!!??!%!?%%%!%%??%!%%?!%%!!%%!%%%%??%?%%%%%%!?!%%%!%%%!!!!?%%%%!!!!%%??%!%%%%!!%?%!!?%?%%?!?!!??%!!!!!%%!%!%!%%?!%!%%?%!!!%!%!%%!!%%!%?!?%%!%!!!?%!%%%!%!%?!?!!%%%%%!%?%!!?!?!!!%%%%!!%%?!??%!!%!!%!!!%!!%%!!%%!!%?%%%%%%?!%%!%?%?%%?%!!%!?%?!%!%%%%!%!!!?!%!%!!%%!!%!%%!%?!!%%?!%%%!%!!%?%!?!!%%%???!!%!%!!!!%!!%!!!%!!!%%%%!%%%??!%%%?%!%%%??%?!%%%!%%?!!%%!%%!%%!!?!%%!!!%%!!%??%?%!%%%?!%!%%!%?%%%%%!!?!?%%%!%%%%%!%?!!!%!%!%%%!?!??!%%%%??%%?%!%%%%%!%?!?!!%%%%!?%!%!!?!?!!%%!%%%??!?%%!!?!%!??%?%%%?!!%%%%!%!%?!!?%%!%!%?!%?%!%%?%?%!%!%!!%!%!??!%%%?%!%!!%%%%%????%%!%!%?%%!%%!!?%%!%!%%!%%%%%%?!%%%!%%?!%!!?%!?%?%!%?%%%!!%%??!%%%%!!!!!%!%?!%%!!%%!%%%%%?%?%!%%!%?!?!%%??%%%!%!?%%!%!%%%!%!!%!!%!!?%%!?!?!?%!%%%%%!?!!!%!%%%!%!!%???%!%??!!!%?%!!!%%%%!%?%%%?!%%!%%%!%!%%%%??%???%?%!!%!%%!%!?%%%!!!%!%%%%%%%%%%%?!%!!!?!%?%%%%!?!%%%%%!%%%!%!%%!%!!%%%!%%%!!?%!%%%!%%!!%?%%!!%?!!!?%!%!%?%!%%!%%!%%!%!!%%%!!%%!%%%%%%!!!!%!%??%!%?%%%!%!%!%?%%!%%!%%%%??%%!%%%%%?!%!!!!%%!!%%!!?!!%!?!!%?%%?%!!%!!?%!%!%!!%%!!!!%!%%!%%!%%!??%?%!!!%%?!!%%%%?%??%%%??%!%!%%!%%!!%%%!%%%%!?%%%!%%%!%%?%%%???%!!%%%%?!%?%??!!!%%!??%%!!%!%%!!%!!!%%%%%%!?%%%%!%?%%??!!?%!%%!!%?%%!%%!!%%%!!!!!%!%?%?%!%?%!%!?!%%!%?!!!%%%!%%%%!!!%%!%%%?%%%%%%!%%!%%!!%%%!%%%?!!%!!!??!%%%%!%%?%!!%!%%?!?%!%??%!%%%??%!!%!!%?!%!!%!%!%%%%%!%?%!%%!!!%!!!%!!%!!!%?%!!%!%%!!%%?!%!%?%%!%%%!%%%?!%%%%%!%%%%%%!%?%?%!%%%%?%%?!%%%%??%!%%%%?%!%?!?%%!%!%!%!!%?%!%%%?!%%%?%%%!!%%%!!!%!?!!%!!?%!??!!!!!%%%%%%!%%!%?!%!?!!%%%%??%%!?%%%%%%!!%%%%%%!!??!?%?!!!%?%!%%??%!%%!?%???!%%?!%!?!!!%!%%!%%%%%%%%%%!!%%%?%!%!%%%?!!?%!!!%!%%!?%!!!%%??%?!!%!!%%%!!%%??%%%!?%%!!%%!%!%%!%!%%%!%!%!!%%%!!%%%!%%%%%%%%?%%!%?!%%!%!!%%!%!!%!?%!%%!?%!?%%%%%!%%%%%??!!?%?%!%%%%%%!!%%%%%?!!%%!%!!%!??%%%!!?!%?%!%!!%%%%!!%%%%%%%?!%!!!%?%?!!%!!?!!%?!%!?%!!?%!!!%!%?%!??!%!?%!!%!%%!!%?%!!!%%!%?%%?%!%!!!%!!%%!%!%%!%!%??%!%%%?%%!!%%!%%!%%!!%!?!?!!??!!?!!%%??%??!%%%?%%!!%?%!%%!!%?%?!%%?!%!%!%?%!!%??!!!!%%!?!!%!!%%%!%%?%%%!%%?!%!!!!%%%!%%%%!%%%%%?%!%%%%!!%%!%!!!!!!!%%%%%%??!%!!%%?%!!%?!%%!%%?%!%%!!%%%!%!%??%%???%!%?%?%!%%%!!%!!%?%%??!%!!!%!!!!%%?%!%!%%!!%%?%%?%%%!?%%!%?!?!!?%%%!!%%%!!%%!%%!!%%%!!!!%%%%%!?!%%!?%??%?%%%??!%!%!%!%%%!?%!?%?%%%?%!??%!!!%%!!%!!%%???!%??!%!%!?!!%?%?!!!%!%!%!%%%%?%%?%%%%%%!?!%!%%%!!!%!!!?!?%!?!%!%%%%%%!%%!%%%%%!%%!!?%!%!%!!%!%%%%%%%%!%!%!%%%%%?!!?%%%%!%%!%??%!!?!?!%%?%?%?!%%!???!?!%%?%%%%%?!?%%%?!!!%%?!?%%!%%%%?%?%%%?%?%%%%!%%!!%!??%%%!%%%%%!%!?%%%%%!!%?%%%!%%%!%!%%%%%%?!?!!%%%!?!%%%%%%%!%!%!?%%%!!%!%?!!%!?!?!!!!%!%%%?!?%?%!%?%%!%?!!!%!%%?%!!!!%!!!?!??%!%!??%!!!!!!!!!?%?!!!!%%?!!?%%!%?!!%%%%%!%!!!%!?%??%%!%%%%?!???!%%!?%!%!?!?!!%%%!%%!?%!%%%?!%%%%%%!!%%%!%!%!?!%%%!%%?!%?%%!!%!?%%!!%!%%!%!%%?%!%%!!%%%!%?%?%?!%?%%!%?!%!%%!?%%!%!%%%%?%?!?%%!!??%!!%!!!%%!%%%%%!!%%%??!%!?!!!!%%!!!!?%!!%??%?!%?%%%%?%%%?!%?%%?%?%!%!%!%%!%%%%??!%!%!%%!?%!???%!%??!?!%!%?%!!??%!%%%!?%!%!??!%%%%%?%?!?%!%!%%%!%%?%?!%??!%%%%%?%!?!?!?!!%!!%!%!!%%%%%%%!?%%!?%!!%!!!%%!!%%!!%?%!!!%!%%%%!??!%?%%%?%!%%%%!%!%%!%!!?%!!!%!%?!?!!?!%%!%%!%%%%%%!!%?%%%!%%!%%?%%!?%%!%?%!!%%%%!%!%%?!?%!!?%%?%!%!%!%%%%%?!%%%!%%%%!%%!%?%%%!%%%%%%!%!!%%?%!%%!%%%%%?!%%!!!?%%!%%%%!!%%!?%!?%!!!!!%%?%%%?%%!%!%!%!%??%?!!%!%!%!%?!%!!???!%%?%!%%%?%?%%%?%%!%!?%!%!%%!?!%?!%!%!%!?!%%!!!%%%%!%!%%!%?!%%??%!%%?%!%%%!?%!?%!!%%%!!%%!!??!%!%%!?%%!!%!!!%!%%%!%!!%?%!!!%!%%!%%!%!!??!%%%!!???%%%%%%%%??%!!!%?!!%%%!??!!%!%%%%?%?%%%!%%!%%%?%%!!%%%%!%%!%%!!!%%!!!%!?!?%%%?%%%%??%%%!%%?%?%?!?%%!%%!%%!%%%%%%%!!%%%%%%!%!%%!!%!%?!%%?%%%%%%!%%%?!!%%!%%!?%%%%%%!!??!%?!!%%%%!?!?%!?%%%?%!%?%%?%!!!%!%%%!%%%%!%?!%%!!?!%!?!!%?!%?!!%!%!?%%?!!%!%!%%%!%%%%!%!%?%%%!%%!%%%!%?%%!?%?%!%%!?%%!?%%!%?%??!?!!%!%%?!!%%%%?%!!!!!%!%%!!?!%?!?%!%?!!?!%!%%%?%!%!%?!%!?%!%%!?!%%?!%!!%%%!?!%%!%?!?%%?!!???!%?%%!!%%%%%%!!?%%!%?%%?%!!%%!?%?%!!%!%?%!!%?%%%%!?!%!!!%!?!%%!%!!%%!%!!%!!%%%%%%%%%%?!!!!%%%!%%%!!!!%!%!?%?%!!%%%%%!%!%???%%%%?%%!%!%?%%!?%%!?!?%%!%%!%!%?!%%?%?!!?!!!!%!?%%%?%!?%%%!%?!%!%%!%%!?!%?%!%!%%?%!?%%!!?%!?!?%%!%%?!!%!!%!?!%?%??!!!?%!!%%%??!%?%%%!%%%%%%!!!!?%!%%??%?%!?%!!%!%%%%%%%!%%%%%?%%%?!%%!!%%?%%%%?!%%%!%!!%%!!%?%!!!%!%%!?%!!%%%!!!?!%%?!!!%%!%%?!%%%?!%%?%!?%%%%%!%%%!%%!%%!!%!%!%%?%!!!%%!%%%!!?!%%%%%%%%!%??%%!%%%%!%%%%??%!?%?!%!!!!!%%!%%!%?%!%%%!!!!!!??%%!!%!!!!!%!%!!%%%%%!!%!%%!%!!%%%%%%!%%!!%?!!%%!!!%%%?%!?!%%!%%!!%!!%%??%!!%!!%??%%%?!%!%!%%?!!%%%?!!!%?%!!!!%?%!!%%?!!??!!%%?!%!?%?!%!!!%!!!%??%%?!!%%!%%?%?!%%!!!!%%%!%!!%??%%!!?!%!?%!%?%%!%%?!!?%!?!!!!?%!?%%?%!%%?!%%?!%!!%!%%%%?!??!%%!%?%%%%%?%%?%%!?%%?!?%?%??%?%!?%!!!?%%%%%??%!??%?!%%?!!%%!%%!?!%%%%?%%?!!!%%!!!%%!!%%!%!!%%?!%%!!%?%!?%%%%?!%%%!?!%?%%%???!%!%%!%%!!??%%%%%%!!!%!%%%!!!!%%%%!%?%!??%!%%?!%%!!!%?!!!%?!%%?!?%%!!?%!%?%?%?%%%!%%?!%!%?!%?!%?!!%!!!%%%%?%!!%%%?%?!!%%%%?%?!%%%%?%!?!%?!!!%!?%!%!!%%!%%%!?%!!??!%%%%!?%!%?%!?!%!?%%%!%!!%%%!!!!%%!??%!?%%%!?%%!%!%%?!!?%!??%!?%!%%%%%?%%!!%%!?!!!%%!%!!!%%%!%?!%%%!!%!?!!!!%?!%%!!%!%%%!?%!!%%%%?%!?%?%!!%?%%!%!%%?%!%?%%%%%????%%%%?!%%!%%%%?%%%%!%%!!!!!!%!%%!!!?%??%%%%?%%%%!%!!!%!%!%%!%!!!%!!!%!!%%??%%%!???%%%%?%%%%%?!%%?!!!%%%!%!?%?%!%!%%%!?!%!%%!%!!?%?!%!!%!?!!%%%!%%?!%?!%%!%%?!%!!!!?!!%!!?!!%?%!?%%%!%!!??!%?%!%%%%!%?%!%?%?%!%%!%!%!!?%!%?%%!%!%%?%%?%%!!%!%%?!!!%!%%!!%!%?%%!!!%!??!!!%??!%%!%!?%!%?%%!?%!!%%!%?%%!!%!?%%??%!?!!%%%!%!%%%%%%!%%!%!%%%!%%!!!!?%!!%%!!%%%%?!!%!%!!?%%%%%?!%??!%%!!%!!%%%!!%!?!%!%%%%%%!%!%%%!%%%%?%%%%%%!!%?%%%!%%%!!?%!%%!!%!%%%%%%!%%%%%%!%%%%%!??!!%%?!%?!?!%%?!??%%!%?%%!!!%%%%%%%?%%!%%%%%%??%!%%%!%?%%?%%%?%%!%%%!!%?!?%!%!!??%%%%%%%%%%%%%%?!%%??!%!!%!!%%??%!!%!!%!!%%%?%%!!%!%%%%?%??%%%%!%!!%!!%?%!!!%%?%%!%%!!%%?!%%%!%%!?!%!%??!!%?%%%%%!%%%!?%%?%%%%!%%%%%%!!%?!%%?%%!%%!??%%%?%!!%!%%!%!%!!%%!!%!%%!!%%!%%%%!%%!?!?!!%!!!%%??!?%?!%!%!!%%%%!!!%%%%%%%!%!?!?%%!?!?%%?!??!%??%!%%%???%?%%?%?!%%?!%!%%!!%??!??!?!%%!%%!%%?!?!%?!%!!%!!?%!?%%??%!!!%!%%!?%%?%??!!!!!!%?%!%%%?%??!?%%%%%%?%!%!!%?%%%?!%!?%!%?%!%!?%?%??%%%!???%!%?%%%%%?!%%?!%%!!?!%!?!%?%%?%?!!!!?%%%?%!!!??%!!?%!!!?%%!!??!!!%?%%!!%%!%%!%%!?%!%?%!%?!%%%!%!?%?%%?%%!!?%%%!!%%%%%!%!??!%%%!!%!%%%!!!!?!!?%!!?%%%%%?!?%%!?%!?%!?%!!!%%%%!%%?%%???%??%%%!?!!%%%%?!%!!?%%!%?%!%!%%!%%!%?!%!??%%%%%%!%%%%?%%%%!!%%??!%!%?!??%%%??!!%!?!?%!%!!%%!%!%%%!%%%%!%%%?%?!!!!%%?!%%!%!!!%%!%!%%%%%%%%!%!%!%%!!%?%%!!!!%!!%%?%??!%%!!!%%???!%%%!%!!!%%?!%?%!?%%?%%!!!!!%!?%%!!?%%?!!?%?!??%%!?%%%%?%!%!!?%%!%!!?%!%!%%!%?!!%!%%%!%%%%!!?!!!????!!!!%%%%%!!!%%!?%!%%!%!!?%!%?%?%!!!!?%%!?%%%!?!%%!?!!!!!%%?%!?!!!%%!!%!!%??!?%%!?%!!%!??%?!!%%%!!%%!%%%%?!?!%%?%!%%%!!%?!%?%%!%!!!%!%%%??%%%%%?!%!%%%%%%!!%%%%%%%!%%%!%!%%%?%%!%%%!!%!%%?%%%?!%!!?%!%!!%%%%%!%!%!%%%!%%%%!??%%%!?%!%%!%!%?%?%%??%%%%%%%%!%%%%!%!%?%!!?!!!!!%!%%%?!%%??%%!%%?!?%!%%%!!?!%%!?!%%!!!?!%!!%!%%%?!!!?!??%?%!%%!%%?%?%%!!%%??!%%!%!%%%!!!%%!%!%!%?%%!!!%!??!%%!?!!!%!%!%%%?%%%%!%%!?%%%%%%%%?%!%?!?%?!!!?%%!?%!%!%!%!!?%?%%?!%!%!%!?!!!!%%%%%%%%%%!%!!%%!%?!%!%!%%%%!%??%%%%%%%%%?%%!!!%!%%!%!!!%%?%%!%!!%!%%?%!%%?%!!%%%!%%?%%?%%!!!?%?%?!%%%%%%!%!!?%??!!?%%%?%%!!?!!%%?%%%%!%!%%%!%%!!!%??!?!!!!?%!%!??%?%%%%!%%%%!!!!%%%!!%%?!!%%?!!!!%%!!%%%!!?!%!%%%?!!%%%%!%%!%%%%!!!%%%%?!!%!%%?%%!%?%%%!!!%!%%%%??%%!!!%?%%%%?%?!!?%%%%?%%%%!%!%!!!?%!%%!%%%%!%!%%!?%!%%%!!%!%%%!%%!!!%!%%!!!%?%%%%%!!!!!%%%!%%%!%!%!!!!%%!?%%?!??%?!?%%%%!%%!%%?%!!?%%%%!??%%%%!%?%!?!?%%????!%!%%!%!%%%?%?!!!%?%!!%!%!!?!%!%!?%%%!!?!!%!?%%!!%%%%%!!%%!%!!%!%%?%??!??!!!!!%%%!%!%%!!%%!?!!%%%%%%%%?%!%!!%!!!?%!!%%%?!?%%%%!?%%%!!%!%%%!?%%%%!%!%%%%!%!%%?%?!!?!%!!%!%%?%%%!!!!%!%?%!%%!%%%%!%%!%!!%%!%!!%???!?%!%%!?%??!%!%%?%%%?!%!!!!%%?%%%?%%!!%%?!%%?%%?%?!%%%!%%%%%%!?!?!%%?!!?!%?!%%%%!?%?!%!%!%%!!%!!%!%?%!?%!%%??%%!?%!!???%!%%!!??%%?%%!%%%%!%%??!!%%!??!?!?!%!!%?%!%%%!?!!%%%!%%!%%%?%%%%%%%!%?!%%%!!%?!%%!%!?%%%%%%?%???!!%%%%??!%%?!!%!?!%??%!??%%%%?!%%%??%!%%%!!%%%!??%%!%%%!??%?%%%%%!!?!!!!%??%??%?%%?%%%%%?!!?%%!%!%!%%!!%!?%%!!%!!%!!!%%%!%?%?%%!%%!%%!%?!%!%!!%%%%!%?%!%%%%%!%???%!!!%!%!!!!!%!%??!%!%%?%%!!%%!%%!%!!%!!!%!%??%!!%%!%%%!%!%?!%!!!!!%%!%%?!%%?%%?!%!?!%%!%%!!%%%%%?%%%??!%!%%!%%!!%%%%%!%%!%%%%?%%%%%!%?!!!%?%%%%%%%?%!%%%%?%%!%!!!!%%!%!!%!!?%%!%?%?!%!!!!!%%%%!!%%%?!%%!!%?%!%%!!%%!%?%!!%%%%%!?%!%?!%%%%?%%%?%?%!%%!!!!!!%%?%?%?!?!%!!%%!??!%%%!?%%%!?%!%%?!!%%%?%?%?%%!%%%?%!!!!%!%?!!?%%!!!%!!%??%%!%%!%?%??%!%%!%%!%%%!%%%!?%%?%%!!%!?%!!%!?%!%!??%?!%?!!%%!%%%!%%!%%%?%%??%%%%%?%%%%!!!?!%%%!!!?!%!??%%!!!!!%%%?%%!%!%!%%!%%?%%%!%?%%%!%?%??%!%%!%!?%!!!!%%%%%%%!!!%?%%!%?%%%%%!%?!%%?!?%%%%%%!%%%!%%?%%!%!%%%?%%?!%%!!%!?%%!!%%%!%!!%!?!!??%%?%!!??%!%!%!?%!%?%%?%!!%!%%%%?%%!%%%%%!?%%%?!!%!%%%%!%?%!%%%!!??%%%?%%%?!%%!?%?%!%%%%%%%!!%!??!%%%%%%%%%!!!!%!%%!%?%?%%?%!%!?!%!%%%?%?%%?!%!!!?!%%%!%?%%%!%%%?%?%%%!%%%%%%!%!?!%%!%!!?%%%?%%%%?!%%%!%!%?!!%!%?!%%?!%?!%!!%?%!??!%%%!%%%?!!%%?%?!%!?%!!%%%!!!?%%%%%%%!!%!%%%%?!%%??%???%!%%!?%%!?!!%?!%!!!!%%?!!%!%%%%!%!%!?%%%!%%%%?!%%??!%??!%%%%%%!!!!%?!!!%!%%%%%%?%%?!?!%%%!%%%!%!%!%!!%!?%%%!!%!!%!%%%!!%%%?%%%%%%%%?%!%!?!?%%!%!?%%%!!%%!!!!%%!!!!!??!!!%!%%%%!??%%!%!%%%!!%%%!%?!%!?%!%%!??!!!!!%%!%%%%%!%%%!%!?%%??!!!??%!%%%%%%?!??!%%%!%%?%%?%%%%!%%%?!!%!%??!%!?!!%%!!?!%%%%?%%!%%!%%!%!!??%!%%!?%?!%%!%?%!%%!!!%%!%%!%?%!%%!?!%%%?!%%!?%%!%?%!!?%%!%??!!!!%%!!%%%%!%%!%%!%%%!%!!%?%%%?%%?!%!!!%%!!?!%%%%%%%?!%!%%??%!?%%%%?!%!!?!%!!%!!!%%!?!!%!%!%!!%!?%?%%!%%!???%%?%!!!%%%?%!!%%%?!%%%?%?%!%%%%%!!%%!%!!%!?!%!!%?!%%%%%?%%%%%%!?%%%!%%%?!?%%!!?%?!!%%%%?%%??%%%!%%%!%!!%%!%%?%?%??!!%!!%!%!%?!%!!%!%?!!%%??%!?%%%!!%?!%%%!%%%%%!!?%%%%!%%%%!?%%%!%%!%%!?%??!%%%!%%%!%%%%!%%!!?%%%!%?%%%!%!%%%%!!%?!!%%%%%%?!%%?%%!!!??%!!%%?%%!%?%%!%%?%!!!!%?%%?%??!%!!!!%?!!!!?!%?!???!!!!%!%%?%!%%%%%?%!?!%?!%%%?%!%%%?%!!%?%!!%!!%%%%!?%!%!!?!!?%??%!%%???%%%%%!?%%??!!!!%!%%?!?!%%%%?%%%%%%!%%%%?%%%?%%!?%!%?%%%?!%%%?%%?%!%!!!!%?!!%%!%%%%%%!%!%!%!??!!!!?!?%%!!?%%?%%%%%%%%%!%?%????!%%!%?%!%?%!?%%%%!%%!!%%%%%!%%%?%%!%%%%!!%?%%!%!%%??%%%%!%!%??%!%!!!??%!!%%%!!%!%%%%%?!?%%%%%%%%%!%%%?!!??%!?!!!?%?!%!%!!!%?!!!%?%!!%%%!%??%!!?%%%%!%?%%%!%%?%%?%%%%?!!!!!%%%?%%?!!!!%!%!!%!!!!%%!?%%?%%!!!%%%!!?!!%%%%%%%!!?%%!?%?%?%!%%?!%%%%?!%%%%%?%%!%!%??%%%%!?!!%%?%!%%?!!%!!%!!!%%%?!!!%?!!%%!%%%%%??%%!%%%%%%%%%%%!%!?!!???%?%%%!%!!%?!!!!%!%!%%!?!?%%%?!!!!!%?%%!%!!%%?%%?%%%%%%!%%?%%%%!!%!%%%!%%?%?%?%%!!!%!%!%?%!%!%!%%%%%%%?%%%%%!!%%%!?%!%?!%!%%%!?%%?%%%%%%%!%%%?!!!?%%?!%?!!!!%!!!?!%%!%%%!%%%%%?%%!%?%!!!%%%!%%?%%%!!!%!?%?%%%%?%%%%!?%?!!%?!!%?%!%%!%!%!%?%??%!%%%%%%%!???%%!??%!%%!%!%%%%%!%!%%%%!%!?%??!%?%%%%!!!!!???!%%%%%!%%%!%!%!!%%!!%!%%%%%%????!!!%%?!!?%%%?%?%%%%%!%%%%%?!%%?!%%%%!%%!%%%%%!!!%%!!???%?%%?%?%%%%%%%??%!%%%?!%%%!!!!%!!%!%?!!%%!??%!%!%?!!%?%%?!%%!%?%%%%%%%%!%!%%%%!%%!!!%%%%!%%%%!?%!%!%%%%%!%%%%!%%%%%%!?%?%!%!?%!??%%%??!%!%?%%%%%?%?!?%%!%!%?%!%%%%?!%!!%?!!!??%%%%%%%%!%!?%%?%%%!%%%?!?!!%%%!!!%!%?!!%%%?%!?%?%%%!%!%!??!?!?%%!!%%%!%%?%%%%?%!%!!%!?%!%!%%!?!%!%%%%!!%%%?%??%%%%?%%?!%!%%%%%!%%!%!%%!??!!%%!!!%%!!%!%%%!!?%%%!!%%!!%%%!%!!!%!!!!%?%!!%%!?%?!!%%%%??!!?%%%!%%%%%??%%?%!!!%%!!?!%%%!?!?%?%%!!!!%?%?%!???%%?%%?%!?%!!%!?%!%%%%??%!!%%!%!%!%%?%?%%%??!!%!!!!%%%!%!%??!%%%?%!%!%?%%!!!?%%%%%%%!??%!!!?%%%%?%!!%!?%!!!%%??%%%!!!%?%%%!?!??%%%!?%!%!?!?%!%%%!%%?!!!%%?!?!%%%!%%%!%!!%%%!%%?!%%!!!%%!%?!%!%%%%%%!%%%%%?%%%?%?%?!%!%%%%%?!%?!!%%!%%%?!?%%?%!%%!%??%%!??!!%?!!!!?%!%?%!?!!!%!%!!%%!!!!?!!!!%%%!%?%%%?%!!!%!%?!!%!?!!%%%%%%?!%!%%%%%?%?!%?%!%%?!%%?%?%!%!!%?%!%%?!?%!%!%?!!?!%!%!%%!!?%?%!%%%!%%!%?!%%!%!%%%!!%%%%%!%%%%!!%%?%?!!?!%?%!%%%!%!%??%!?%!???!!!%!?%%?!!%%%!%?!%%!!!!!%%!%%%%%!%!!!%!!?%!?%%?%?%%??%%?!!?!%?%%%!%%%%%?%%%!!%!??!!%%%%!%!%%%%!!!!!!!!%%!%%!%!%!!!%!%!??%%?%%!!%!%!?!%%%!%!?%?%%!%!%%%%%%%??%%%!%%!%%%%?%!?%%!!%?!%%!%%%%!%%%%?%%!!!%%!?%?!!!!!%%!?%%%?!%%?%!!?%%?!%!%%?%%%%?%!!%!%??%%?!%%!%!!%%%%%%!!%!!!?%%%?%??%!%!?!%%!%%!!%!?%%%%%%%!%?%%%%%!!!!?%!%?!%%%%?!!%%!%%?!?!??%%!%%%!%??%!!??!%?%%%!!??!%!!%%!%%!%!!?%!%?!!%!%!%%?!%!??!!%%%%!!!!!???%%%%!!%?%!%!!!%%!%!?%%???%%%!%%!%?!?!!%?%%!!!!%%?%!!%%%!%!!?!%%%%%%!!%%?%%%!!!!%%?%%!%!!!%!?!%!%!%?!!%%%!?!!!%%%!%%%!!!!%!%!!%?%%%%?!!%!?!%?!!!%%!!%!%%!??%%!!%%%%!!!%%%!!?%?!!!!%!%!?!?!?%%%%%!!%!!!%%%?%%??!%!%???%!%%%!!%%%?%??%!!%%!%!%%%!%!%%%?%%%!!!!%%!?%!%%!?!%%%%%?%!!%!%!!!!!%?!%%%!!!?%%%??!?%%!%??%??%%!!%%%!%%!!%?%%!%!?!?%!%%%?%%?!!!??!%!!%%?%%%%%%%?!!%%!%%?%!!%%%%%?!%?!??!%%%%!!%%!%!%%%?!%%%!%?%%!%!%%%%?%?!%%!!!?!!?!?%!%?!%%%!%!%%%%!!!%?!!!!%%!%%!!%!%%%!%?%%!%?%%!%!!%%!%!%%!??%!%%!%%%%%%%!!!!!??%%!%!%!%!??%?%!!%?%!%??!?%%%%!%!%!!%??!!%!!%?%!!?%!?!%!!!%!!!?%?%%%!!!%%!%%!!%%?%?%%%%%%%%%%?!%?!!%%!!%!!?%?%%%??!???%?%?!%!!!!%!%%?%?%%!%%?%%?!%!!?!!???%!?!!!%!%%?!%%?%%%%!%!?!?%!%?%%%%%!!?!?!!!%!%!%%!!%%%?%!!!?!!!%%%?%%%%%%%?%!%%%?!!%%%?%!!%!!%%!!?%?%%?!%%?!?%!%%%%%!!!%%%!%%??!%%%%%?!!%!%!?!%!%?%%?!!%?!%%%!%%%%?%!!%%?!%!?!%%%?!%%%%%%!!%?!%%%!!%%!%%%%!%%%%!!%!!%%%?%%??%%!!%!%%%%%%%!!%!?%??%%!%?!%!%%%!!%?!%%!%%%!%%%%?%!%%!?%%%%%!%%%%!%!?%%%%%!%%??%!%%%%%%!?!!!!!%!?%%?%!?%?%%?%%%%%%?%%%%!!%%%?%!%!?%!!%!%%%%%%%%%?%!!%?%!?!!%%!!!!%?!??%!%%%!?%%!%%%!!!!%%%%!%!?!%%%!!!!%?!%%%!?%%!!%%%%%!%%??%%?!%%%??!!!?%?!%%!!%?%%!%%%!%%%%%!!!!%%!%%%?!?%%!%%!!!!%%%%!%?!%!!%%!%!%%%%?%?!!?!%!%?%!!!?%!%%%%%?%?%?!%%%!%?!?%%%%!!!!%%?%%?!?%%???!!!?%!%!%%??%?!%%!!!?%?!%?!%!%%%?%%!%!!!!%?%%!!%%!!?%!%!%%%?!??%!%%%!%%?%!%!%%%!%%?!%%!??%%?!!%%!%%%%%%%%!!!!!?!%?!%!%!%!%!%!%!!%!!!!%?!?%??%%%!!%%%!!!!!!!?%%?%%%%!%%!%%%??!%!?%%%?!%%%%?%%!!%%?!%!!%??!%!%!!!!%%%%??%%?%!?%!!!?%!%%?!!%%!!%!%%%%!%%!%!%%!%%!?%!%%%%?%?!%!%%!%??%!!?%?%%%%!%!%%?%%??%!%%!%?!%%!%%!%%%!%??%%%%?%?%%%!%!!%%%?%%%!%!%?!%?%%%%!!%%%%?!%%!%!!%%%!!?!!%%?%?%%!!%%%?!%?%!%!!!%%%%!%%!%??!%!?%!%%!%!%!%%!!%!!?!%%%!%!%%%%!%!!?%%%%!!!%?!?%!%!!?%!%%!!!%%%%?%!%!%??%%?%%%?%!%%%%???%!!%!%?%!%%%%???%%%%%!%%!%?%?%%!%?%!?!?!!%%?%!%%%%%%%??%!%!%?!%%!!!!%%?%%%!%%%%%!?!?!%%%%%?%%%!!%%!%!!!!!%%%!%%!???!?%!%!!?!!%%%%!%%???%!!%%%!%?!?%%%%%%!%%!!%%?!!%!%%?!%%%!!%!%!%%!!?%%%!%%%%%!%?%%!%!%!%?!%%!%?!%?%%!?!%?%%!!%%?%%%!?%%%%!%%%?%%%!!%!!%?%%%!?!%!%!%%%?%?!%!!%%%%%!%!!!!!!%%%?!%%%%!!%%%?%%!%?!%?%??%?!!!?!?%!!!%%%%!!!?%%%!!!!!?%!!%%!%?!%??%!%!?%???!!%%%!!!!!?!!%!!?%%!%%%%!!%!%!!%!%%!!!%%!%!%??%???%%%!%%%!!%%!%%%%%!%?!%!?%!%%?!?%%%!!%!!%?!%?!???!%!!%!%%?%%%?%??!?!!%!%!%%?!%%!%!%!%!??%%!?!%!!?%%%%!?%!!%!!!?!%%!%%?%%!%!!!%!!?%%!!%?!%!!%%%??%?%%%%?!!?!?%%?!?!%!!!!!%!%!%%%%!%!%%!!%?!%%!!%%!?%!!!!!?!%!%!!!?!!%%?%%!?!%!!%%%!%?%%%?!%!?%!%?%%%%?!%?!%!!%%!%%?%?!%?!%%!%%%%%!%!!!!%!%%?%%??%?!%%%?%!!!%%%!%%%%%!!??!?!!!%?%?!%??!?%!%%!!%%%%%!!%?%!%%%%%%?%!!%%%%%%%!!!!!?%!%%?!%!%!!%!%%!?%!!!!%%!!!%%%!?%%%%%%%!%%%?%!%???%??!%%%%!!?%!!??!%!%!!%%!%%?!%!!?%!!!??%!%!??%!%%%!!!?%!%?%%%%!!%!%%!?%%%%!!%%%??%%!?%%!!%%%??%%!%!%??%%%!%?!%!!!?%%!%?!%%?!%%%?%??!?%%%!%?%!%!%%?%!%%!%!%%!%??!?!%%??%%!!%%%!%!?%!%%%%?!%%??!%!?%%!%%%!!%!!%%%!%?!?%%%!!%!%!%!%%%?%!?!%%?%?%%%!%!%%%%!!?!!%%%%?!%%%!%!!?%%%??!!%%%%?!!%%!?%?%!%%%%%%%%!%!!%%?!%!%%!%%%!!!!%!!?%%!!?%%%%?!%!%%!!%%%!!%%%%!%%!%?!!?!!!%%!!%!%!?%!%!!%!%%%%%!!%?%!%%!!!!%%%%!%!??%??%!%!%%!%%%!!!!!?!%%%??%!!!!%%%%!%%%!!?%!%%%%%!!%!!!!%!????%?%%!%!%!%%%%%%!%%%!!%%%%%!!%??%%%%%!%%!%?%?%%?!%%!!%!?!!!%%%%%!%%%??%%%%!%?%!%!!%!!?!?%!!%!!?!!%%%!%%%?%%!%%%%!!%?%!%?%!%!?%%!??%%%%?!%!!?!%!%%!??!%%!%%%?%!%!%!%!%%%??!!?!%?%!%%%%!!?%%%!!%!%%!???%!!%%??%%!!!%%?%???%!?!%!!!!%!!%%?%%%%!%!!%!?%!!!%%?%!%%%%?!%!%!!%!!!%%!%!!%%%%%%!?%%%%?!?!!?%%%?%%!!!%%?%!!?%%%%%%%%!%%!?!%?!%!!!%!%!%?%?!%?!??!%%%?%%%%%%%?!!%!%%%%!%?%??%!%%!%!!%!!%%!%%!%%!%%%%%!!%%?!%%!%!%?!%%?%%%?%!%%!!!!%%%%?!%%%?%!%%%%%?!!?%?%%%%!%!%??%%!!%%!!%!!%??!%!%%!!%!?%?%!%?!!%!%!!!%?!?%%!!%%?!?%!?!?%!%%?%!%!!%%%%%?!%%%%!!!%?%!!!?%!%%!!%!%%!!!!!?!???%%%%?%%%?!%%%!!%%%?%%%!?%%?!!!%%!!%?%?!%%!%!!%%?!?%%%%!%?%%!!%?%!%%!?%%%?%%%%!!%!%%??!%%%??!%!%%%%%!%%!!!!%%!%?%%!%?!!%%!%!%%?!%%!%%%?!!?!!!!!%%!%?!%!%!!%%%%%!!!?%%%%%?!?!%%%!!!%%%?!%!%!%!%!!!!%%%%%%?%?!?!%?%!!%?!!%%?!!%%!%!!!!%%%?%%!%%?%%%%%%??!!%%!%%%%!%?%%!%?%!!%%%!?%!%?%!%!?!%%!%%!%?!!%!%%%!!!%%%?%!!%%%%%?%!?!!%%!?!!%!%!!%!%!%!!!!%%%%!?!?!%%%%!%%?!!%%?!%!%!?!%!!!%%%%!!!?!!!%%%%%%!%%%%%?!%!?!%%%!%!%?!%%%!%!%%!%!!%%%%%?!?!!!%!!%?%%!!!!!?!!?!%%%!!!%%%?%!%%%!!%!!%!%%!!%%%!%%?%%%!!?!?%!%!!%%%%%!%?%%%!%%%%%%?!%!%??!%%?!!%!%?%!%%!!%?%%!?%%%%%%%!!%%%!!%??%?%!?%!%%%!?%%%%%%!!??%!!%!!!%%%!!!%!!%%!?!%%!??%%%?%%%%%%%%?!%%!??!%!%%!?%!!!%%!%%%?%!!%%?%!!%%?%!%%?%!%%%%%%?%!%!!!%?%!%!!?!!%!!%%%%%!!%!%%%!%%!%!!??!%%?%!!%%%!%%%%!?%%%???!!%!!%%%!%!%%%%%!%%?%!%?%%?%%%%%%%!%!%%%!%%%!%%!%%!?%%%?!?!%!!%%%%%!!%!%!%!!!!%!!!%%%%!!!!!%%!%!!%%%%!!!%%??%?%!!!%%%%%!%?!%%!%%%!!%?%!%%%%!%%%?%%%!%!%!!%%!!!%%!%%%%!!!!!!%?!!%!%!!%%%!%%%%%!?!!!%%??%!%%!%!!?!!!!%%%!?%%!%%!%?!%?%%%%%%%!%%%%%%?%??%?%%!!%!%?%!!%?%?!!%%???%%?%!?!!!%!%!!%%!%%%%!!%?!%!?!?!!!%?%!?!!%%%!!!%!?!%%%?%%!?%?!%%!%%!!?%?%!???!%%%??%%%%%!%%!%!%%%%%!?%?%!%%%%%%!%%!%!%!%%?%!%??%!%%?%%%%?%?%??%%!%%!!%%%!%!%%!?%?%%%!%!!!!?%?!!?!???%!!!!!?%!%??%!%!?!%?%%!!%%!!!!%?%%%%%!%%%!!!!%%%!%!%%!%%%?!?%%%!%%?%%!!!!!%%%??!%!%!%%?!%!!!%!!%!%?!!!%%!!!%!%%!%!!%%%!!%!?!!!%%?%!%!%%%?!!?!?%!?%%%!%%?!!%%%%%!%%%??%!?!%%%%?!!?!?!!!!!%!!%!%%?%%!%!%%%?%%??%!%%!!?%?%%%!%??%!!!!%%%%%%%%!!!!%%%%%?!!!%%%%%%?%?!%!!%%!%%%%%%!%%!%%%%!?!%!%%!!!!%%%!!%?%!%%%%%!!!?!%!%%%%!!%%%!?%%%!%?%%%%%!%%?%???%%?%%!%%!%%!!!!?!%!?%%?%!%%%%%!!%%!%%%%%%%%%!%%!?%?!?!%!!%%!?!%!!?!!%?!%%%%%!%%??%!!?!?%%!%%?%%%%%!%!??!!!!!!!%!!!%!%%!%!%%%??%?%?!!!!%%%%%?%%!!!%!%%%!%%??!%!?!?%?%!%%%%??!%??%%!!%!%%!%%!%%!%%%%%%!%?%%?!!%%%%%%%%%%%%?%?%!%%%?%?%!!%!%%%?%%%%?%!%%%%!%%%%%%%%!?%%?%%?%%%!%!%???%!?%%!%%%!%%!?%!!%!%%!!!!!%%?%?%%!!%%%%!!!!!%%!%!!%%%%!%%%%%!!??%%?%!??%!?%!!!!%!%%%%!%%!%?%?!%?%!!%!?%!%!!%%%!?!!%%!%%!?!!!%?%%!%%?!%!%%!%?!%%%!%%%!%!%?!%!%?!!??%?%!!%%%!?!%!!%%!%%!%%%!?!?!%%%%%%%!%%%!!!%%%!%?%!%%!!%%??%!%%!!%%??!!?%!%!%!%%%%%!?!%?%!%%%%?!!%%!%!??%%%?%!%!%%!%%!%!%!%%!%??%%!!!!%%?%!!%!%!%%%%%!!%!?%?!!!!%!%%%%%!?%%%!%!%%?%%%%%%!!%!!??!%!!%%%%%!!%%%!?%%%%%%%%%!!%?!%%!%!!!!?%%%?%%%!!!?%!%!!!!%%!!!??%%?%?%%%?%%!!!!%!!%%%%%%%!%%?%%%%%%?!?!%!!%?%%%%??%!%%%!?%?%%%%!?%!?%%!?%%%%??%!%%%%%!!!!%%%!%!?%%%!%%!%?%??%!%!?%%!?%?%%%%%%%!%%%?%!?%%%!!%%%%!!%%%%%!%%???%%?!%%%!!%%!!%!%!%%!%?!%!!%!!?!%!!%%%%!%%%%?%%%?%%%!!?%%!%%%%!%%%%!%!%!!%!%!%!%%!!!%%%%?%%%%%!%%!%?%??%?%!%%??%%!?!%%!!%%!%?!%%?!!%!%%%%%?%%?%!%%!%!?!%%%%!%%!!%%%!%%%?%%%!?%%%!%!%?!!%!%%%%?%%%!%%%%%?%!!?!%?%!!%!%%%!%%%%%?!??%%?!?%?%!!!%!!%!!!!%?%?%%%%?%?%%%%%?%%%!?%!!%%%%%%%!%!%%%!?%%%%!!%!!%%%!?%%%%%!%?%%%?!%%!!?!%!!%%?!%%!%%%?%!!%%!%%%?%!%!?%?%?!!?!!!!%?%!!%%%!?%??!%%%%%?!%%%???%!!%?%%?%%%!!%!%!!%%%%%%!%!%%%!%%??%!!%!!%!?!!%!%%?%?!!%%?%%%%!%%!!!?%%!!%!%%%!!%%?%??!!%%?%%!!!%%??%%%%!?!%!!%!%!%%%%??%%%!%%%%%!%%!%%!!!%%!%!??!%%?%%!?%!%?!!%%?%%!!?%%%%%%!%%?!!!?%!%%!!?!!%!%%?%%%!%!%!%%!??!?%%?%%%%%?%%%?%!%!%%!!!!!%%%?%%%%?%?%%!!%!%?%%!!%%%%%?!%!%!%%%%%!%%??%!?!!!!%%%%??%%%%!!!?%%!!!%!?%%%!%%!%?!!!%!?!%%!??!!!!%!%%?????!%!%%!?!!%%%!%%!%%%!!!!%!!%!!!%?%%%%%%%?%%!!!!?%%%%%!%?!%!!?%!%!!?%?%%!?!%%?!%%%%?%%%?!%%%!?%%?%?!!??!%!%%!!%%%??%%?%%!%?!%%%%%!%!!!%!%%%%?%%!%!%!%%?%%!%?%%?%!%%%%%!%!%!%%!%!%?%!!!!%?%!!?!!??!!%%!%%%!!%%%%%%%!!%%%%%%%!%!%?%?!%!!?%!%%??!??%%!%%!%%%%!%!!!%!%!!%?%%!%!!?%%?%%%!?%!%?!%%%%%?%!?!?%%%%?%?%!!%%%!%%%%?%??%%%%!??%!%!??!?!!%%??%%%%%?%%%%%!%!%%???%%!%!%?%%%%%%%!%%!?%%??!%!%%!%%%!?!!!%?!%%%!?%%?%%!%%!%%??%!?%%%%!!?%!%%%!?!!!%%%%!%!?%%?!%%!%%?!%%%?!!%%?%%%%?!!!%%!?%!!!%%!?!?%%!!!!%%%%%%%%%%!!%!%!!!!!%%%%%!?%?!??%!?%%%%!%%%!!%!?%%%!%??!%!!%!!%%!??%%?%!!%%!?%%!!!!?%%!%!???%?%!!!%%%!!%!%!%%!?!%%%%!!!!%!!%!%%%%!%?%%%!%%!%%!%?!%!?%%!?%%??%!%%!?%!%%?!%%%!!%!!%%%!%%!%!%?%%?!%%!%%%!?!?!!%%?%!%%%?%%?!%!??!?%!%%!!!?%%%%%%%%!%%%%!%%!!%!%%%%%%?%%!%%%!?%%%%%%?%!%%%%%!!!%?!?!?!?%?!%!!?%?%%%?!!%%%??%%%?%%%!?%???%%%!%%%%%%!%%%!??%%?!?%?%%%%%%%%!%%!!%%?%!%!%!%!?!%?%?!%%!%%?!?!%!%?%%!!%%%%%%!!%%%%?!%!!?%%%!%?!!!!!?!?%%!?%?%!%%!%%!%!%%%!!%!?!?!%?%?%%?!%!%%%%!%!!!!!%!%!!???%%??!?!%%%%%%%%?!!?%%!??%%%%%%%!!?%%!%%?%!?%??!%?%%%%!%%?%%!%%!%!?%%!!%%%!%%%%%?%!!!!%%??%??%%%?%%%?!!!!!??%!!?%%!?!%%%%%%!?%%?%%%?%%!%!%??!!%%!!%%!%%%!!!%!%!?%%!!??!!?%!??%!%!??!%%??%%%%%!%?%?!%?%%?%%?%%%!%%%%%!!?%?%%%%!%!!%!!%!!!%??!%%!!%?!%%%?!%?!!!!!%%!!%?%?%%%!%%%%!!?%%!%?%!!%!?!%!!%%!%?%?%!%?%%?!%%%?!%!?%?%?!%!%%?%%!%%!!!!%%%!!?!%%?%%%!%!%!?!?%!%%!!%!!%!%??%?!%?%?%!!!%!%!%%!!%%!!!%%!%%%!!%%!!?%%?%?%?!!%%%!%%%??%!%?%%%?!%%%%!%%?!%!?%?!!%?%%%%%%%%!%%%%!!!?%!?!!!%?%!%!?%%?%!%!?%??!!!%!?!%%!!!!%%%!%??!%%%%?%!!%%%!%!!!%%!%%%%%!!%%!%!%?!!?!%!!!%%?!%%?%?!!%%?%???%?%%%%%!?!%?%%!%%%?!%%!%!%?%!!%%%%%!?%?%!??%%?%%%!!%!%%%!!!%!!!?%%!?%%!!%%%!%%!?%%%%!%%%?%%?!!!%%%%!?%!?%?!!%%??!?%%!?!!?%?%?%!!!%!%%%%%??%%!!%%?%%!%%!%!%%%%%%%!!!%!%%!!%%%!%%?%%%!!!%%%!!%%!!?!!!?%!%!%!??!!!%?!!%%%%?!?!!!!?%%?!!%%!!!?%?!%%%%!%%%%%%%%%%!%%%!?%!!%%?%!%%%!!!!%%!!%%%?%!?!!%%?%%?%?%?%%%%!%?%%!%%!?%??%?!%?!%%!%!!%%%!?%?!%?!!%?%%%%!%!!?!%!%%%%!%%%%??%%!!!?%%!%%?%?!!%%%%!%!%%!%?%%!%?%?%%%!%?%%??%??%%?%?%!%!!%%%!!%!?%??%%!?%!?%?!?%%!%%!!%!?%%!%%!!!!?!%!%%!%!%%%%%!???!%%%%?%%%!!%%?%!%%!%!?%%!!?%!!%?!%%!!%!!!!!!%%!!%?%%!%%!!!%%%!%!!!%%!%%%??!%%!%%!%!%!%!%!%%?%%?%%%!%!%%%%?!%%%%%%!!!%%%?!%%?%%%%!!%!??!?!%??%%%%%!%%%!%%%!%!?%%??!?%!!%%%?!?%%%%%%!?!%%!%%%%%?!!%!%%%!!?!%%%?%%%!%%?!?!?!%%!%%%%%%%%!!%%?!!%?%%!!!!!%!%%%%%%!!%!??%%!%??%%%!%%%!???%%%%%!%%%%%!!%!%%%!%%!?%%!?%!!%!%??%?!%!!!!%%%%%%!!%?%!?!%!!!%%!?!%!%%%!%!%!???%%%%!%%?%%%%!?!!%%%!%%%!%%!%%%!?%?%%%!%%?%!!%%?%!!%%%!!!%?!!?!%?!%%?%%!%!!%%%%%!???%%%?%!!!!%!!%%?%%%!!?%%?%%!!!!!%%?!%!!!!%!??!?!!%!%!%%?%!!%!!%!?%!%?%?!%%!%%%!%%!%%?%!!?%!!%?%!%?%%?%%%!%%!!%?%%%%%!%!!%!!%?%%!%!?%!%%%!!?!%?!!%%!!?!%?!%!%%%??%?%!%!!%%%?%?%%%%%!?!%!!!!!%%?!%!%%%!%!%%%%!%!%%%?!!!?%%%%!!!?!?!!%!?%%!!!%%%!%!%?%%%%!!!!!!%%!%%!?!!!!!!!!!!?!%!%%!%!%!???%%%%%%%%%%%?!!%!!?%%%%!%%%%%?!!?!%!%?%%%!!%?!%?%!?%!!%!!!!%%%!%%!%!%%%%%%?%!!%?%?%!!%%%???%%?!%!%!!!%%%??%%!%%%?!%%%?!?%!%!?!?%!%!!%%%?%!?%%%%!%%!%%?!?!?%%%%%%??!!%!%!!%??!!%?%!%!!!?!%?%?%%%%%?%%!%%!%%%?%%?!!?%%!%!?%!%%%!!%%?!!!%!%?%%!%??%%%%!!?%%!!%%%!?%??!%%!!%!%%%!??%%?!!%%?!!%%%!!!%?!!!%!%!%??%%!!!!!%%?%%?%%!%%%!!!%%%??!!!%%?%%?!!???%!!%?%%%%?!!%%%%!%%%%%!!%%?!!%%%?!%%%%!%%?%%!%%%%%!!!%%!%?!%!%???%!!%%!%!%?!%%%!%%%?%%?!%%%!%%%%!%%%!!%%%%?!%!!!%!%%%!%!%%%?%%%%?!%?!?%!%!?%?%?!%%%%%!!%!?%?%%%%%%%!%%!%%!???!!%%%%!!%%??%!!!%!??!%!?%%%%?%!%%%!!%%!?!%%?%!!?%%%%?%!?%?%%?%!%!%%%!%%%?!%%??%??%%!?%!%!%%!!%!!!!!!!%%%%!!?%%!%?%%%%!!%!!%!%%%%?!??%%?%%%%!%!%%?!!%%%%%!%!!??!!!?!!!??%%%!%%%!!!%%%!%%!%!!??%!!!%!!%?%?!%%%%%%?%%%%%%%!!!%?%%%%!%!!?%!%%?!%?!%%!%%%%%%%!%?%!%%!%%!!?!%%!?!%%%%%!%!????%%!%%!!%%%!%%!!%!%?%%!?!!%%!?!?%%%!%!%?%?%%%%%!%!!%%?!!%?%?!%%%?%%%%???%%%?!%!!%%%%%!!!%%%!?%!%%!%??%???!%?%?%%?!%!%!?%!%%??!!?!!%%??%%%!%%!!!!%%%%%%!%?!%%%!%?%%!!%%%!!%!!!!%%??!%%%%!!%!%!!%%!%?!%???%?%!!!??!%%%%!!%!!%%%?%%%!!!?%!%!%%%%!%%%%!!?%%%!%%!!%%%%?%%!!!%!!?%%%!!!?%%?%!?%%%%%??!!%!%%!%!!?%!%!%?!?%%?%%!%%%%!%!?%%?!%%%?%%%%!%%!!!%%!!!%%!!!!%%%%!?%%!!%?%%?%%%!!?!?%!!??!!%%%%!%%?%!%!!%%!!!%!?%?%%%!!%!%%%%%%%%%%?%!%?%!%!%!!!!%%!%%%!?!!!!!%%%%?%!%%%!%!?!%%%%%%?!%!!%!!!!%!!?!%!?!%%!%!?!%!!!?%%%!!!?!!%%%%%%%?!?!%%%%%%%!%!%%!!%!!!!!!%?!?!%!!?!%%%!%%%!%!%!%%%!%%%!%%%%%??%%!??!?!%!%%!%!%%%?%!!!?%?%%!%%?!%%%?%%%?%!!!%%!!%!!???%?%%?%%%%%!!%!%!%%!??!!%%!%!!%!%%!%?!%%!?%%%!%!!!?%%%%!%%!%%%!!!%%!?%%%%!%%!%???%??!?%!%%??%%%%%%%%%%%!!!%!!!!?%??!%?!?%!%%!%%%!%!%?%%!!%%%!?%!?!%%!%%%?%%%!!?!!%?%%?%!?!%%%!!%%?%%%%%%%!%!%!!!?%%%??!%!%%%!??!?!!!?%!!%%!%!%%!?!?!%?%!!%!!!%?!???!!%%%!%!!%%%%!!%%%!!%%!%!!%%%!%?%?!%!?%%%%%%?%!%%!?%%!!%??%!!?!!!%!%%%!%!!%!!!%%!?%%!!!?%!%%?!?%!%%%%!%%%%%%?!!!!?!%%%!%%%%?!!!!!%!%%%!%!%!%?%%?!!!!!!%%%?!?%%%?!%%%!%??!%%%%!%?%%!!??%%%%%?%%%!%!%%%?!!!!%%!%!!!%%%%??%?!%?!%!%!!%%!%!?%%%%?!%!%%%??%??!!?!!%%!%%!%!%%!??!!%%!%!!%!%!%%%?%%?%!%!%%?%!!%?!!%?!!%?%?!%%!!!%%!%!%%!%?!%!!?%%%!%%%?!!%%?!?%?!!%?!!?%%%?%%?!!!?%%%?%!??!%%?%%%%%?!%%!!%?%!!!!%?!%%%%!%?%?%%!%%?!!!%%%%!?%%%%??%!?%%%!??%%!!%!%?!%??!%%%??%!!%%!!%%!?!?%?%!%!%%%%!!!%%!%!%!%??!!!!%%!!!%%%!%%!!!?%?%%!%!%?!%!?%!!!%%%%?%%%!!!%%%!!!%%!!%!%?!%%!!????%??!%?!!%%%%!???%%%%%%?%%!!%%%%%%!?!?%!%%%%?%!??%??!%!%%%!%!%%%%%?%!?%%%%?%%!%!!!%!?!%%!%?%!!!?!!%!!%!!??!%!!%!%?%?%%!%!%!?!?%!!!!?!?%%%%!!!!!%!!%%%%!%!%!%!%%%%%%%!%%%??!%%%%!?%%%!!!%%%%%%?%!!%%%!%!%?!%!?!!%!%!!%%!%%%%%%!!?%%%!%?!%!%!%%?%!!%%!%%%%%%%%!%!%!%?%??%%%%%?!?%%?!!!!!!%?!%!!%%%%%%%!?!!?%?%%%!!%!?%!!%%!%?%?!!%%%!!!!!!%%%%%?%%!!%%???!?!?%?%%%!%%%%%??!?%!%!%%%?!?%?!%!!!%%%??!!%%%%!%!!!?%!?%%!%%%!!!!%!!!!?!!!%!%!?!!%!!!?%!%%??%!!%!!%%%!!%%%!?!?!%!??%%%%%%%?!%?!!%?%!!%!%%%!%%?%!%%!%%!%?%%%%!!!%%!%%!!?%%!%!!!%!?%%?!!%!?%%%!%%%?%!%!?%!!%!!?!?%%?%%!%%!%!%!!!%%%%??%!!%%%%?%%?%%!?%%!!!!%%!?!%!%%?%%?%%%!%%%!%%%??%!%%%!%?%!!%!!%?%!!%!!??!?!!%%%!%!%!%!%%%%?%%%%??%!?!!%%%%%%%%%%!?%!%???!!?!?!%?%!!!%!%!!%!?%!??%!%!%%%%%!%%?%!%!!%%!%!?!%%!!!?!%%!%%%%!%%%%%%!?%!%%%!!%!%!!!!?!!%%!%!!%!%%%!%???!!%!!!%%%!!!%?!?%!?%!%%?%?!%%!!%???%?!!%!%!?!!%%!%%%!%!!%!%%!!%?%%%%%?%%?%%%!!%%%?%?%%?%%%!%%!!%??!%%!%!!?%!?!%%!!%???%?!%%!?%%%%?!!??!!%%%!!%!!%%!!%???%%%%?!%%!%%!?!!%!!!?!%%%%%!%!%!?!%?!!%!!!?%%%!%%%%?%%!%%!?%%!%!?%%%!?!%%%!!%!%?%%%!%%%!!!!%!?!%?!%%%%%%!%!%!?%!?%?%?%?!%%!?%%%??%%!!!!%%!%!?%%?!???%%!%!%!%?%%??!%%%%!%!?!!!%%%!%%%%!!!!%????%?!%!%?%?%?!%!%%%?!!%%!%%%!%?%%!%?%%%!!!!!?!?%!%!!%%%!%!%!!%%!%%%%!!%!!%!?!!%%%%%%%%%?%%%%?%%%%!!%?%%!%!%!?%%%!%?!!%!%!!?!?%%?!%!!!%?!%!!!%%!%!%%????!?%?%!!%%?%%%??%!?!%%!?%%%%?%!?%??!%?%!%!!?%?!?!!!!%?%%!%%%?%%!?!%%!%?%%%%!!?%?%!%?!%?%%?%%%%%%??%!!%%!%%?%%??%!!!!%%!%!%!%!%??%!%!!%!!?!?%%!%%%!%!!!%!%!%%%%%%!%%%!%%??%!%!!!%!%%!%%%%%!%%!%!!!%!%%%%!?!%%!%%%%!%!%?!%!%!!??!%!%%%????!%!%!%?%?!!?%!%%%%%!%??%%!%!?%%?!%%%?!%?!!?!%?%!!%%?%%%%!!?%%%%%%%!%?%!%!!?!?%!%!!%%!!?!%%%!%%!!%!%!%?!!%%%!%%!!%?!?%!?%%%%!%%%%%%%?%%%??%!%??!!%!%!!%!???%!!?%!!%%!?!!!%%!%!!?%%!%%%?%%??!%!%?!%%!?%%!%%!%%%!?!!!!!?%?%?%%%!!%%!?!!??%%%%!%!?!%%??%!?!%!!%%%!%%!%!%%%!!!%!??%!%%??!!!?%%%?!%%!%!%!%%!%%%%!%!%%!!%%%%%%%!?%%!%%%!!!%%%%%%%%%?!!%%%%%%!?!%%!!?%%%?!?%%%%?!%!%%%?%!%?!!?%?%?%%!!%%%%%!%%%%?!!!%!!%!!!!%%%%%%!%!!!!?%!!?!?%%!!!!?%%%!%%!%%%%%%%%%%%!!%%%!!!!%%!?%!%?!??!!%%!?!!%%!!?!?%!!?!?%!%!!%?%??%%!%%%!%%%??%%!??!!%!%!%%%%!!?%%!%!%!%%?!%!!!%%%?!%%%!%%?%!%!%?%!%?%%%!%%%%!!!!%%??%%!%?%%?!%?!??%!%?%%%!?!%!%?!%%%!%!%%%%%%%!%!%%%!!?%!!%%?!%%%%??%!!%%!?%%!?!%!?!%!%%?!!%%!%%%?%!?%!!!%%!?%%%%%!%!!%%%!%??%!!!%%%%%!!%%!%%%%%?%!%?%%!%!?%!%!!!!!%%%%%%!%!?%%%?%%%%!!?%%%!%?!%%%%%%!%!!%?%!%%!%?%!!%!%%%?%!%%!%%!!%!%%%%%!!%?%%%!%%%!%%%!%!!!%%!!%%%!%%!%!!?!?%!!!%%%%%%%%%!?!!%%%%%!?%?%%%%!!%%%!%!!%!%?%?%!!!!%!!!%!%%%%!%?%%!!%!!%%%%%?%%!%%%%%%%%%%%!?!!??!?%!!%?!%?!%%%?%!?%?%%%%%%%?!!?%!!!%%!??%!!?%?!?!%!%%%??!%!%%%%?%?%!!%%!!%?!!!?!!!??!?%%%?!%!!%%%%!????%?!%%?!%?%!!%%!!!!%!%%%!!!?!%!?!%!!!%%!!%%?!%%%%!??%%!%%%%%!?!%!%%%%%%?%???!%!?%%%!%%%!!%!%!%!?%?%!%!%?!?%%!%!??%%!!%?!?%?!%!%%%%%%%?!%!%%!!!%%!!%%??!!!!%!??%%!%!!%!!%%%%??!%%%%!%%?%?%%!%%?%!!%!%%%!!!%!%%?!!%!%%%%%%??!%%%%%%%%!%!!!!?!%%%%%%%%!%!%%?%%%!???%?%?%%!!%?!!%%%%!%%%%!!!!%%%%!!!%?!!%!!?%!?!?%??!%%?!%%!%%?%!%%!?%?%?%%?!%%?%!!%!!%%!?%%%?!%%%%%%?!!!%%%%%%!!%%!%%%!?!%%%?!?%%!?!!?%!?%%%%!!%%%?%?!!%%?%%?!%?!%!%!%%%?!%?!%%!!!%%?%%%%%!%!%!!%%!%!%!?!%%%!!%%??%%%!%%%%%!%!%%%%?%!%!!!%%%%?%?%?!!!!?%!%!%!%!%%!%%%%%!!%%%!%!!?%?!%!%%?%!%!%%!!%%%?!%%%??!%%?!%%!?%%%%?%!!%%!!?%%%%!!?!!???%%??%!!%!%%%!??%%%%?!!!!?%!?%!!%!!!%?!??%%!%%%%%!%!!%!%?!%!?%!!!%!!!!!!%?%%!?!%!?%!?!%!%%%!?%%%%%%!%!!%?!!?%%!?%%!%!?%!%%!?%!%%%!?%?%!!%?%!%!%!%%????%!!%%!%%%!!%!?!!%%%%?%!!%%!?%%?!?!?!?!?%?%!?%!%!%%%%%!!!%!!%%%%!?!?%!!%%%!%%!!!%!%%!!?%?%%!%%?%%%%%!!%?%%?%%!%!!?%%%%!?!?!??%!%%%%!?%?%!!%%!%%%!%!!!?%%%!%?!%%%!%%!%!%%%%%!%%?%!%%%%?!%?!%%%%%%!%%%!%%!!%%!?%?%?%?!%%?!??%%%!%?%?%%%!?!!?!!%!%!!!?%%!?!%!%%!!%!!%%%%!%!%%%%%!!!?!!!!!!??!?%!%%%!!!%%%!%%%!!%!%!%?%!!%!!!??!!%%%%%%!?!!!%%%!?!!!%!!%!??!%!%%!?!??%%!%%%!%!?!!?!!%!!%!%!!??!%!?!%%!%%!!%!!!%%%?%!%%!%%%!!%%!%%%!?%%!%%%!%!???%%%!?!%%!!!%%!%!%!%%!?!%!%!%!?!%!%%!!%?%%%?!!?%%%!!!%!!%%%%?!%!?!%%?%%%%%%%%%?%!%?!?%!!%%%?!?%%?%!%%??%!%%!!?!!!%?%!%%?!!!%!!%?!%!%!!??%%%!!?%%!!%!?%!%%!!%!%?%%!%!!%%?!%!!%!?%!%?!%!%%?%!%??!%%%?%%%%%?!!!%%%%?%%!!%%%%!!?!%%%%!!!%!!%%%!%%%?%!%!%%?%??!%!%!%%%?!%!%%!%%%%%!%%???!%!%!?!?%?%!?%%??!%!%%!%?%%!%?!%%!?!%!%??!!%%!?!!%!%!%?%%!!%!%%!%?%?%!!%!?!?!%!!!%%!!?%%?%%??!!%!!!!%%!%!%!%?%!!!!%!!!%!%!%?!%!%%%%%!%!??%%!%%!!%!!!?%!%!!%?%%?!!!!!!%%%%%%%?%%!!?!%?!%%!%!%%?%%%?!!!!!!!%%%!!%%!??%?%%?%%%%%%%%!%%!!!%!?%!!!!!%!!%%!??!%!%?%%%!%!%?%?%%%%!%%%%?!!%%%%!?!!!!!!%%%!!!!!%!!!%%!%%!!%?%??%?!?%!!!%%%!!!%!%%%!?%!???%%%%%!%?!%%!!!%?!%%%%!?!%?%%%%!%%%?%!!%?!%%%%%?%!!!!!!!!%?%!%%!%%??!!%!?%?!!%?%!%%!%!%%?!?%%?%!!!!!%%?!?%!%!%%?%?!!%!?%%%%%!%?!%%%!??%%%%?%%!%!!!?!%%!!%??!!%%!??!%!!%!%!%!%%%?%!!!%??%!!?!%%%%!%%%?!%%%?%!%?%!!%%!%!?!?!%?!!?!!%!%%!%%!!!!!?!%%%%%!%?!%!?%!?%!?%%%?%%%!%%%%%%%%!!%??%%!!%%!%%%%!!%%!%%%%%%%%%??!?%%%!!!?!?%%%!!%!?%%?!%!!%!!%?!?%%!!%?!%!!%%!%%%%!?%!%!%%?%??%!!!!!!?!%?%!%?!!%%%%%?%%%%%%!!%%!%!%%%%%!!%%!%%%%!!%?%%!%?!!%!%!!!%%!!%%%!??!!%%%?!!%%%!%%!%?!%!%%!%!%%!!%%!!!!!!??!%%%%!!!?%%?%??%!%%%%!%%%!%%%!!?%%!!%%?%?%%!%%???!?%%%%%%%%?%???%%!!!%!%%!!!!?!%!%!!%%%%!%%!!?%!%!?%%%%?%%?!%?!%!%!??!%%%%!%%%%%%%!!%??!?!%?%%%!!%?!!!%!%%!%%%%!%!??!!%%?!!%%!!%%%!!?%!%!%!%%!?%%!!%%!!%?!%?!!%%??!!?%!%%!!!?!%%%?%%?%!!!%!%?!%?!?!%%!%%%?!!%!!?!%%!!!!!%%%%%%!%!%!!%!%!%!%!%%?!?%%!%%?!?%%!%%!%!%%?%!!%!!%%!!%!?!%?%?%%%%%%%%%%%%%?%!!!!?!%!!?!!%%%%%!%?!?%%!??%%!?%%!!%%??%!%!%%%%?%%!?!?%??%?%%!!!?!?%%?!!%%%?%?!!%?!!%%?%?%%%%!%%%!?%%%!%%%!?!!?!!%?%%?%%%%%%%%!?!%?%%!%%!%?%??%%%!?!%?!%%%%%%%!!%!%!?!!!!%%!!!%%!%!%%!%%%!?%%%%%?%%!%!%!?%?%!%?%%%?%%%!%%%%!!%%%%!!!%%?!!!%!%??!?%!?%!%!%?%%%%%!??%!%%!%!%%!!%%%?%?!%%!!!!??!!!%!%!%!?%?%%!!%%%!%%%%%%!?%?%%!%%?%!!%?%?%!?!%%!%!?!%%%%%%%!%?%!%%%!!%!%?!%%!%%%%!%%%%!%!!%!%!%%%%!?!?%?%?%?%!!%!%?%%%%%%%!!!!%%%?%!%?!%%%%!!!%?!!!%%?%%!%?!%%%!?!%%?!%!!??!!?%!!!%!%!!%%!%?!%%%!%!%!??%%!%%!!!%%!!!%!?!!!%%?%?%!??!!%%!%%%%!!%!!!%%?%!%%!%?!?!%%?%!%%!%%!!!?!??!!!%?%%%%!!%?!%%%%%%!!?%!%!%?!%!!%!%%!%%!?!%%%%!?%!!%!!!!!%%%!!!!%%%%%!%%!!%%%%?%!%%??!?!!%%!!%!%%%%%%%!!!!!!%%%%%!!!?%!??%%!?!%%%%%%!!%!!!!!!!%!%%%%%%%!?!%%%!?!!%?%%??!!%?%%!%%?%?%%?%%!%!%!!%%%%%?%%%!%!?!%%%?!%%%%%%%%?!%?%%?!!!!%%!!??%%!!%?!%%!%%??%?%%?%!%%%!%!%!!%%%%%%?%%%%%%!%!%??!%%!%!%%!%%?!%%%?!!!%%!%!%!!%!!?!%?%%%!%%%%?%!?%!%%%%!%!%!!!?%%!!!!%%%!%%!?%%!??!!%?%??%!%%!%%!!%?%!?%%!%%!%%!%?%%!%!!?%%!?%!!!%!!%%!?%%?%??%!!!%%?%!!%!%%%!%%!!%%%?!%%%%!!%%!!!%%%%%!!%!%!%%!?%!%!%%%!%%%%%%%%%%%%!%%%!%?!%!%?!?%??%%%%?!%!%%%%!?%!%%!%%%!%!%%!%%!!?%??%!%!%!%!%%%!?%?%??%!%%!%?!!?!%%!!!%!%?!!%?!%!?%!%%%?!%?%%?!!%?!!%%%%!%%?%?%?%!%%!!?%%%%!!%%%!%!!!%!?%!%%!%?%!!!!!%%%?%%%!%!%%!!%%!!%%?!%%%!!%%%%!%%!%%!!?%!%???!%%?%!%?%%%?%%!%?%!%!%!%%!%%%?%?%%?!!!%?%?!!!%%!?!%!%%%%%%%!%%%%%%!%?%%!?!!%!!??!%!%!%%%%%?%!!%!!%%!%?!!?!!%%%!%?!%%%%%!%!%%%%?!%!%!%%!??%%%%!%%%?%!%!%?%!?%%!?!%%!?%%!%%%%%%!%%!%?%!%%!!??!%?!%%%%%%%!%!%%%%%!??!%!%%!%%!%%%!%%!!!?!!!!!%!!?%%%%!!%!%%%???%%%!%%%!%%!?%?%%%%!%!?%%!??%%%!%!%!%?%??%%?!%%%%%!%%!%?%%?!%%!%%!!!%%???%%%%%!!%%%!!?%!%%%!??!!?%!%%!!!!%%!?%%?!%%%?!%%!?!?%%%%??%%%%!%%%%%%??%!%%?!?%?!%%!?%%%%%?!!?!!%%?%%!%%%?!!!!%%?%%!!!?%%!%%%!!%!!!!!%!?%%!!%%%%?%??%??!%!?!%!?%%%%%?%%!!%!!%%!%!%%!!!!%%%?!!%!%%!!?!%!!%%%%?%?!%!%%!!!%?!%%?!%!!??%%%%%%%!%?!!%%?%!%?!%%%%!?!%!!%%!?%%%?!!%!!?!%%?!!%%%%%!%!%?%?!!%%%?%!?%%!?!%%%%%?%%%!%%%%%!!!!%%?!%!%%%!%!%%?!!%!??%%%%%%%%%%!%!!%%%??%%%!%!!%!???!%!%%%?!!%%?!%%%!??!%%?!%!!%%%%%%%%%%%!%%%!%%!!%%!?%!!?%!%%!!%%%?%?%%%!!%%?%!?%%!%?!%?%%%%%%%%%?!%!!%%%%!%%%%%%%?%%!%!%!!!!%!!%?%!%!!?%%!%%%!!?%!!%%!%%%!!%!!%!%?!??%%!%%!%?%%?%!%%!?!?%!!!%?%!!!%%!!!!?%!%%%!%?!??!%??%%%%%!%!%!%!?!%!!%?%%%%!%!?%%!%%%%%?%%%?%%!!%!!!!%!!!%%%%%%!?!!!!%?%?%!%%!%%%%!!%!!%?!!%%%%?!!!?%!%%%!%%!%!%!%%%?%%%%?%!!?%%!%?!%%%!%%!%%%%!%!!%%%?!%!%%%%%%%?%%%%!!%!%%?!%%%!!?%%%%%%!%!%!!%!%%%?!!?!!%!%%%!%%%!!!!?%%%%%%%??%!%%!%%%?!%!%%%!??%%!%??%!%%?%%!%!%??!%%%!!?%%?%%??!!%%%%%%!!%%!!?!%%?!%%%?%%?%!%?!%%?%??%%%!!%%%%%?%%%%!%%!?%%!!%!?%?%%!%?%!%!?%?!%%%!%?!!!!%%!!%%!%?!!?%?!!?!%!%!%!!%!!%%!?%%%!!?%%!%%%?%%!!!!%%!%%%!%%?%%%!%!%!?!!?%!%%!%!?%%!!!!%%!%%%%!%%?!%!!%!%%%%?%!%?%!%%%%?%%!%!!!!%%%%!%%%?%?%!%!%!%%!%!?%!!%%%!%%%??%%%?%%%?!!?!%%%?%%!%%%!!!%%%%%??%!%%%??!%%%?%?%?%%!?!!%?!%!!!??!%%!%%%%!!?%%!%%%%!!?%%%%!!!%!%%%%%!%!%?%%!!%!%%%%%%!%?%!?%%%%%%%!!%%!%!%%%??%%%!?!!%!!!!?%%?%%%!%%?%?%!%%!%?%%%%%%!!%%%%%%%%%?!?!%%%!!??!!%!%%!%%?!%%!%%%?%??!%?!?%!%?!%%%?%%!?!!%!%%!!%?%!%?%%!%?%%!%!!%!%!%%!%%!!!%?!%!%%?%?!!%?%!?%%%%%%%??%!!!%%?%!%%!!%!%%%?%%!!!!!%?!!%?!%!%%!!%%%!%%%!%%!!%%%%%!%%!!%?%%?%%%%!!?%%?!%?%!!?!?%????%%!%!?!!!%!!!?%%!!%%%%??%%%!%%!!!!?!?%!!!!?!!%%!!!!!?%!%%?%!!%!%%%!%!%?%%%?!%?%!%%!?%!?%%%%%!?%%!%%%%%!%!?%%!!%!?!!%!%!?%%%%%%!%%%%!%%%!??%%%%!!%?%?%%!!%?%!!!!!!!!%%!!!!%%%%?!%%%%??%%%%!!!!!!%%!!!!%%%?!?%%%%!!%%%!%?!!%!%!%%!%?%%%?!%!!%!%%!!%%!!!!?!!%?%%!?%%%%%%%%!?!%%%%!%%%!%??!%%?%!!!?!!?%%%%%?%!!???%%!?%%!%%%%%?!%%!%??!!?%%%%?%%!?%%?!%%%!%%!%!!!%%!%?%%!%%?!!!!!%!?%?!!!%%%!!!%%?%?!%%%!%%%?%%??!!%%??!!%%%%%!?!%%%?!%!%%%%!%%!!!%%!%%%%!%!!%%!%%%%!?%!%!%!%%%??%!?!%!%!!%?%!?!%%??%!%!%!%%!%!%%?%!!%!!%%?%%?%%%%%??!%!!!%%??!%?!?%%!%%%!%!?!!!!%!!!!!?%!%%?!%%%!?!!?%%%%%%!!??%!%?!%?%%?%?!%%!%%%%?!!%%%%!%%%?!?%%??%%%%%?!!%!%?%?!?%!!%?!!!%%??%%?%?%!%!!!!!%!%%%!%%!!%%%!%?%%%!!!?!?!!%%!%!!%?%?%%%%%%!!%!%%%%!?%!%?!!!%!%%!%?%??%%%%%?%%!!!!%%??%%!%%!?%%?!?!!%%%!%?!%?!%!%!%%%?%%%?!%!%%?!%?%%!!!!%%%%?!%%%!!%%%!%%%?!%%!!%!!!%%!!%?%!%%%%%%!%%!!!%?%??!!%%!!!%%%%?%%%%%%!!%!!!!%!%?!!!!?!%%?%%?%%%%%!!%?%!%%%?%!%!!!%%%%%%%%%%%!!%%!?%%!!?%!!%!!?%?!!?!%%%?%%%!!!%?%?!%!%!!?%%?%!%%%%!?!%%%!%!!%!%!!!!!%%?%!%!?%%%%?%!%%??%%%!%!??%?!!%!!!?!!!!%%?%%!!!%!!!%%?!!!%%?!?!?%!%%%%%?%%%?%!%?%?%%!!?%%%!?%!!!?!!%%%%%?!%?%%!%%!!%!%%?%!!%%!%%%%!%???!!%!%%!?%!%!?%%%%%%%%%!!!?!!?%%%!%%!%%%!%%!%%%?%!!!%%%!!!%%!%??%!%%?!%%%%%?!%%?!!!%?%%?%!!%?!!%!%%!!%%!%?%?!!?!%?%!??!%!!!%??%!%%%%%%%!%%%%%%%%%%%%%%!%%??%!%!?%%!!%%!!%%%!%?!??%%%%%!%?%!%!%%!%%!%%?!%!?!!?%?%%%%!%%!?!!!!%!%??!%%!%?!?!%%!!%%%!!%???!!!%%%!?!%%!%?%!%?%?!??%!%??%!%!%!?%%%!!!!!!%%!!!?%!!%%!%!%%%!%!%%%%%%??%%!?%!%%!%%%!%%%%!%?%%!%!!!!%%?%%!%!!%%!%?!?!%%!%!%!%!!!!%%%!!%!%?%%%%%??!%?!?%?%%!!%!!%!%?%%?%!?%!!!%%?!!!%%!%%%%?!!%?%%%%%!!%%!%%!%%!?%?%%%%!!!!?%%%?%!!%%%%%!?!!?!%%%!%?%??%%%!??!?%!!%%%%!!?%%!%!!!%%%%!%!?!%!!!?%%%?%!%%?!%!?%%%?!%%?%%%!!%!??!!!!%!%!%%!%?!!%%!%%%%%%!%%!%%?%!%%%%?!%%%!!!!%?%%%!%?!%!!%%!%!%%%%%!%?!%%%%%!%!?!%!%%%?!%?!!!%?%?%!%!!%%%%%%%%?!!?!%%!!%!%!?!?!%%%!!?!%!%%%!%%%%?%%!%%%?%?%%%!!%!?%%!?%?%%%!%??!?!%!!%%!!?!!%%%%?%%!!!%!??%?!!%%%!%!!!!%%%!!%%%?%!!%%?!%!!?%!?%!%%%!!%%%!!%!%%!%!!%%%?!!%%%%%!?%!%%%?!%!?%%%%%%!!%!%%%%?%%?%!!%%!?!!%%!!!?!%%?!!%?%!!%?%!%%!%%?%%%???%%!!!?%!%?%!!%%%%?%!%!%!!%?%%!%!%%!%%%?!!%%%?%%!!%!%??%%??!%%?!%%!%!!?%?%%%!%?!!!%%%%%!%!%!!%%%%%%%?!%%%!!?%!!%%%%%%%%!%!!!!%!?!%%%!?%%!%%!%%!!%%%?!!?!!%!!%%!?!%%%%!%!?!?%!???!%%%!!!!!%%%%?!!%!%%!!!%%?%!%%%%!!?!!%%%!%!?%!!%!%%!?!!!!%!%?%%%!%!!%%%!%%!%!!?!?%!%%%?%%%?%%!!%%!!%%?%!%%%%%%?%?%??%!!%%%!%?%!!!%?%?!%!?!%%%!?%%%?!%%!!%?%%%!%??%%%!%%%%%!%!%%??%!!%%!%!%%!?%!%!!%!%%%%!%%!??!%%??%%!!%%!!!%!%!%??%%%!!%!!%!%!!?%!%!%%!%??%%!%%%!?%%%%%%%!%%??%%%%%!%?!?!%?%?!%!!???%%?!?%%%%!%!?%!%%%%!%!%!!%%??%!%%%%%%?%%!%?!?%%%%!?!%?!%!!%%!%%??!!?%%!!%!?%!%!!?!!!%!%?%??!!!%%%%!%!!%%!!!%!!!%!!!!!%%!%!?!!%!!!?!%%%!!%%?%%?%%!%?%!?%!%%%%%%%?%!!!!%?%%%??%?!%!!%?!%?%%?%!!%?%%??%!%%%!%%%?!%%%%%%%!%!!!%!%%!?%?!!%?!%%%?%%%%!%%%?%!?!%%?%%!!!%%%?%?%%?%%%!!!!%%!%%%%?%!!%!%!!!!%!???%%%?!?%?%!?%%%!%%%?%%?!!%%!!!!%%%!%%%!?%!?%?%%%!!?%%!!%%%!%%!!!!%%%?%??%!%%%%!%%!%%%?%!%!%!%%!%%%?%?%!%%?!!??%?%%%!!?!%%%!%!%%%!%%?%!%%%%?%!%%?!!!%%?%%?!%%%%!%!%!!%%%%%%?%!%%!%!%%!!!!!%%!%%!?!%!!!%%%%%%!!!%!%!???%!???%%??%!%!!%%!!%%?!%%%?%%%%?!?!%!%%%%%%%??%!!%!%%!!?!!%!%%!!%%?%%%!!%?%%!??%!%!?%!%!%%!%?!%!!!?%%%%!?!%!%%!?%?!!%!%?!%%%?%%%%%!!!!!!!?!%!!%!?!!%%%!%!!?%!%%%%?%!%!!!%?%%?%%%%%?!!!!%%!?%!!!?%?!!?!!!?%%!?!%%%?%!?%%!%%%%??%%!!%%!!!!%!!%??%%!?%%!!?!%!!!!!?%%!!%??!!%%%%%%%%%!?%!?!%??!!%%%!!%%%!%?%!%%%%!%!!!!%%%!?!%%?%?%%%%%!?%!!%!!%!!%%%%%%!!%???%%??%%?%!!%!!!!!?%%?!%!%%%!!!%!%%?%!%%!!%?!?%%%%%!!!!%!!%??%%%%%!!%%??!%%!!%%?%%!%!?%!%%!!%!%%!!?!!%?%%!!%%%%%%%%%%!!%%!%%!?%%%%?!?!?%%%!?!!?%%!!!!%%%!%!%!%%%%?%?%%%!%?%%%!%!%?%%%!%!%%%%!%%%%!%%?!!!!%%%%!!%%?!?!%?!%?%%!?!%!%?%%%%!%!%%%?%%%%!%%??!%!!?%!!%!?!%%?%??%%?!%!?!?!%!!%%??!!%%%???%!%??!?%%!??%?%%?%!?%?%%%%%?%!%%%!%%!%%?%!!?%!%??%!!??!%%%%%?!?!%!%%!!?%!!?%?!!%!!!!%%%%%!!?%%%%!!%%%!!%%%%%??%%!%%!%!!%??%!%%%%%?%%!!%!!?%!%!!%!!%%%!%%?!%!?!??%%%!!%!%!%%%!!%%??%!%%?%?%!?%!%%%!%%%%??!!?%%?!%!!!%!!!%!!!!!!??%%!!%!!?%%%%!%%%%??%%?%%?%%??%%%!%%%!%?%%%?%!%!!!%!!!!!%%?%%%%!?%!!%%!%!%%%%%?%%%%%%%?!!%?%!!?%%!%%!!%!!!%!%%%%!!%!!!??%%%%!!%!%%%!?%?%%%!%%%!%%!%?!%!%!%!?!!%%%!%!?!?%%!%%%!%%?!%?!%%%?????%?%%%%!%??%%!%??%!!!%%%!%?%!%%!!%?%!%?%!?%%!!??%!%%!!%%!%%???%?%%?!?!!%!%%!?%%??%%!?%!%?%?!!%%!!?%%%!%%?%%!!!!!!?%!%!%!!!?%%%%%!!%%%!!?!!??!!!!!?%!!!%%!%%%%!?%%!%%%?!?!!!!!!!?!?%%!%%!!%%%!%%%%%%%%!%!%%%!!!!%?%%%%?%%%%!%%!%?%%?!!%%%%%%%%!%!%%%?%%%?%!%!%%?!%%!!!!???%%%%%??!!%%%!%%%!%%!?!?%%!%?!?!%!?!%!%%!!!?%%%!%!??!?!%!!!!%%!!%%%!%!!%!%%%%%%%!%?!%!%%%%!%!%!%!??%%!%%%%%%!!!%%!!%!?!%%%?!%%!!!?!%!!!?%%!%!!!?!!%%!%!%%%!!?%%?%!%!?!?%!%!!%%!!%?!%%%!!%%!%%%!!%!?!!?%%!%!%!%%?!!!%!!!%?%!!!%!!?!!?%%!!!!%%!!%%!!?%%?!%%!?%%%!??%!%%!%!%%%%?%%!!!%?%%%%!%%!%%%%%!??!!%%?%%?%%%%%%%!!!%%??%?!!%%!%!?!!!%%%%%%%%!%%%!%%!%%?%?%!!!?%%?!%%%?%%!!%%%%%%%!!%%!%%%%?!!%%%??%!%%%%%!%!%%%!?!%%%%%!%!%%%%!%?!%!%!??!%%!!%%?%!%!%%%%!%!!%%%%%%%!%!%?%!!%!%%!%!%%?!!!?!%!%%!%!%%!%%%%!%%%%%!%!!%?%!??!%?!%%%%%%?%!!%%?%!!!!?!!%!!!%%%?%?%%%%%!!!?!%?%!%%!!%%%!%!%!%!%%!%%%%%!!!!%!%?!%!%???!!%!%!?!?%%%%%!%!%%%!?%!%!%?%???%%%%!??%%!%%?%%%!?%?%%!!%%%%?%!!?%%!?%%!?%%%?%%!!?%!%%%!!%%!%!%!%%%%?!%!!?%%%%!!%%!%%???%!%%?%!%%%!?!%!?%%!!%%%!!%?!%!!%%!%!%%?!%%!!!%?!?!%???%?%%!%?%%%?!!%!!%!%%%%?!%%!!!%%%!%%%%%%?%?!!%%%?%!!%%?!%?%%%%!%%%?%?%%%%!!%?%!!%%!%%%!%?%!%!?%%%?!%!!%?%!%%!%%%?%!??%!%%!%%%%%!%%!%?!%!%%!%?%%%%?!%%!!!%!%!!!!!%%%%%!%%!!!%!?%!%%%!%!!%%%?!!%%%?%%%%???%!%!!?%%%!!%%%%?%!%?!%%!!??%%!!!%%?%?%!%%%!%%!%?%%%%%%%!??%?%%%%%!?%!!%!!??!%%!??!%%?!??%%?!?!%%!%!%%%%%!%!%%?!%%%?%!%?%%!%!?!?%%%%%%!%%!!??!%%%?!%%???%!!!%!!%?!!!?!%?!!!%!%!%%!%%%%%??!%!%%%!?!?%!%%%!!%%!??%%!%%??%%?!%!!%!!??!%%%%%%??%%%%%!%%?!?%?%!!%%%!%!%%%!%!%%?%?%!%%%%%??%!%?!%??!!!!!!!%%?!%%?%?!%%%?!%!?!%%!!?%%?%%!?%%%%!?%%!?%!?%???%!%!%!%%?!%%!??%??%%?%%!%??%!?%%%%!%?%???%!%%%!!!%!%%%%%%?%%?%!!!%!?!%%%?%!%!%%%!%%!%!%%%??%!%!!%!%!!%!%!%!!!!%%?%!!%%%!!%%!%%%%%!%%%%!!!?!!%!%!?%?!%%!??!?!%%!%%?%?%!!%%?!%!%!!?%%%%%%?!!?%%!?!%!?%%??%!!?%?!%?%%%!!%???%%%!%%%!??%!?%%!!%%%%??!%%!%!!%!!!%%?!?%%!%?%?%%!%!!!?!!%%%?!%%%!%%%%!!!!!%?%!%%!?%!%!%%!%%?%!%?!!%%%%??!?%%%%!%!%%%%%%%!!!!!!%?%%?%?%%%%?!%%!??%!%?!%?%!%!%?%!!%!%%!%%!!%%??!!?!%%%%%!%!%%%!%%!?%!%%%!%%!%%!%%%%!%?!%%%%%?%%?!%!%!?%?!%?!%!%!?!!%%!%%!%?%%!%!!!?%%!!!!!!!%%%!%?!!%?!!!?%%!!!?%!%%%%%%%%%!%%?%%!%%%!%%?%!!!!%%%%%!?!!!%%%?%%%?!?%%?%%!%%?!!?%!%?!%%!??%%?!%???!%%%%%%!!!%?!!?%!%!%?%%?%!!?!?!%?!!%?!!%%!?%%?!!?%?%%?%%%!%%%?%??!%?!%%!%!%!%?!%%!%%%!%%%%%!!!??%!%%%!%!?%%%?%%%!%!????%!%!?%!%!!%%?%?%%%?%%%%%!!?%!!?%!!%%%?%!?%!%?%%?%!!!!!%!%!%!%%??!%!%?!%?%%%%%!%?!!??!!?%%%%?!?%!!!%!%!%!!!!%%%??!??!?!!!!!%%!!%?%%%!%%%%%%%%!%%%%%?%!!%%%%!%?%!%%!!!%?%?%%%?%?%%!??%!!%%%%%?!!!?!!!%??!%?%!%%?%%%%!?%!%%%%%%!!?!!%%%?!%%!!!!%!!%?!%?%?%%!!?%!!%%!%!!%?%%!!!?%!%%??!%?%?%!!!%!!%%??%!%%%%%??!??!%%%??%%%%%%%?%%!%?%%%%?%?%!!%%%?!%!%%?!!%%%%?!%!!!!%??!!%!%!%?!?%%!%?%!%?!!?%?!!!%%%%!!%%?!%!?%%!???%%!%!!%?!%!!%%%%!?!%%%%!?!%%!%%?%!%%%%?!!??%%%!%%%%!%?%%%!!!?%!%%?%%?%%!!???!!??%?%%!!%%%%?!?%%%%!%!%%!%%%??%??!%!!!%?%!%!!%?%?%?%%%%!%!%!%?%?%%%%%!!%!!?%%!%?!?%?%?!!?!%!%%%?%%!!%%?%%??!%!%!!!%%%%%%%%?!%?%!?%?!?%%!%%%!!%%!%!%!!%!%!?%?%!%!!!!!%?!%!?%!!!%?%%%!%%!!%%%!!%%%!%%%!%%%%%!!%%!!?!!%%%?%??%!?%!%%%!!%!!!%%%!?%?%%%!??!??!?!%!%!%%%!??!!!!?!%??%!%%%%%?%!%!!%%!%?%!!%%?%%!!%%%!%!!%%?%!?!%!%%!???%!%%%%!!%!!%%%%!%!!%!%%?%?!%!?%!%?!!%%!%!?!%!%%?%%%%%!%%%!%%??!!%!%%!%%%?%!%!?%?!!%%!!%?%%%!!!%%%%%?%!%%!%!!%?!%%!?!!%!%%!!!!%!%%%%%%!%!%!%%?%?!?!%!!%%!!%%?%!%!%%%%!%%%!%?%%!%%%!!!%?%%%%%%%!?!%??%%!%%%!%!%%!%?%?!%!%%!%!%%?!!!%%!!%!!!%!%!%!!%%%%?%!?%?%!%!%%%%%!?%%%%%%%!%!!%%?%%!%!%!!?%%!%%%%%%%%%%!%%??%??!!!?%!%!%%%%%%?%%?!%!?%%%!%!%%!%%!%%!%!%%%%!!%%?%?%%%!!%%!%!%!%!!%!%%%%!%%%%%!???%!!!%%%?%?%!??%%!!?!%?!%?%%?%%%%%%%!?!!!!!!!!%!%!!?%%!?!!%?%!!%!!%!!!%%!!!%!%!!%%%!%%!??%!%%%?%?!%!%%??!%%!%%?%%%%??%!?%!!!%%%?!?!!!!%%!%!?!!%%!%%!?!!!%?!%%%%!%?!%??!%!?%%!%!%%!%%!!?!%??%?%!%!%%%?%%%!?%%!?!!?!!%%%%!!!!%!!%!%%%%!!%%?%?!!%%!%?%?%??%!%%!!%%?%!!%%!!!!%%!%%%!?%%!%?%!%?%%%!%%%!%%?%%%?%%!?!!%%%%%?!%?%?%%!%%%%?%%%%%%%!%%??%%?%!?%!%!%!%%!%!%!%%%%?!%%!?%!!%!?!!%%!%%?%!%!%%%%?%!?!!%%%%!!%!%%%%?%!%%!%!??!%!%%%!!!!%?%!!!!%!%%!!%?!%%!!%%?!!!!%%%%%%%%!??%%%!%%%%!%%!?!!!!!%!%%%!%%!!%??%%%!%%%!!%!%%!?%!?%%%%%%%!%%%%??%%!!?!%%%!?!%!%!!!!%%%%?%%%%%%%!??!%!%%?%!?!%!%!?%!%!%!!!%%?%!%!?%!%!!%%%%%%%%%!%%%%%%!%%%%!%!!%%%%%%!%%!%%!%!%%!%%%!?%!%%?!!!?%!%%!%!%?!%!?!!%%%%%!%!%!%!%%%!!!%?%!%%%!%?%%%%!!!!!!%!%%!!!?!%!!?%%!?%%%?%%%%%%?%?%!!!%%%?!%%%?!%!!!%%%!!?!%??!?!%!?%%!%?%!%%%!%%!?!!!%%%?%!%%!%!%!?!?%%!?!%!%%!%?%?%%%!!%!!!!%!!!!%%%!?!?%%?%%!%%%!%!%!%%%!%!?!?%%!%!%%%%%%!!%!%%!!?%%%?%%%%%!!!%!%%%!!%%%%!!!!?!?%!!!?%%!!!?!!?!%%?%%?%!!%?!?%%!%!?%%!!!%!%%%%!%!%%%%!%%!%!?%?%%!?%%%%%!?%!%?%!?%?%%!!!%%%?%%%%%!??%%?%!!%!?%?%??%%%!!!?%%?%?%!?!%%%!!%%%?!%%?%%!!%!%%%!%?%?%%!%??%?!%?%%%%%!%%%%?!!%%!%%?%!%!?%!!!%!!!!%%%%%!!?!%%%%%%!?%?%%%%!%%%!!?%?%?!%!!%%%%!!%!?!?%?%%%%%%%?!!%%%?%?%?%%!%!!?%%?!%!%%%%%!%!?%%%%%%%%%!!??%???!!?!%%%%%%%!!!%??!?%?!?%%!%!!%??%%?%!%%!%%!%%!!!!%?!%!%%!%!?!?%!%?%????%?!!%%!%!%%%?%%!??!%%!!!!%?%!?!%!%%%!%%!!!!%%%!%%!?%?%!!%!%%?%%%?%!!!%!%%!?%!%%?!%?!%%%%%%!%!%%?%!?%%!?%%%!%%!??!?!!%%%!%?!%?%%!%!!!%!!?!?%!!%?%!%%%!?!!%!%%!%%%%!%%%?%!?!%%!!!?!!%!%%?%!%!?%!!?!!%!?!%?!!%!%!!!!??%%!%!%%%%!%%%%%!%%!%%%!!!?%%%%!%?%%%%%!???%!!!%%!!%!%%!%?!%%%!!%%!%%!!!!%?!?!%!!%?%%%?%!!??%%%?!?!!!!%?!!%%%??%!?!%%%!%%%%?!%%!!%?!%!?!%!!%!!!%%%%!!%!%!?%!!%!%?!%%%!%%%%!!%%%!%!!?!%%?%%!%?!%!?!!%%%%?%%%%%!%?%%%??%%%%!%!!%%%%??!%%!%!!?%%%?!!%%?!%%%%%%%%%!%%!!%!%%%%!%%%!!!?%??%?!!%!%!%!%%%?!!?%?!%!!?%!!%%!%??%!%!!%?!%!!%!%%?%?!%%!!!%%!?%%%%!!?%%%%%%%?%!??!%??!!?%!%!%!!%!%%!?%%!?!!%!?%!?%!!%%!!?%?%?!!?%%%%%!%!%?!!%%!!%!%?!%%!?%!%?%!!?!??%!%%%!?!%????!%%%%%%?!%%%!%%!!!??%%%!!?!?!%!!%%%%%%%!%%%!%!%?!!?%?!%?!%%%!!!%!%%!!???%%?!%?!%%%!??%%%!?%?%!!%?!%?%!%?!%?!!%%!!??%?!%?%%%??%%?%%?%??%!??%%?%!%!%!%?%!?%!?%!%!%?%??!%%%%%%%!!%%%??%!%!!%%%!!%%%%%%!?%!!%%!%%%!??%?!%?!!%%?!!!%%!%!%%???%%%!%%!?%?!%??%%?!?!!?%!%%!%!%!?%!%!%%!%!%%?%?!!%%%!%?%%!?!!?%%!???%%!%%!?%?!%!!%%%%!?!??!?%%%%?!??!!!?%%%!%%!!%!!!%?!!!?%%%!%?%?!%%!!?!!%!?%%!?!!?%!%%!?%%?%?!%!%!!%!%!!%%!!%!!%!%%?!!%%!!%%?!?%%!%!%!?%%%%??%%%!???!%!!%!!!%!%?%%!%!??%%!%%%!!%%%%%%%%%%??!!%??!!%%%!!%!!%%%%%%!!!!!?!%!%%!!%%%%%!?!?!%%%%!!!%!!%?%%!!?%%%?!?!%%%%%!!!%!%!?%??!%%%?!!%%%!%%%%!!%!%%%%!%%%%%!!%!!%%!?!%%?%%%%%%!?!!!%?%%%!%%%?!??%?!%!%!%%%!!?%%%%%%!%??!%%!%?!%%%?%!%%%%%%%%?!!%?%%!?%!%%%??%%!!?%%%%?%!!%%%?!%%??%%%%?%!!%%%!!%!?!!!?%!%??%!%%!!!%!%?!!%%%!%!%%!%%!!%?%!%%!?!!%%%!%%!%%??!!%??%!!!!%?%%!%!%%%!?%!%?%%%!?!!%%%%%%%!%%!%!!%%!%!!!%!!%!!!%%?%!%!?!!%%!!!!%!!!%?%%%%!!!!!%!%%?%!%!%%%%%?%!?%!!!%!!%!%!%%?%!%!!%!?%?%?%%!%%%%%!!%%!!??!!!!%%%!!!!?%!!%%%???%?!%!?%!%%!?%!!!?%??%?!?%!%!!%%%%%%%%%!%%!%%!!%?%%%%%%!%!?%%%!!?%%%%??%%!%!%%%%!%!!?!!!!%%!!!%!%?%%%%%%%?!!%%%%%%!%!!!%!%!%%!!%%%!%?%!%%%?!!%%%!%%%!!?!!?!%%?%%%!???!!%%%?!%!!%%%!%%!??%%%!!!!!%%%%%?!!!%%!%%!%%!!%!%?!!!%?!!??%%??!%?%!!!%%?%!%%%!%%!%%!%!%!!!!?%!??%!?!%%??%%!?%%!!!%??!!%!?!%!!!!!%%?!%%%!%?!%%%??!%%!!!??%%%%!%%%!%?%%%?!%!%%!!!?%%%?!%!?%%!%???%%!!?%!!%%%!!!!!%!?%?%%!%%?%%%!?!!%!!!!?!!!??!%!%%%!?%%!!%%%!!?!%!!%!%%%%%%!%!%?!%%?%!!%!%%%%!%%!%!!%!%%?!%!%!?!%!!%%%%%!?%!?!%!!%%%!%?%%!!%?%%!!%%%!!%!%%!%%!!!%%!%!%%!?%%!!%!!!!?%?%%?%!!!%!%%%?!?%%%!%!!!%!!!!%!%!!!%!?%%%%%%%!!?%!%!!!%!%%%%!%!!%!%?%!%???!??%!!!!%%!!!!!%!%?%%%!!!%%%!!%!%%%?!%%%%!%%!%%!%!!?%!!!!%%??!%%%%%%!!!!%!%%%!%!%%?%%%!!%!%!%?%?!%%%?%%!?%!%%!%!%!!?%!%%%%%%?%%%%%%!!!!!!%%%!??%%%%%%%%?!%!!%?%!?!?%?%!?%%!%%%!%?!%!?%?%!!!!%?%%!%%?%%%!!?%%%%!!%%!?%%%!%??%!%%%%%%%%%?!%%!!!!!%!%%!%%%%%?!%%%!%%??!!!%%?!!%%%%%%%%!%%?%!%!%!%%%?%%?%%%!!?%%?!%%%!??%%!%!!!%%%!?%!!!!%%!%%%!%!!%!?%!!%%%!%?%?%%!!!%?!!!%%%%?!!%!!%!!!!%%%%?%?%%%%%%%!?!%%!%%?%!%%%!?!??%!%%%%%!%!?%!!%?%%%%%%?!!?!%%!!%!%%!??%%%%!!?%%%!%%!%!%%%%!%!%?%%%?!%%!%!%%!!%%?%%!?%%%!%%?%%%!!%%!?!!!??!!%%!!%!?!!%!?%!?%?%?!%%?!%!%%%?!%?%!%%%%??%?%%%!%!%?%%%!!%%!!%%%%!?!%%%%%%!?%%%%%?%!?%%%%?!%?%%?!%%%%!??%%%!%!%%%??!%!%%%?%?%%?!!%!!!!??!%!?!%!%!?%?!%%!!%%%%%%!?!%!!%%%%%??!%%?!%%%?%%%!!?!%%!%?%!%?%%%!%%%%%?!!!%%!??!!?%!!!!??!%%!?%%%!%??%%!%!%?%!%%?%%!%?%%%%%!?%?!%%!!?%%!%!!!!%!%%!%%!?!!!!!%%!?%%%%%!%?%?%!%!?%!%%?%%!%%!?!!%%%!%!%%?%%%!%!!%?!!!%!!%%%%?!!!%%%%%%%%!!%%%??%%%%%%?!!%!%%%!!%!%!%%!!?%?%!?%%??%!!!%%%!%!?%!%%%%%?%!!%%!!!%%!?%!%!!?%%!%%%%!?%%%%!!!!%!!?!%!%%%?%!!%?%!%%%%%!!%!%?%!?%!?!!!%!%%!!!%%%!%%!?%?%%%%%!?!%%!!%!!!?!%%%!%%%!%!%%%!%%!%%%?!!%!!%%!%!!?!%??%%?%%!!?%?%%%!%?!%%%%%!!%!?%%%%!!?%!%!%?%%%%?!%%?%!%!!!!?!!?%?%?%%%%%%%!!%!?!!%!!%!?%!%%!%!!%%??!%%%%!%%!??%%!%%!!%%?%?!%%!!!%%?%!!???%?!!%!!?%%%%!?%??%!%!!!!%!!!!!%!%?%%!?!!%%%?%!?!!!!%%?!%%%!%!%!%%?!%!!?%%!?%!%%!%%%%!!!!%!%!!%%%%?%?!!?!%!!!!!?%!%%!%%%??!%!?!?!%%!!%!%%?!!%%?!???!%!!!%%%%%%!?%%!%!%%!%%!%!%!?%?!??%%?!%!%%%!!%%!!%%%!%!%?%!%???%%%%?!?%?%!!%!%%!%%?!%%!!%%!%?!?%%%!%!%!%%%!??%!!%!%%?%??!!!?!%!%%!%%%!%!!!%%%%!!!%%%!?%%%!!%!%%%%!%!%?%!%%%%!?!%!?%!!%?%%%%%%!?%?!%%%%%!!?%!%!%%%?!??!!!!!%%%??!!%%%?%%%%%?!??%?%%!!%%%!%%%%%??%!%?%!?%???!!!%?%%!%%!%%!!%%%%?!!%!!!!!!!?%%!!!!%%%??%%!?!!%%!!!?!!%?%!?%!??!!!%??%%%%%%!!%!%%???%!!%%%!??!%?%!!%?%%!%%?!?%?!%!!?!?%%%%%!%%%!!!%?%%%%%?!%%?%??%%!%%%!%!%!!%?%!!!!!%!!%%%?%?!!%!!%?%%%%!%%%?%%!?%%%%!%%%%%%!!!!%%%!?%%???%?%%%%!%!!?%??%%?%%??!!%!!!%%!!!?!%%%%!%?%%!!!??%%?!%!%%!%!?%?%!%!%%!%%%!%%%%??%%%!!%%%%?!%%%?!!!%?%!%?!!!?!%%?!%%%???%!?!!%%!?%%?%?!!%%!%%%!?%????%%??!%%%%%!!!%?%?!%?%!%!!?%?%%%%!%!%%%%%!!%!?%%?!??!%%%%%%%!%!?%%?!!??%%!??!%!!?%??%%!!%!!!%?!!%%!!!%%?!?%%%!%%%?%!%%!!!!%%%!!%%!%?%!%%?!?!!%!!%%%%!%!??%%!%!!%!%%%!!%%%?%%!%??%!%%%%?!%??%%!%%%!?%!%%!!?!!%!?%!!%!%!!%%%%!%!!%?%?%%?%!%%%%%%!%!?%%%!%!%!%?!%%!%%%%%?%%!%?%?%%???!?%%?!%!%!%%%%%?!!%%?!%!!!?%%!!%!?%%?%!%%!%%%%%%??%%%%%%%!%%%%%%?%%%%!%!!%?!%%%%%%%%?%%%!%%!?!%%!%!!!%%!%%?!%%??%%!%%%%%?!%%%!!?%?%!!%%??%%?%!%!%!%%%%!?%!?!%!?!%%!%%%%%%%%%%?!%!!%!%!?!%!?!%!!%%%!%%!!!%%%%!%%?%?%%%!%!??%!?%%%!%%%!!%?%?!!%!!?%%!!?!%%%?!!%!?%%!%%%!?%%!!?!%?%%!!%!%!!!%!?%%?!%!%!!?%!%?!%!%!?!%%%!%%!%%!?!%?!%%?%%%%!!!%%%%%??%!%?%%%%??!%%!!%!!%%!%%%!%?%?!%%%%!%!%!!????!!!!!!!!?%%!%!?%%!!?!?%%%%%%%?!!?!?%!%!!!%?%%%!%??%!%!%%?%!?!%%%%!%%?!!%%%!%%%??%%!!%?%!%%!%!!%%!%!!%!!%%%??%%!%%%!%!%!??!%!%%!?%!%%%!%%%!!%%!%?%!%!?!?%%!%!%?%!!%!!%!%%!%%?!?%?!!!!!%%%%!??%%!%%!!%!?%?!%%%%?%%?!!?%!!%!?%%%!!%!%?%%%!!?!!%!!%%?%%%%!%?!?%%%!!!%?!!%%%??!?%?!%!?%!?%?%!%!?%!%%%%!?%!?%?%%%!!%%!%%!%!%%%%!%!%%%??!!!!%!?!%%%?!!%?!%%%!%%!%%?%%%?!!?%!%!!!!%!!%!%?%!!%!%%%!!!?!!!!?%!%%!?%%!%%%?%!%%?%!%??!%%?%!??%%??%!%!!%%!%%!!%?%!%%?%%%!!!%!!!%%?%!!%!%?%?%?%%%%!!%%%!%!%%?%%!!?%!%%!%?%%%?%%%%?!%?!%?%!!%%%%?%!%!!%!!%?!%%!!%?!%!!!!!%!%%?%%?!%%%!?%!%%!%%%!%%%!%%!%%!%!?%%!%%%!?%%%%?%?!!!!!%%%%?%%!!%%%%%?%%%!!%??!%!!%!?!%%%%!%%!%%!%%%?%!!?%%!?%!!!?%%!%%!!%!%!!!%%%%!!%%!%%!%%%%%%!?%%!%%%%?%!%%!%%?%??!%?!!?%?%%%!?!!%%!?%%!%%%%%?%!!!%%!%?!!!?%%%!!??%%!%%!%!!%%%%!!?%%?!!%?%%%%%%!%%%%%%?!%%?%?!%%%!!!??%!!!%%!!!%!%%?!?%%?!!?!%??!!%%?%!!%%%%%!%%%?!!!?%!?%%%!%!%!!?%!?!!%!!%!!%!%%!%!!%%%!%!%!%%?%%%%?%!?!!%?%!%%!?!?%%%%?%!?!%%%%%%%!!!%%%!!!%?%!%%%%??!????!%%!%%!?%%%%%?!!%%%%%%!%%!%%!!?!%!%!!??!?%???!!?!!!??%%?%!?!%%!!%%?!%%%%!%%!%!!!%%??%!%!!?%%!!%%%!!%!?!%?%%%%?%!%%%%%%!?%??!%%?!!%!!%%!!?!?%%%!!%?%!!%!!?%%%!%!!%!%%%!%!?%!%!!%%%%%!!%?!%%%%%%?%!??!%%!?%!%%!!!!%?%!?%%%?%%%%%?%%%?%!!%%?%!!!%!!%!!%%%%?!??%%%!?!%!??!%%%!!%!?%!!!!%%%%%!%%%%?%%!%!!!%%%%%?!!%%!%!!%!!%!%%%%%%?!?%%?%%!!%!!%!?!!%!!%%%%%?!%!%%!%!!!!%!!!?%!!%%!%%?%!!%%%%!!%%?%%%!?%!%%%!%!?!%%%?%!%?%?%%%%%!!!%%?!%?!!!??%!%%%%!!%%!?%%%!%%%!?!!%?!%%!%%%%%!!%!!%!!%?!!!%!%%%!%%%?%%%%%%!%?%%!%!%%%%%!!?!%%%%?%!!?!?%%%!?%%%?!?!?%?%%?%!%?%%%!%!?%!!%%%?%!%%?%!%%%??%%!!!!%%%%%!!%!!?!!%!?!%%%%%?!??!%!!%%!%%??!%!!%!%?%%%%!%!%%%?%%??!%%%%!%!%!?%%%?%%!%!?%%?%%%!%?!%%??!%!%%%!!%?%%%%?!?%%%%!%%!!%%?%!%%!%%%?!?%%%!%?!%%%%!%?%!!%%!%%%%%%!%%??!?%?%?%??%%!%!%%!?%%%!!%%%%?!!?%!%?!%!%!%%%%%!%!%%?!?%%%!%%!?!?!%%!?%%?%!?!%?%%?%%%%%%?%!%%%!?%%%!!%!!!%!%%??%?%%%!!%%!!%!!%!!%%%%%%%?!%?%%!?%%%!?%%%%%!%%%%%%!!%!%!!%!%?!%!?%%%!%!!%?%?!?%%%!%??!!!!!?!%!%%%%!?!!%!!!%%!%!!!%!!!%%?%%?%!!%!?!%?!?%?%%%%!%%%!%?!!%?%??!!??!!??!!!%!%%?%%%%?%%!??%%!%!%%!!!%%!?%%!!!%?%%%!!%%!%%?%!?%!!%%!?%!%%%%%!%!%!??%!%!!!%!!%%!%%!%%!%%?%%!%!%%%%%%%!?!???%!?!%%%%!?%!!%%!!!%%%!%%%%%%%%?%?!%%%?!%?%%?!?!!%%?%%%%%!!!?!!?!!!??%%!!%%%%!?%!!%%%%!!%%!?!%!%%%!%???%%%%!!%%?%%!%!!%!%%%%%%?%?!!?%!!%%!%??!%%%!%%?!!?%?%%!%%!!%?%!%?%%??%?%%%%!%!!%%??%%%%%%!!%%!%%%%%?%%!%?%%?!%%!%%??%%%!%!?%!%!%%%!!??!!???%!%?!%?%!%%!%%%%?%%%!?%?!%%%!?!?!?!%%%!!!%%%!%%%!%%%!%%!%!%??%%?!%%%%!?!?%%!%!!!!?!%!??%%%%!%%!%!%%!%%%%%%!!!!%%!!!%!%!%!%!%%!%%!%%%??%%%%%?!!%!%%%!%%%!%!!!!%%!%!!!!%%!%%?%?%!?%!!?%!?%?!!%?%%?%!?%!!%!%%%%!!%?!??%%!!%%%!!%%!!%%???%%!%!!?%%%!!%%%%!%!%?%%%!%%%!%!%%!!%%%%!%?%!%%%!!?!!%%%%!%%%%%!!%%%?%?!!!%?%%%??%%%?%!?%%!!%%!%!!!%%!!%?%%%!?%%!%?%%!%%!%%!!!%?%%%?!%!%%%%%!%!?!!!?%%%!!%%%?%%?%%?%!%?%!%?!%%?%!%!%%%?%%?%?%?%!!?%%?!!%!%??!%!!!?%%%!!%%!!%%!!%%%!?!!%%%%%%%%%!%%!%%%!%%%%!%!!!!%%!!!!%!%!%%%!%!!%!!%!!%??!?!!%%!%!%!%%!%%!%?!%?%%??!%!!%%%%!%%%!!%!%!%?!?%!%%??%?!%%%%%!!?%%!%%%!%?!%??!!%!!%%!%%%!!!!%%%!%?%%?%?!%%!?!%%!?!!%%!%?%%?%%%%%%%%!%!!%!?%%%%%%!!%%!!???%%!%%%%!%%%?%%%?!%%?!?%!%!%!%!%%!%!!%%?!!??%%!?%%%%?!%!?!!!!!%%!!%!%!!!!%%%%??!%%!!??%?!%!%%%!%!%%%%??%?%!%%!!!%%!%%!%!%%!%%!!%!!%%%?!%?%!!%%%!!%!!!%!%%!%%%%%%?%%%!%!%%%%%!??????%??!%%%!!!%%?!%?%?%%?%!%%??!%%!%%?%%?!%%?%%!%!!%%!!?!%!!%!!%%%!%!!%!!!%!%!%%!?!?!!%?%?%%%%%??%!%!%!!?%!!%!!%?%%!!%%%%!?%%%!!!!%%!!%%!%?%%?%!?%%%?!!!!%!?!%?%!%%%%%!%?%%%%%%?%!%%%?%!%%?!%%?%%%?!?%!%%!!!!!!%%!!?!%!%!%%%??!%%%%%%!!!!%!!%!!%%?!!?!!!!!?%%!??%?%%%!!%?!?%%%!?%%%!%?%?%!!!?!%!!?%%!%?%%%%!%%%!!%!!!%%!?%!%!%%%%!%%%%?!!%!%%?!%!%??%%!!%%%%?!%?%!%!!!?%!!??%%!%?%!!!%!%%%?%??%%!!!%%!%!%!%?%!%%%!!%!!%%%!!%%!%%!%!??%?%!%!%!!%!%?%%%%%%!!%%?!%!!%?%!!%%%?!!!%!!%%%!?!!%!%??%!!%%!%!%%!%%!%?%!!%?!%!!%%???!?!%!%%%%!!!?%!!!%!!?!%!%%%%%?!?!%!%!%%?!!%!%%%?%%?%?%?%!%?%?!!%%%%%%%?%%!!!?!!%%%%%?%%%%!!!%%!%?%%!%!?!!%%!!%%%?%%%?%%!?%!%?%%!%!!%!%%!%?!?%!%%?%!%%%%%%?%!?!%%%%%!!%%?!%%!!!??!?!%!%?%?%%?!%%!%%%%%%%%!!%%%!%%??!!%?%%?%%!%%?%!!%%%%%!!%!?%%%?%?%%%!!!!%%?%%!%%!%!%!%%?!?%%!?%%%?!??!%!?!%?!!%!%%%%%!!?!!??!%!!%!?!%!%!%%%%?%!%%?%?!%%%!%%?!%%!?!%%!%!!%?%%!%?%%%%!!!!!%%!!?%!!%!%%?!%%%!!!!%!%%??%%!?%!?!%!?%%?%%!!%%?%!%?%%!%?%%%!%!?%!?!%%%?!!%%!!?%%!%!%!!%?%?!??%%?%?!%%%%%%%%%%!%!%%%%%%!%!!%!%!!%!?!!%%%!!%!%%%!%!%??%??%%%?%!%%%%%!?!%%%%%%%!%!%!!?!%!%%%%!!%%%%%?!!%!!!%%!!%!%%!!%%!%%%%!%?!!%%%%?!?%??!%!!%?!%%%%!%!!!%%!!!%?%!!??%!!%%!!%%!%%!??%%!!%?!%?!%!%!%%!%!%!%?!%?!%!%!!??!%!%%%%%%%?%!%??!%!!%%%?%%!!!%!%%!%!%%!%%%??!%%%??%!!%?%!%%!%?!%?%!!%!%%%!%!%!%!!%%%!?%!%?%%!%%%%?!!!%?%?%%!%!%%%??!?????%?%!?!%!%%!%%!%%%?!?!!%!!%%?!%%%%?!%?%!??!?%%!!?%!!%%%?!%!%?!!%%%?!?%!%!???%?%!%!%%!!?!!!!!!%%!!%?!?%!??!%!%%%!!%!%!%!%%?!%!%%!%%!%!%%%%?%%%%%?%!%?!%%?%!?!%!!%%%!!%!%%??%!!?%%%%%?%?!!%%?%!?%%!????%%%!%%%%%!??!!%!%%?%%!!!?%%%%??%!?%!%!%%!%%?%!%!%%%%!%%%!!%!%%!!!%%!!%%%!%%%?%%%%?!%?!?%%%%?!?%%%%!!?%%%!!?!!%%%!!%!%?%%!%?%%%!!!!%%??%!!%!%%%?!%%%%?!%%!?!%%%%%%?!%%%!!?%!!!!!%!!%%!!!?%??%!!%%%!!!?!%%!!!!?%?!%%%%!%%!!%%%%!%%?%%!!?%%%%%!!%?!%?%!?%?%%!?%%%!%%%%%%!!%!%%%%!%%!?!%%!!?%!%%%%%%%%!%?!!%%!?!%??%%!?!%%%!%%!?%!?%%!%?%%!!%%%!!!%%?!%?!%%%%%%!!!!?!%!%!!!%%%%%!%%!!?%!%%!%!%%%!%!%!!!%%%?%%!%%%!!!%?!%%!?%%!%!!%!%??%?%%%%%!%!!!%%%%%!!%%!!%?%!%?%%%!%%?%!!%%%??!%!?%%!%%?%%%!!?%!%!%%%%!%%%?!%%!%?!%%%?%!??%%!!???%%??%!!!%%%!%?%%%!%!%%%%?!!??%%%%%%!!!%%!!%?%%%%%!!%%%%%%%%%%%!!%%%?%%?!!%??%!%%?!%!!%%?%%!!%%%%!%?%%%!?%%%%%?%%!%!%%%?!%?%!?%%!%?%!%!%%%!!%%!%%%?%%%?%%!?%!%%!%%%%%%!?!%!%!%%%!??%?!!%!%!?%!%%%%!%!?!%!!!%!%!%%!!%%!%%?!!!%!%%%!%%!%%%%%?%!%%%?%%%%%!%?!!!!!%%%!!%!!!%?%??!%?%%??%!%!%!%%%%%?%%%?!!!%%%%!!!%!%!%%?!%!!!?%!!!??%%?%%!%%!!!%!!!!%?%!%!%%!!%??!!%!??%?%?!%%%!!%?%!%!?%?%!?!!%%!%%%%!%!!!%!%%%%%%%%!%!?%%!?%!%??%%%?%%?%%!%%%%%!%%!%%%!%%?%%??%?%!%??!%%%!%!?%!?%?%?%%%!%!%%!!%!!%%%!%!%%??%?!?!%!%%%%%?%!?!?%!%%%%!%%!%!!%??%%%%!!?!!%%!?%%!??!!!!%%%?!%?!%!?!?%!!%%%%%%%?!%%???!%%!?%%%%!!%%%!!??%%%!!?!%!%%!%%!%!?%%%%%!%?%!!!?!!%?%%!!%!%!%?!%?%?%!!%!??%%%!%%!?%%%%!!%?%?%?%%!%!!?!?%%?%%%!%?%%%!!%!?%%!!!%!%%!?!!%?%!%%!!?%%%??!%%!%%?%?%!%!%%!%%?!%!%!%!%!?!!%%!!%?%%%!%%%%?%%%!!%!%?!%!%%!%!!!%!%?%%!?%!?%???!%%%?%!!!!%!?%%!%%%%%%%%%!%%%%!%%%!!!!!!%!%%%!!%%%?%%!%%!%?!%%!!%!%!!%!%%!??%%%!!!!%!%%%%%%!%%%!??!!%??!!%!!?!!%%%%%!?!%%%!?%!!!%%!?%%%?%!!!?!!%??%?%!!!%%!%?!!%?!??%!%!%!%%!!!%!%!%!!??%!%%%?%%!!?%%%!%%%%%!!?!%%%!%!!%?%!%!%%?!%%%?%!?%%%%%%!?%%!%%%!%!?%%%%%!!?!!!%%%!!??%!?!%!%??%%!%%%%!!%??%%?!?%!?%%%?!!%!%!%%?%%!!?!!%?%!??!!?%?!?!%%?%%!!%%?!!%%%!%%!?%!?!%%!%!!!!%%%?%%!%!!!%%%!!?!?!?!!!%%!!%%?!!!%%%%??!!!%!!!!%%??%!!!%%%?!?%%?%?%!%?%!%%!!%%!%?!?!?%!!!?!%%!%!?%?!?%?!!%!%%%?%!!%%!%!%?%%?!%?!%%%%!!%%!!%!%%?!%%??%%%!?!?%%!?%!%%!!!?%!%!!!!!%%%!!!%%!??%%%%%%!!%!%!!%%%?%%?%!%%%%!%!%%%!?%!?!%%!%%!%%%!!%?!%?%!!%!%%!!%%%?%!%!!!!%!%!%%%!%%!%?%!!!%!!%!%%!?!?%%%!%%%%%%%%!!?!!?%%!%!!!%%%?%%!%!%%%%!%??%%%%%!?%???!%%!%%!%!%!%%!!?%!%%%!%!?!!!%?%%%?%!!%?%!!?%!!?!%!?%%!%%?!%!%!!!!%%%%%%%!%!?%%?%!!%?%!%???!%?%%?!?!?%%!%!%%!?!!%!%!%%!!?%%!!%?%?%!!!%!!%%!%%%?%!!?!!!%%%%!%?%!!!%%?%!%!!!!!!%!?%%!!?%!?%!!!!!%%%?%!%!%%?%%%?%!!?%??!%%%?%!??!%!?!%?!??%%!?%?!!!?%?%!!%%%%!%%%%?%%!!?%%!%?!!!!!%%%?%!?%%!?%!!!%!?%?%%%!!%%?%%?%!?%!!!%%!?%??%!!%??%?%!!%!%?!!%%??!%!!%!??!%%%%%!%%%%?%%!%%!%!??!%!!?%%!?%!%!?%!!%?!!%?!?%!!%!%!??!!%!??!%!%!%%%?%%!!!%%%%!%%!??%%%%%%%%%%%!%?!%!%%!?!%!%%%%%!!!!?%!%!!%%!!?!%!%%!%%!?%%%!%!%?!!%%?%%%%!!!?!%%?%!%%!!!??!?%?!%%%%!%!!%%%!!!%?!?%%?%!%!%!!%!?%%!%!!%%%!!%%%%???!%%%%%!%%!%?%%!%?%%%?!%?%%%!%%%%%!?%?!%?%?!%!%!%?%!%!%%!??!%%%!%?!!%%%%%?%%%!%%%!!%%!?%?!!%!%!!!!%!%?!?%%??%!!?%%!%!?%!!%%%%%?%%!!!!%%%%%%!?!%!!%??%?%?!???%!!%?%!!!?%??%%!!!!%!%%%%!!%!%%%%?!%!?%!?%!%!%??%!%?%!!%!?%%%%%?%%!!??!%?%%!%!%%?%%!%??!%!!!!!%%%%%?%!?%!%!%%%%%%%!%!?%!?%%%?!!%!!%!%%%!%!?!!!%!%%%%!%!!%%%?%%?!%%!???!%!!?%!!%%?%?%?!%%!?%%%??!!%!?%!!!%%%%??!%?!!!!!%!??%!!%%%!!?!!!!%?%!?%!!%%!%%!!!%!!!?!%!?!%??%%!!!!?%%%%?%!%!!%!!!%%%!%?!%??%%%%!!%%?%%!?%!%!%!?!!%%!%!!%?%%!!!!??!%!%%%?!%%%?%%%%!?!!!?!!%%%?%%%!!%!%??!!!!!%!%!%%%!%%%!%!%%%!%!!!%?!%!?%!!%%%%%%%!!!!!?!%!!!!%%%%!!!%!!!!!%%%!!%%%%!?%!%%!%%!!%%?%%!%%%%!%%!%%!!%%?!%%%!%%%%%!!!%!%%!!%%%!%%?%!%!!%%%%%?%%%!?%!%%!%%?!%?%!!%%%%%!%?%%%%!%!%%!%??%%%%?%?!%%%!%?!?!?!%%%?%?!%!%%%!!?!%!%%!%%?%%?!%?%!%!%?!%%!%%?!!!%%%!%%%?!!!!!%!%%%%?%!?!!!%!?%!!!!?%?!!?!!%%%!%%%%%%?%?%%?%%!!%!!%%?%!!%!!??%%%!!%%!!%%%!!%?!!%%?!%%!%!%%%%%%%?!!!!!%%%%%%%%%!!%%%!!?%%%%%%%!%!%%%!?!??!?%!%%%?!%%!%%%?!%!%!%%%%?%!!%%%?%%!!%!%%!!!%!!%%?%??!%!!%%%?!?%%!!%?%!%!%?!%?%!!%%%%!%%!%%%!%%!?%%%!%!!%??!!?!%%!!%%!!%%!!%%!%%%!!%!?%!%?%?%%%%?%!?%!%%%?!!?%%!%!%???%%%!%%?%?%%!%!!!%%!%??!%!%%%!%!!?%%!%%?!%!%%!!!%?!%%?%%%%%?!?!%%!%!!!!!!%!%!%%?!%%!?%%!%?%!%?!!?!%!!%!%!%%%?!!!!!!?%?!%!?!!!%!??%!%!??!!?%%%%%%%%%!!!%!%?!%%!!%%%?%%!??%!%?!!%%%?!!%%%!%%%!!%!!%!!%%%!%?!!!%%?%?%%%??!%!%%!%%%!%%!!%%%!!!!%!%%%!!%%%!!%!%%%!%!%%!%!%!?%%%!%%%%!%%%??!?%!!%!!!%!%!%%!%%%!??!!!%?%%%%%?!%!!!?%%?%?!%%%!?%%%?%??!!%%%%%?%?%%%!!%%%!%%?%!!%%%%%!%%%?%%!%%?%%%!%!%!?%%?!%!!%?%%%!!?!%!?%%%?!%%!%!??%!%!?!!%!?!%%%%%%%%!%%?!!?%??!%%%%%?!%%??%%%!!%!%!!%%!?%%!!%?%%??%?!?%!%!?!??%!%!%?%??%!%!!%!%?!%?%!%!%!%!!%!%!%%%%!%?!?!!?%%???%%%!!!!%%%!%%!%%%%%?!%!!!%!!?%%%%!%!%%?!!?%%%%%%%%%%!?!%!%?!!%!%%?%!!?%%%!!?!%?!%%!%!%%??!!?%%%%!%?%%%?%%!!!%%%%%??!%%?%!%%%!%%!%%%%!%!%%!??!%%%?%%%%!%%%%%?%?%!?!?!%?%%?!!!%%%?%%!%%%!%%!!%%%!%!!%%%?%%?%%%?%%%!%%%%!?%%%%!?%?!!!%%!!!%!?!!?%!??%%!?%!%%!?!!?%?%%%%%?%!%%%%%%!!!%%%%!?%?%%%?%!%?!!?%?%%%%!%?!!%%?%%!!!%%%!?!%?!?%%?!%!%!?%???!%!%%?%%%%%?%!!%!%%%!%%%%%%!!!?%?!?%!?!%%!%!%%??!%?%!%!!%%???!%!!!!!?!%%%%!%%%%%%%!!!%??!%%!!!?%%!!??!%?!!!%!%%!?%!?%?%!!%%!?%!%%!?!!!!%??!?!%????!?!?!!!%%%%%%%!!!!!%%%?%?%!%!%%!%%!%%!!!%%%?!?!%%!!%?%?!?!!!%%%%%!!%%!?!%%%%%!%%%!%?!!%?%?!%!!?!%%!%!?%%?!!%%!!%!!!!%%%?%%%!%%%!!%!%%%?%!%%!!!!!%%???!!?%%?!%%!!%%%%%!%!%??%!%%%%%!?!!%!?!%%!%%!%?%!?%!!!??!%!%%!%?%!%?%%!%!!!%%%%%%%%%%?%%!!%?%!%%%!!%%%%%!%!%%%!?!!%%!!%?%%!%!%?%!%%!?%?!?%?!%%%!%%%!!%%!%%%!%!%%!%%%%%!%!??!%!!%?%%%!?!!%%%?!%%!!%!%%!%%%!%!%%%%?%%%%!!!%%?%%%%%!!%!!!!%!%%?!!%!!!!%%!!%!%%%?!%%!%%!%!%%%%%?!%!!!?%%?%%!?!%%%!%%!!%!%!!%%%!!%!?%%??%!%!%?!!!%%?%%%%%!!!%%%?%%?!?%%%%!%%%?!%%%!?%%%!%%%%!!%!%%%!?%!!!%!%%!%%?%%?%!%?%?%%!%!%!!%??%!%%?%%!!%%!?%%!%!%??%!?%!!%%!%!%%%!%%%%%!!%%!!%!%!!%%%!!?!!!!!!%%%!%%!%!%!?%!?%??%%%!%%!%%%%!%%%!%!%!%?%!%?%%%%?%!%!!%?!!%%%?%?%!??%?%!!!!!%!!!%?%!?%%%%%?!%!%!??%%%%%!%%!!??%%!?!!%%!%%!%!%%!!%%!!!?!!%%%!!%?%%%?!!%?%!!!%%%%!%?%!%%%%%%%???%!!!!!%%!!%!!%?!%%!%%%!!%!%%!!!%!%?!%?!?!%%%!%?%?%%!%%%%%%%!%!!!!%%!%%!%???%!!!%%?!!%?%%!%!%!!%!%%??%%!%%!?%%%!%!!%%%?%%!%!?!?!%%!!%%%%%?%?%!%??%?%%%?%%?%%%%%%!!%%%!!???%%!!%%%!!%?!!%%??%%?%?%!%%?%!%!?%%!?!!!!?%%%%%!%%%%%!!?!!!%!!!%%?%%%!!???%!%!%?%%!%!%%%%!?!%%%%%!!?!?%%!?!%!%!!??%%?%%%%!?%%%%?%??!!!%%!!!!!%%%!%%?!%%?%!%!%%!!%%%%!%%%!?!%!%!%%??!%%!%%!%!%?%!!!!!%?!%%%!%%%!%?!%?!%!!?!!%%%%%%%%%%!!!?!!!!!?!%?!%%%!%?%!%%%?!!!%%!?%?!??!%%??%!%%!!%%%?!%%!!!?%!%%!!!%!!!!?%?!!%?!?!%??!?%!%?%!!%%?%%!%!!!?%%!%!%!%%!%%%!%?!?!%%??!%!%!!%%%%%!!%!%!!%%?!!?%%%%%?%%?%%%%%!!%%%%!?%%!??!%%%%?%!??!?!!!%?%?!!!%!!?%%!!%!!!!%%!%%!!%?%%?%%%!%%%?!%%!%%%%%!%!!%?%%%!%!!%%!!%%%%!?%%%%%?!!%%%!%!!!%!!%?!%!%%!!%%?%?%%!?%!%%%?!%%?%%%%!%%%%!?%%%?!!!%!%%!%%%?!!!?!?!???%!?!%?!%%!%!?%!!?%%?!??%%!%!?%%%%%!!%!!!%!!!?!%%?!!%%?!%!!!%?%%%%!!%%!%%%!!%!!?%!%%?%!%%!%?%?!%%%!%!%%%!%!%%%%?!%%!%!!!%%%!%%%%%%!%?%!??%!%%%%!%!??!!%??%%%?%%!?%%!%%%!%!?!!%!!?!%!!??%%%%!%%!%!!!%%?%?!%%%?!!%!!%?!%?!!?!!%!!!!%%%%%%!!?%%??!%%?%%%!%%!%!%%%!?!!!??%!%%!?!%%%%%%%!!!!%%%!??%%%?%%%!%??%?%!!?%%!%%!!!%%%%%%??%?%%%!!!!%?%%!%%!!%?!%!!!%!%?%?!!%!!?!?%???%!?!%!%%?!!!%%!%!!!!%!?!%%!%!%%%%%%%!%%!!!%%%%%?!!?%%!!?!%?%?%?%%?!!!!%!%%!!?!%%%?!%%??!!!?%%%%?!?%%%!%!!!%?!!!%%%!%%?!%%??!!!%!!%?!?%!?%%%!!!!%%!?!?%%?%%??%!!%%!!%!!?!%%!?%!!%%%!!!%!!?%%!%%?!?!%!%!!!%?%?%???!%!?%!?!%%%%?%?!!!%%%%?%%!!?%%%%%!!?%%%?%%%%!!%!?%!%!?%!!?%%!?!!%!%!%!??%?%%!%%%%!?!?!!!%%!!%!!%%?!%%?!!!!%?!?!!%!%%%!?!%%%?%?%!!%!!%!%%%!%?%?%!?%%!??%%!!?%!%%!%%%%%%%??%!!!!%?%%%?!?%!!!%?!!%%%!?%%?%!%%!!!???%!!%?!%!!!?%%%%%!!%%???%!!%!%%%%!!!!%?!!%!?%%%%!!%?!%?%%!%%%%%%?!%!!!%?!?!!?!%%!%%%%!%!%%!!!?%?!%!!%%!%????!%%%!?%%!???!!!?!!%!%%%%!!%!%!%!%%!!%?%%?%??%%%!!%%%%%%%!%%!%!!!%%?%?%!%!%%!%%%!%!?%%!!!?%%%%%%%?%!%!?!%%%?%?%%%%%%??!%%%!%%??%!%!%%%?%!%%%?%%!%%%!!%%?%!%?%%%%!??!%%%?%%??%!%!?!%!%%%!!!%%?!%!%%??%%%%%%%!!%%!!?!%%%!?!!%%!%%%%%!%!%%%!%?%%!?%%%!%%?!%%%!%!?%?%%%?!!!%%!?!!%!%%%?!?!%%%%%!!%?!!!!%???!!!!%%%!%%!!%%??!?%%%%%%%%%%?!%%?!!?%%?!????%%??!?!%%%%??!%!!%%%!%!%%!%%%%%%?%%?!%%!!%!?%!?%?!?!%!%!!!%!!%!%!%%!%%?%%%%%!%%?!??%?!!!!??!!%%!%%!%%%%%%?!?%%%%%%%%%?%!?%%%!%!?!%%?%!%!%?%!%%%!!%!%!!!%!!%?!%!%%%%!?%%%%??%?%!%!%!!??!?!%!!!??%!%%!%%%!!?!%%%!%%??%!!!%!%%%!%?%!%%!??!!!?%%%??%%!%!!%%%%%%!%%%%%%%?!??!?%%%%!%!?!%%%!%?!!!!%!%%%?%%%!?!%%??!%%!%%?!!!!!%?!%%%%!!!!!%!%?%%%!%%!??%%!%?%%%!%%?!!%%!!!!%!!%!!%!%%%%%%?!!%!%%%%%%?%!?%%!!??%!!%!?!%!!%%??%%%?!!%%!?%!%%%!??!!!?%!%%%!%!%?%?%%!!!!?!!!?%!?%!!!%%!!%%%????%%%!%%%%%?!?%???%%%!!!!?!%%%%!!?%%%?%%%%%%!%!%!%!%?%%%!%%%%!!!!%?%?!!%?!%%!?%%%!!%%%%!!%???!???%%?!%%?%%??%%%%%%!!!!!%??%%!%?%%!?%!%%%!%!%%?%!%%%?%%%?!%%%!!%%?%!!?!?%%?!!%%!!!!%!%??!%!??%%%!!%%%!!?%%%!!%%!%%!%%%%%%?!%%?!%%%!%%%%?%%%??!%%!?!%!!!%%!%%!!%!!%%!%%?!%!%%!%%?%%?%!%!?!%%%%%%?!!%%%%!??%%!!%%!%%%%!%!!!?!!!%!?!%!%%%%!!?%%!%!!%%%!%!%%%%?%!%%!?%%?%?%?!%%%!%%%%%%!%!?%!%!%!%%!%%!%%%%%!!%!??%!!%!?%?%%%!!?%%%%%!?%%!!%%%%%%!%!!%?!%%?%?!%%%%!%!%%!!!!!?%?%%!!!%!?%?%?%!%!%%%%%%?%%%%%!%%%%%%%!!%!!%%!!%!!%!?!%%!%%??%%!%!!?%!%!!%!!%%?%%%!%%!%!?%%!!%%%%!!!!%%%?!!%%%%%!!!%%%?!%%!!?%%?%%!%?!%%%!%?!!%%%??%!%%!%%!%%%%!%%%%%!!!%!!%!!%!?%?!?%!!%!!%?%!!%%%%%%%!?!%!!%%??!?%!?%%%!%%%%%%%!%%!%!%!%!%%%!!%%%!%%!!!%!?%!!!%%%%!!!!!%!!%%%%%%?!%?%!!!!%!%?%%%%%?!?%!!!%?%!%%!%%!%?%%%??%%%!%?!%%!%%?%!??%!!%!!%%%?%!%%!%?!!?!?%?%%%%?%%!%%??%!!!!%!!!%!!%%?!%!!%!!!!!!%%%%%%%%%?!%!?%%%%%%%%%?!%%%!!!!%!!!!%!!!%?%!?!!?!?%?%%%?%!%!?!%!!%%?%??%%!%!%!%%!!%%%%%!%%%!%!%%%%%?!??!!?%?!%!!?!%!?!%!%%%?!!%%%%?!%%%%!?!%!%%!!!!!%%?%!!%?%??!%!!!!!!%!%%%!!%%!%%!!%!???%!%%%?!%?!%!%%?!!!!%?!!%!!!!%!%!?!%%!!%!%!%?!!?%%?%%%%!%!!!%%?%?%%?%%?%!!!%%!%%%!!%!%%!%%!!!%%!%?!%!%!%?%%?!!%?!!?%!!?%%%!%?%!%?%%%!?!!?!!!%%?!%%?%%?!?%%!%!?%!!%!?!%%!!%%%!%?!!%%%!?%!!?%%?!%%%!%??!%!?!!?!%!!!%%%%?!?%%%%%!%%%%%!!%!??%!!%!%!%%!%%?!!!!!!?%!!!%%!%?%%%%!%%%%%???%??!!%%!!!%%%%%!?%?%%!!!%%!%!%!!%!%%?!!!!!!%%!%%%!%%!%!%!%%%!%!?%!!!!?%%?%%!!!!%%?%!%!??!%%%%%%%!?%%%!%!%!%!%%%!??!%%%%?%??!!%%%%?%%%%!%!!?%%!!!?%%%!!%!?!!%!%%!%%%!%!!%?%!%%%%%?!!!%%!?!%%!?!%%%!!!???%%!%!?!!!%%%%%%!!??!%%%!%%?%!%!%%?%?%%!!!%%%%!%%!%%!%%??!!!%???!!%?%?!%%%%%%?%??%%?%?%%!!%%!%%%!!!%!%%?%%%?%!!!?!!?!%%!%%%!%!!?%%%%%!!?%%!!%%!%%%%%!%!%%!%%%!%!%!%!?%%%!!%!%!!!%%%!!!?%?%%%!%%%!%%?%!%%%?%??!!%%%%%!%%?!%!!!!?%!!%%%!%!?%%%%!?%%!%?%%%!%%!?%?!%%!%?%!%!!%?%%?!!%!%?!!!%%%!%%?%!%!%!!!!%?%?!!%!!!%!!!%!%%%%!%!!%%%!!%???%%?!!%!?%%!%%%%%!!%%%!!%?%?%?!%!!!?%%!%!%%!%%%!%!?!??%%%!%%!%%%%%%%%!%%!!?%!%%%!%%%!!%%!??!%?!%?%%!%??!%!%?%!%?!%!!!%%??%?!%?%!?!!!%!??%?%!?!%!!%!%?%%?!?%?%!%%!?%?%!%?!??%%%!%%!!!%!%%%%!!!%%%??!%!%!!!!%%%%?!%?!!%??%!!?!!%%%?%%%%%!!%!%%%%%???%%!%?%%%%!%?%%!?!!?%%?%!%!%!%!%%!!%!!%?%%%?!!!?%%%%%%%%?!%?%!%?%!%!%!?%!!!%%!?%!!?!?%??%!?%!!%!%!!%!!!%!?%%%!?%?%!!!!%%!!!%%?%%!%%?!!?!!!%?%!%!%??!!%%%%%!!?%!%!???!%!!?!!!!%%%!%?%??%%!%??!%%!!%!%%%!!??%!!!%!%!?%%!%%??!%!?%%!%!%!!!!??!!%%%!!!!%%%%%%%%%%%%!%!%!?%?!%!?!?%!!%%!%%%?!%%%%%!%%!!!%%%%!%?!!?%%?%!%?!?%%?!!?%!!??!%!!%%%%%%%%%%%%%!%!%%%%%??!!%!%%!%?!%%!%!%%%%%%%?!%%%?%%%%%%%!!%%%!%!!?%!!!!?%%!%?!!%!!!!%%%%!%%!!?!%??%!%%%%??%%!!%%!%!!%%%??%%%%%%!!??!%%%?%%!%!%!!%%!?!%!!%%%%%?%%%%!!??!!!?%!%%%!%%!!%!!!?%%%%!%!?!%?%%!%?!!%%%%%%?%%!%!!%!%%?%!%!!?%!!%%!%%!%%!%%%?%%!!%!!%%?%!%%%%%?!!?!!%!%%%%!!!%!!!%??!%%!%%%%!%!!!??!%!%!?%!%!%!%%!%%?%%?%%!?!%!!!%!%!%%!%%%%%!!%!%%!%?!%!!%%%!!%%?%?!%!?!!%!%!%%%%%%%%!%%?!???!!!?%%!%%%??%!?%%?!%!?%%!%?!%%%!?!%!!%%%!%%%%?%%!?!%!%!!!!!?%%%%%%!!%!!%!%%?!?%%%!%!%%%%?%%%%?%%%!%%%%!!!!%%%!%%%!?!!?%%!!%?%!!?!!!!!!%%!%!%%!!%%?!?%!!%%%%%!%%%?%!!!!%!%!%%??%%?%??%?%!%!%??%%%?%!%%%%!%???%%%%%!%%%%%%%%?%!%%%%%!?%!%!?!?%%!%%%!?%%!%%!!!%%%!?%!%%?!%%!%?%%?%%%%%%!?!!??!?!!%!%!%!!?!%!!!%%%?%%!%%!!%?%??%!%%!%%%%%!%!%!%!!%%%!%?%%%!%%%%%??%%%?%%%%%%!!!%%%%!%%!%%!%%%!!!%!%!?!??!!!!!!??!%?%%%?!%?!?!?%!!!%%%!!!!%%!%!%!%!%%!%?%!!!%%%%%%!%!?!%%?%%%!!?!%!?%!%%%!%!!%%!%%!?%!!%%%!%!%?%!%%!%!%%?%%!?%!!%!%!%!!%!%?%%?!%%?%?!%%%%?!?!%!%!?!%!%!%!%!%%!%%%!!%%!!?%%%!%%!!!%%%!%!!!!%%!%%!%%%%%!???!!%?%!%!!%!%?!?!!!%%%%%!%!!!%!%!!!?%%%%%%!?%%%%%!%%!?!%%%%!%%%?%!%%!%!!%%!!?!%!%%!%%?!%%!?%%%%%?%%%%!!!%?!%%!%!%!%%%%%!%?%?%??!!%!%!!%?%!!!!%%%%%%%!!%%%!%%??%%!!!%%?!%%!%!!!!%?%?!!!%!?%%%!%%%??%%%?!%%%?!%?%??%!?%!!%%%%%!!!!?%%?%%%%%!!%%!?!?%%%!?!!%!%%!?%%?!%%?!%?!%??%?%%!%?%%%!%%%%%!!!%!%!??!%%%!!!!!!%%?!??!!?%%?!!!%?%!?!%%!%%%%%%!!??!%%%!%%!!%%%%%%!%?!?%!%%%%!%!%!%%%%?%%%!%%%?%?%%%%%!%?!?!%?!!%!!!%?%!!!%%%%!!!%?!?!%%%!%??%%?%!!!!!?%?!!%%!%%%?!%?%?%?%?!%%%!?%%!!%?%%%!%!??%??%?!%?%%%!!!%??%%%?!!%!%%!?%%??!!??!%!?%%%!%?%%%!%%!!!!!!%!%%!%%%%?!!!%!!%?!!!%?%%%%%%?%%%??%%?!%%!?%!!%%%!%!%!???%%?!?!!!!?%!%%%%%!!%%!!%%!!?!?%%?%%!%%!%%%%!!?%%???!%!%!%%%!%!%?%%!%%%!%!%%?!!%%!%?!!%?!%?%%?!%%%!%%!!?%?%%%???%?%!%%%!%%%%!%%?%%%!!%!%??!!%%?%!!%!%%?%%%?%%!%?!%%%???%!!!%%?!%!??%%%%%?!%%%%?!%%!%%%%?%%%%!%%%%?%%!%%%%??%%?!%%%%%!!?%%%%!%!%%%!?%%%?%!!%%%!?%%%!!!!!%%%%!?%!%!%!%!%?!!!%?!%!%%%%%%%%%%!?!%%%%!%%%%!%??!%%!?!%%?!!!?%%!%!!%%%?%%!%%%??!!%!%%%%??!!%%%!!%%!%??!%!!?%%%!!!!%!!%%%%%%?!?%?%!!?!!%%!%%%%!%%!!!!%%%?%%%%!?!%%%!!%%%!%!%%%%!%!!!%%?!%%?%??%??%!!%!%%?!%%%%!?%%%%%%%%?%!!%!!%%%%?%!!%%!??!!%%!!!!%%%%!!?!%%!!%%%%?!%%%%%!%!%!!%!!?%!%????!%!%!!%%?%%%!?!%%%!!%?%!?%%%!!!?%?%%%%!%%!%%%%%!!!!%!%!!?!?!!!!!%%%?%!%%%%!?!%%?%%%%!?%!%%?!!!%!%!?%!?%!?!%%%%?%%?%%?%?%%%!%%!!!!!!!%%%%!%!?!!%%!%!!%%?%%!%%!%!!%!%%!%%!?%!!!%!%!?%!!%%!!!?!?%%!%!%!!!%!!!%%?%%!%%?%%?%%%!%%?!%?%!%?!%%!%%%?!%%%%!?%%!%%%!%%!%%%?%%!%%%!%%%%%%%%%!!?!%%!!???%%%%!%%!!!!%?!!%%??!%!%%?%??%%%?%%?%%!!%%!%?%!!!!%%!%!?!%!%%?!%%%%%!?!!%%?%!!!%?!%%!!!?%%!??!%%!%%?!!%%!%!!%!%!%%!!!!?%%%!?!%!%%??%%%%!%%%%!%!%!%%%%%%%%!!!?%%?%!!%%?%%!%!!!%%?!%!!%%%%!!%!!%%!!!!!?%%%%?%%%%!%!!!%?%%!?%!%%%%%%!!??!!!%%%!%%?!!?%%%!%?%?%!%!?%!!%?!%%%!%%!!!%%!?%%%%%?%!%!!!%%%!%??%%%%!!!!%!%!!?!%?%%%%!%%!?!!?%!?%%!!%%%!%%?%!!%%?%%%?%!!!%%?%!!%%%%!%%??%?!!?!%%?%%%%%!%%%?!?!%%?%%!%%!!!!%%?%!%?!!%?%!%?!%%!?%%%%%!!!!%?%?%!?%%%%%%%!!%%%!!%!?!%%%?%%!%!?%!%%%%%!!%%%!!%!?!%?%%!!!?%?!?!%?%!%%%?!%%%%!!%%?!%%%%?!%%?%!!!%!%!%!%%%!%%%%%%%!!?%%%!!%!!%!!%%%!?!%!?%%??%%?%!%%%%!?!%!%%%%%%%%%?!!%%%%!%%!%!%?%%!?%!%%!!!!!%%?%%%?%%!%%%!!%%%%!!!%!!!%%!!%!%?!%%!?%!%!%%!%!%%%%%%?%%%!!!%!%%%!!%%!!!!!?%!?%%!?%%%%?%!%%?%!%!!%!%%%!%?%?%?!?%%!%??%??!%?!%%!!%%?!!!!?%%%%!%%%!!%!??!%!%%%!?!!!%%!%%%%!%%!!%%%%!!%!%%!!%%!%?%!!%!!?%?%%?!!!%%%!%?%%?!%%%%!%%!%!%!??%%!%%?!?%%!%%%!?%%%%?%!!!??%!%!%%%%?%%!!!%?%!!%%%!%%%%%!?%%!?%%!%%%%!!!%%%%!?%!%%!%%!!%%!?%!%?!%%%%%?!?!?%%?%%%!!%!??%?%%!%?%%%!?!%%%?%?%!%%%%%!!%!%!!%%?%%%%%%%!%%?%!%?%%%%%%!??!%%?!!%%!%%!?%%!%???!!%%%%!%!%%%!!%%?%!!!%!!?%%%?%?%!!?%!%!?%%%%!%?%%%%%%?%%?!%%%%%%?%!!%%?%%!!?%?%!%%%?%%?%!%%!%!?!%%%%!%%!!%!?%%?%%!?!?%%!?%!%!!%?%!?%!!%!??%!%!%?!%%!%?!%?!%??!%!?%!?!%?%?!%?%?!%%!%%!!?%%!!%?%!%%!!!??%%%!?!%?%?%!%%%?%!%%%%%%%!%%%!??%?!%%%!!!%%?%%!%%?!!!!%!%%!!!%?!%%?%%%?!%%!%!?%%%?%!?%%!??!%%!%?!%!%?%!%%%%?!!%!!%%%?!!??!%%%!!%%%%%%?%%%??!!!!?%!%%%?!%%?%?%!%!?%%%%!%!%%%!%%?%%!%!?%%%???%?%!!%%%!!?!%%%%%?!%%!!?%%%%!!!?!%!!!!%!!?!%%?!?%%%%!!%!%%!!%!???%%%!!%%?%%%%%%%%!%!%%!?%%?%!???!%!%%%!%?%??%%?!!!%??!?%%!%%??!%!!!%!!%??%??!!%%%!%%%?%?%!!%!%!!%!!!%%%%%%%!%%!?!??%!%!%?!!%%%%%!%?!!%%!?%?%%!%!!%%!%%%%%%%%%!%%!!%??%%!!%%%%?%?%%%?!%%?%?%!%!%%%%?%?!%%?%?%!!%!%%?!%%?%%!?%?!!%?%%!%%!!!%!!???%?%!?%%%%!!%?%%%%??%%!!%%!!%?!!%!%%!!?%!%!?!?%%!%%%%%%%%!?%!!!%!?%!%?!!!%!%%%!%%%%%%%%%%!?!?%?%%!!!%!!?%%%!!%!!%!?!%!!%%%%!%!!?%?!%!!!!!%%?!%??%%!!!%%!%%!%!!!!%?%%%%!%%!!!!?!%%%?%%?!%!!%!%%?!%!!!!%!!%!%%!%%!%%?!%%%%!!%%?!!%!!!!!!%%%?%!?%!%%%!%%%%!!%%?!!?%%!!!!%%%%%!?!!!%!!%!??!?%%!%%!%%!!!!%%%!%%%?!!!?!%!!%%%?!%!%%%?!%?!%!%?%%%!%%%%%%%%!!%?!%%?!%!%?%!%!!%%%%?!%!?%%%%%!!?%%%%!!?%!?%%%!!%!!!%%!!!%!%%!!!?%%!!!%%!%%??%%!!!!?!%?!%!!!!%%!%%%%!%%?!??%%!%!%%%?!?!%?!%%?%????%!%!!%%%%!!%?%!?%%?%!??%%!%!!????!!!%%!%?%!!%?%%?!!!!!!!%%!!?!!%%!?!!%?!%%%!?!?%!!!!!%!%%%??%%???%%%!%%!%!%!!!!?%!!%%!?!!%!!!%%!?!?%!%%%%??%%!!!?%%???!??%%%%!%%%%%?!%!!!!%??%%!%%%%%%%%!!%?!??!?%%%!!?!?!%?!%!!%!%?!!%!%%%?!!%?!%%!!!!%%?%%%%?%%!?%?%!%%!!%%%%%%?!%%!?%?!!%%%%?!%!%!!?!%!?!???%?%%!!%?!?!%%!!%!!!%%%!%%%!%%%!%!%?!!%!%%?%%%??!%!%!!!%?%%%%!%!?%???!%!%!!?%!!%!%%%!%?!?!?%%%%%%!%%!!%!%!%%%!?%!??%!%!%?%%!%!!?%!!!?%!!%%!%!!%%?%!!%!%%!!!%%%%%!!%%%!%%%%!!!?!?%%%%?%?!?%!!%%%%%!%!!%?%?%%%!%%!?%%%%!%%!%?!??!%%!%%%!%%??!!?!!!%!%??%!!!!!!%%!?%%!!%?!!!!%!!!!?%%%%!%?!!!%!!?%?%%%!%!!?!%!!%%%!%%!!!!??%!%!!!%!%%!%%%%?%%!%%%??%%%!%???%%%?%%%!?!%%%!?!%%?%??!!!%!!%?!!!?%%!%%%%%%%%!!%%%!%%%%?!%!!?!%!!%!%?%!%!!!%%%!%%!%%%%%??%%?!?%?!%%%%?%%!%!%?%!%%%%?!%?!%?!%%!%!%!?!!%!%%!%!%%%!!!%%%!??%%!!%%%%%%%%!%?!%%%%?%%%!%??%%!?%!?%%!?%%%%!?!%%!%?%?%?!%!%?%%%%%%%%%%%?!!%?!%!!!%!%!!!!!!%%!!!%%%%!!!%%%%%!%?%%%??!?%??%!%%??!!%!%!!%?????%%%!%!!%%?%?!?%?%%%??%!!!%%?%%%%%%!%!!%%%!!!!%!%%?!?%%!?!!!%?!%%!!?!!!?!%%%!!!?%%%!??%%!!!%%%!!%%%%%!%?%%%%%!!!%!!%!%!%!!?!%%!%%%!!!?%!%?!%!!??%%%%%!%!!?!!!%%%!%%%%??%%%%!%!%!%?%%%?!?%%!%%!%%!%!!%%!%%%!!%!%!%%%?!!?!%%%!!%?!%%%%!??!%??%!%%!%%%?%%!%?!!%!!?%%!!!%?%%%%%!!%%!%?!?%%%?%%!%?%??%%%!%%%!!?!%!%!!%%?%%%!!!!?!?%!!%%!??!%!!%!!!%?!!!%%?!%%?%%%%!!%!!!%%!!!!%%?%%%!!?%%!%!%%!!%%%%%%%!%!!?%%%?!%!%%%?%?%!%?!!!%%%%%!%!?%%%!%!%%!?%!%?!?!?!!%!%%%?%!!%%%!!%!!!?%!%%!%%%%!!%%??%%%?%%%?%??!%%%%%?!?%%%%%%!!%%!%%%?%%!!%!!?%%?!!!%%%%%%%%?!!%%!%%!!%%?!%!%%?%%%%!%%%%??%%?!!!%!%!!?!%?%!!!%!%!!?%%!%!%!?%%%%?%!?%!!%%!!%%%%???%?%?!%%%!%%%!!!!%%%%!!%!%%%!%!?!%!%?%%%!%%%%?!%%!?!?%!%!?%?%!?!%!%%!%!%?%%%?%%%!?!!%?%%%??%?!!%!!?!!%%%?%%%!%!%!%?%!%%%?%%!%?%?%??%!!%!!%%!!%?!%??!!%%%%?!?!%!%%!!%?!%%?%!!%?%!%%%%!%%!!%!?%%!!%!%%?%!!!!?%!%%%%%%%!%%?!%%%%%%!!%!%%!!!?!%?%%%%!%!!%??%!!!%!!?%%%%!!%?%!%%!%?!!!%%%%!%%?%%%!?%%!!!%%%!%?%%?%!?!!%%%?%?!!%%%!?!!!!!%%!%!%!!!%!?%%!!!?%!%!%!%%!!?!!%!!%!%%!!%!!?%%%?!!?%?%%%%%%!!%?%!!%%?%%%%%%%%%%%!?%?%!!%%%!?%?%%%!%!!%!%%?%%%%%!%%?!!%??%?%%%?!?%!%%%!!%%!?!!%!!%!!%!%%!!!%!!%%!%!?!%%!%%%%%?%!?!!!?%!%%%%%%!?!!!%%%%!!%%%?%%!%%!%??%!%%!?!%%%?%%%!!!%!%%%?%%!?!!%%!%%?%%%?%%!%?%?%!%%!!%%%%%%!?%%!?!%!%%%%?!!!%!%??!!%%%%?%!%%!%%%!%!%%%?%%!%%%!?%%?!%%%!!!!?%%?%?!?%!%%?!!%?%%?%%!%%!%%%?!%!%!%!?%!%%%!%%%?%%%?%%%!!!%?!%!%%!%?%?!%%?!!%?!!?%!%%!!%%?!?%%??%%!??%%!%!?!%%!!!%%!%!%?%?%%%%%%%!!%!%%%!?!%!!%!!%%!%?%%%??!%!?!%!!%%?%%%!%%??%%?%%?%%%%%!?%%?%%%%!%!%%%%%!!%%?!%!!?%?%?%%!!%%%?!!%%%?!!??!??%%%!!%%!%!%!%%!%%!?%%!%%%!?!?%%%%%%!%%%!%%!%?%%!%!%?%!%%%%??!%!%%?%!?!?%%?%??!%!?%!%%%%%!!%!!%!%?%!%!?%%!?%??!?%%%?%%%!%!!!?!!%%%%???!%%??!?%%%!!%!!%!%?!!%?%!%!%%%?!%!?%!%!%!?%%!!%%%?!%%%%!%%%%%%%%%%%!%%%!!%%%%!%%%%!%!!!???%%%%??%?!!?!%?!?%%%!?%!%!!%!!%%%!!!!%?!%%%!%?%!?%!%??%%%!%%??!%!%%?%%?!?%%%%%%!%%%?%!%!%!!!%!!%%%%%%!%%!%%!!!?%!?!%%%?%!??%?!??%%!?!%!?%%%!?%%%?%%%%!%%?%%%?!%!%%%!%%%%%?%%?%!%%!%%!?!%!!%%!!!%%!??%%%%?%!?%?!?????!%!!!%%!!%!!!%%%!!%%!%!?!!?!!%%?%%%%%%%%!%!!%!!!%!!%%?%!%?%!??!%%?!%%%%%%!%!%%!%%%!!!%%%?!!?%%?%!!!!!%!!!%?!!???%%!!?%!%!%!!!%!%!%??%%%!!!!%!!?%!%?!%??!%%%!!!%!%???%%%%%%??%%%!!%%!?%%!%%%%%%?%!%?!%%!%??!!%%%!!%!%%%!%%%%!%!%!%%?!%!%%!???%%?!%!!!%?!%%?!%!?%?!%%%%!!!%%??%%%!%%%!%%%!!%!%!!%%%%%%!%?%!!%?!%%%%!?!!%%%%%!!%%!%?!?%%!!!%!!?!!%?!%!%%?%!???!!!!?!?%%%%%%!%%!%%%!!?%%%%%%%?%%%%%!?%%?%%!?%%%???%!?!%!?!%%????%!%!!%!!%!!%%%??%%!%%!?!!!!%%?%!%!!%%%!%%%%%%%??!%%!!%!%%!!?%%%!%!%!%?!%!%%!%??%?%%!%!%!%!%%?!?%?!%!!?%%!!?!%%%!%!?!!?%%?!!%!!!!!?!!%%%!!%!%%%%?%?!!!!%!??%%!%%%%%?!!%?%%%%%%!?%%?!?%%?!!%%!!%!!%%%%%!???!%?%%!%%%%%?%%%%%%%%?!!??!%?%%%%%%%!?%!?%?!?%%!%!%%!!%%!!?%?!%??%%%?%%%%!!!?%!%%!%%%!!%%%!!%!%!?%?!%%%%!%%%%%!?!?%?%?%!%%?%!%%!!!%!%%!!%%!?!!%%%%!%%?!!%!!%!%%%%%!%%%%%%%%%%??!?%%!%%%%%%%%%%%%%%!!%!%?%%!%%!%%?!%%%%%%%%%!!%%?!%%!!%%%!!!?%%%%!!!!%?%%%!%!!%!!!%?%!!%!!!%!%!?%%%!%%%?%?!%%?!%%%%%!%%%%%%%%%%%%?%%!%!!!!%?%%?%%!%%!%?!%?%?%!%!!%%%%%!%%%%%?!%!!?!!%%?%%%!%%%!!%!%!!!%!!%!%%%%%%!!?!?%!%?!%%!%!%%%%??!%%%!?%%%??%??%%%%%%?!%%!?%?%%!%%?%%%%%%%%%!%!?%?%%%%!!?%%%%%!%%!!%%?!!%%!!%%%!%!!??!!%%?%!!!!!?!%?!%!%%!%?%%%%%%%%%?%%!!!!%%!%?%%!?%%!?%!%!!?%%%!?!!?%!?!!?%!!??%!%?!?%?%%?!?%??!%%%%%%%%%%%%%?%!%%!?!!!%!???%%??%!!%?%!!%?%!%?%%%!!%%?%!%!!%%!%%%!%%%?!%%%?!!%??!!%!%%!%!%?!%%!%%%%%%!%??%?%?%%%%%?%%%?%!!%%!%%!%!??%%!%%%?!?!%%!%%??!%%?!!%!??!!%%%%!%!!!%%!%?%!%%%%%%?!%%!%!!%%%%%%!%%?%%!%?%!?%%%%??%%%?!%?%?%!%%%!%!%%??%!!%!%!?%??%%%?%%%%!%%!%%%!%?!!%!!%%!%?!!%?%%?%!?%!%%??%%%!!!?%!%%%!!??!!%%%%?%?%%!%?%%%%?!%!%!%%%%!!!%%?%?%%?%%%%%%%?%%%%?%%%!%%%%%!%%%%!!%!%!%!!?%%!!!!%%!!?%!?!%%?!?%!?!!%%%!!?%!!!%%%%!%!%%?%%%%%%%%%%?!%%%%%%?%?%!%?!%%%!%%%?%???%%%!!%!!!?????!?%?!%%!%%%!!%?%!%%?!?%%%?!!!!%!!%!!!%!%%%%?%%%?!%?%?!!?%!?%!%?%%?%%!%!%?%%%%!??%!!!!!%?!%?%!?%%!?%%%!%?%?!!%%!!%%%!?%%%?%%%?%!!%%%!%%%!!%!!?%!%%!%??!!!?!%%%%!?!%%%%?%?%%%%%?!%%%!%!%%%%%?!%%!%%!%%%!!?%!%%!!%%!%%!%%!!%?!%%?%?%?%!%%??!%%!%%%%!!%??%?%%!%!!%?%?%!!%!?!!?%!%!%?%%%?%%%?%!!!%?!%%%!!!%!!!?%??%?%?%%!%%?!!%!!!%!!???%!%%!?%!%!!!%?!%!?%%%%!%%%%!!%%%!!!!%%!!?!%%%%%%!%!?!%!%?%!!!!%%%!%?!%%?%%%!?%%%%!%?!!!?!%!!%!%%%%%?%!!%%%%!%%!!%%!%%!%%%%%?!!!%%!?%%%%!%?%%!%?!%%!%%?%%%!%!?%?%%!!%%%%%!%!%%?%%%??!!!%!?%?%?%%%%!!%%?%?!!%%%!!??%!%%%!!?!%%%!%!%%!%!%%!?%!!!%%%%?!?!!%!%%%!?%!!%!?%%%%%%%!%%!?%!%?%!%?%!%!!!?%!!!%%!%!!!%%!!%%%%%%?%!%%%!!%%!?!%!!?%%%!%!!%?!?!%%?%?%%%%%%!%?%%!%%!!%%!%!%%%?!%!!!%?%!%!!!!?%?%%%?%%%?%??%%%?%%%%!%%%!%%%!!%%?%%!!!?!!%???!%?%?%%%!%%!!%%%!%%%%%!%%!!!%!%!!%!!!!?%%%%!!%?!??!%!!!%!%?!%!!%%?%%?!!%%%?!%!!%%%%%?%!?%!!!%!%!!%!?%%??!!?!%?%%%%%?%!%%%?!!%%%!!!!%%!!?%!%%%!%?%!%!!%!!%%%%%%%?%%%?%%%%!%%%!%%%%%%%%%!!%!%%%%?%%!!!%%!%!%%%?!!%%?!%!?%?!!!?!%%%!%%%%!%%%?!!%%%%%!!!%!%%?%?%?%!!%%?%!!%!!!%%?%!!!%!%!%%!!?!!%?%!%%!%?%%%%!!%%%?%!???%!!!!!%%%%!%%%!!%!%%!!%%?%%?%?%!%%?%!%%?!?%!%!?%!%!%?%!%!?!%%%?%!%!%%%%%?!%!%!%!%%!?%?%%%%!%!%?%%!%%!%!!!!%%%????%%%%%%%??%%?!!!%?!!%!%%!!%%?%!?%??%!!!?!!!!!%%!%!%!%%%!!%?%?!!%!%??%%%?%%!!!%%!%?%?%%!!%%!%%!%!%%%?%%%%%%%%%!%!!!%%!%%%%%!!!!!!%%%!?!%!%??!!%!%%%%%%?%!%!!%!!%%%%?%!!%!%!%!?!!%%?%!%%%%%%!!?%!!!?%%!%%!!%!!%!%!?%?%%!%%!!%!!!%!!%%!!%%!%!%!%?!!!!!%%%%%?!?%%!?%%%?%?!!!?%%%?!!%%?!!?!!%!??!!!??!%!?%%%%%!%%!!!?%%%%%%!%!!??!?!!%?%!%%%!%%!!!%?%!!%%!%%?!%!%!!%%!!%!!%!!!%%!%%%!%??!%%%???%?!!!%%!%%!%!%!!!%%!%%!%%%%%%%%%?!%?%%%!%%!%%%?%?????%%!?!!!%%!!!!!?%!%!%%%!?%!%!%%%%%?!%?!%%%!%%%?%%?%?%??%!%%%%%%?!!!?%%?%%%%!!??%!%%!!%!!%!%?!!%!%!%%?????%!%!!%%!%!%!%!?!%%!%!%!%%%?!!!!!%?!!!!?%%?%!!!%?%%?%%?!??!%!??!?!%!%!!%%%!%!?%!%!%!%!!!%%?!%!!%%!%%%%%?%%?%%%%!?!!!%!?%%%%%%??%%!?!%%?!%%%%%%??!%%!?!%%!%!%!%%?!%%%%%%%%!!!!%%%!!!?%%?%?%!%!?%!!%%!%%!%!!%%!!%%%%%!?%%%?%!%!!%?!?!%%%%%%!%%!%!!%!???!%%!?!!!!!!%!%!!%%%%!%%!?!%!!!!?!??%%!%!%?%%?!!?!!!!!!%%!%!!%%??!%!?%!%%%!%%%!!%!%%!%%%%!%!!%%?%!%%!%?!%%%%%??!!%%%%!?!%!%%!!%?%%?%!%%%!?%%?%!!?%%%?%%??%%%%%%!%%%!%!%!%!%%!!%%?%??%??%%%%%?!?!!%%%%%!?!%%%!%%%%%!%%!%!?!%!%??%?%!%%?!%?!?%%!!?%!?!!!%%!%%%!%%%%?!%%!?%%?%!!!!!%!!!%%!%!%%!%%%!!%%%%%%!%!?!%!%%%?%%!?%!%%!%!!?%%%!!!%!%?%!?%?%%%!?%!!%!%!!%%%%%%%!!%!!%%!%!?%!!?%%%?!%!?!%%%!%!%!!!!%%%%%?%!!%%%!%!%%%%%!?!%?%?%%!%!%!!??!%?%%!%%!%!!%%%!%%%!!?%%%?%%%!%%%%?%!%!%%?%%%%!%%%%%%%%?!!?!!%?!%%?!!%?!!%%?%!%%%%%!%%!%%!!!%%%?!%!%%%%??!!%%%%%%??!%!!%%!!%?%!%%?!?%!!%%%!%%%?%%?!%??%?!%%%??!%!%%!?!%?!!%?!!?!?%%?%%%!%?!%!!?!!?%%?!%?%!%!%%!%!!%%!%%!?%??%!!!!%!!%%!%%?!%?!%%%!%%!%%!!?!%%%%%%!%%%?%%%?%%%%!%?!!?%%!%!%?!%%%!%%%%%!%%!%!!%%%!%%!%!%%!!%%%%%?%!?%%%!!?%%%%%%%?%%!!%%%%?%%%%!!%!?%%!!%%!!%%%!!!!%%%%!!%!!!%!%!%!!%!%??!!!!?%?%??%%!%%?%%!??%%??%!%?%!%%%%%!!!%!%!!%%!%%%%!%%!%!!!!!%!%%%%!!?%!?%%%??%%!%!%%!!%%!!?%%%!??%%%%%?!%%!??%%%!!!?!%!!!%?%%%!!!???%!%?%%%?!%!!!%%%%?%%!!?!%?%!!!!%%?!%%!!%!%%!%%!%%!%%%!%!%%%%!!%%%%%!%!%%?!!!!%?!!!!?%!%??!!%%!%!%%%!?!%%!%%?!!!!%??!!%!!?%%%!!%!?%!??%!%!%%%!%??%%%%!%%!%?!%%?!?%%%%%%%%%%?!%%%?!%?!!!%%?!??%%?!!!?!!%!%!!?%?%%!%%%%!%!?%??!%%%!!%%%%!%!!?%?%%%!%%%!!%%%!?%%?!%%!%!?%?%!%!!%%?!%%%!%%%%!?%!!!?!!!%%%%!%!?%!%?!%%%%%%%%?!?!%%!%%???%%!%%?%%!%!?%!!%!%%%!!!%%%!%!%?%%?!%%%!!?%?%!%?%%?%%!?!!%%%!%%!%!%%?%%%!%!%%%%%!%%%!!!%%!%%?!?%%%%?%%%%%!%%%!!?%!%!!!%%%%!!%%!%!%?!%%!!??%!%!%%%??!!!%%?!!%!!!!%!%!!?%%!!%!%!%%!%%!!!?!!%?%%!%%%!!!%!?%%!%?%%!%%!%%%%%%%!%!!??%%!%%%!%%?%!!%!%%!!?%%%%?%%%!?%%!%%%?!%?%??%?!!%%!%!!%%!!%!!!!%!!%!?%?%%%!!%%!!%!%%%?!!?%%!!%?!%%?!!%!%??%%?!%%%%%???%!%!%?%%!%%%%%%!!!!%?!%%?%?%%%%%!!!!?%!%%%!!%%?%%%%!%%%%?!%!!%!!!?%?%?%!?%!!%%%%!%!%%?%%!%!?%%??%!%!%!%%%!?%%!%%%%%%%!%%%%%%%%!!%%!%%!%!%!!?%%%!%!%!!%!%!%!!!%!%%!!!%%!!?!%?%!%?!?%!%!!?!!!%?%%??!%?!%%%!!%!!!%!?%%?%??%%%%%%%!%?%?%?!??%!%%!!%%%%%!!%%?!!??%!!?!%%!%?%!%!?!!???!%%%%?%!%!%!!?%%%!!?!!?!!!%%%?%%%!%%!%!!!%%%!??%%%?!%%%%!%!!%!?%%!%%%%%?%%%!!%%%?%?!?%!!!!!%!%?%%%%%%?!!!%%!!!!%%%?%!??!!%?%%%%!?!%!!!?!%!%%!!%?%!?%!%?%?%!%%?%!!!?%?%%%!!%!?!!%!%%?%%!%?%%%!?%%%%!!!?%%!!!%%%%%?!%??%%?!!!!%%!!?!!!?!%%%%!%%?%%?%%%??%!%%!!%%%%?%!!!%%%!%%!%%%!%%%%?%%?!?%!!%!%%%%!!%?!%!!%!%%%!!%!%%?%%%!!!!%%!!!!%%!?!?!%%!!%??!%%!!!%?%!%!!!!?%%%%??%!%%%!%%%%%%!%%!!!%%%?%!%%!!%?!!%%!%!!%%%%%!!%%%!%!%%%!?!??!%?%?!%!!??!!!!%%%%%!?%!%!??!!!?!!?%!?%!%%%!??%!%!?!%%%!!%%!!%!%%!!!%%?!?%!!!%?%?!?%%%%?%%%%%!%?!%!%%??!!!!%!%!!%%%?%%!%%%?%%!?!!!!%!??%%%!%%?%!!%%!?%!%?!!?%!!??%%%%%?%!?!%%???!%?%?%%%!%??%!%%!%!?%%?!%??%%%%?!%!!!%%!%!%!?!%!%!!%%%!%!%%%%!!!!?!?%%%%!!??!!!%!?%!%%??!!!%%%%%%!!!%!!%%!%!!%!??%?%!!!%%%?!!%%!!!!%%!%?%%%?!%?%!!%%!%!??%%!%%%?!%%!%%%%%%!!%%!!%!%%!%%%%%%%!%%!%!!%!%!%%!%?!!%%%%%%%%%%%!!%%%!%%%%??%%%!!!%%!?%!%?%%!!%!%%!%!%%%!!?%!%%%!%%%!!!%%!%%%%!!%!?%!%?%%%!%%!%%!%%%%?!!%%?!!%%!?!!!%!%?!%%%%%%%?%?%%??%%%!%%%%?%!%!?%?%%!!%!%%?%!!%?%!%%!!!!!%%?%%!!%%!%%!!%!%?%!!?!%!!!%%%!?%!?!%!!!%%%?%!!?%%%%!!?%%!?%!%!?%%!%%%%?%!%%?!!!!?%!%%!!%?%!%?!?!!%?%%%!%?!?%?%%%?!!%%!%%%!?!?%%!%!%?%!!!!!!?!%!!%!%!%%%?%!??!?!%%%%%%!!!!!!?%%%%!?!!!?!%%!%?%!?%%!?!!!%%%%?%!!%%%!!%%%%?!?%%%!!!!%!!%!%%%%%!?!%??!!%!%%!%?!!!%%%?%%%!%%??%%%!%!%!%!?%!!!%!%!%%!%??!%?!!%%?%!!%!?%%%????%%%!!!%%!!%!!!%?%%??%%%%!?%!%!%!?!%%%?%!?%%!?%!!!%??!%%%%?%!%%!%!?%??!!!%%%%?!?!!%%?!?!?%?%!!?!%%??%%%%?!%?%%%%!%!%%%%%%%!!!?!%!!?!%!!%!!%%%%%%!!%%%!?!%!%%?%!%?%!%?%!!!!%%%?%!!!!%?%!!?!%%%?%?!?!?%%!!%?!%%%%%!??%%%%!%?!%!%!!!?!%%%%%%!%?!%%!!!!!!%%%!%%!%%!!!?!%!%%%!!%??%%!%%!!%??%!!?%!!?%%%!%!!%%!%%%%%%!!%!!%%?%%!?!!!%%!!%!!%!?!%%!%%%%!!%!%!%%%%%%!%!!%!%!%!?!!%?!!%%%%%%??%?%!!%%%!!%?%?%!!!!!!?%?!%%?!!!%!!%%!%?%!?!%!%%%%%!!%!!%?!%??!%%!!%!%?!%%!%!?%?!%!%%!!%%?%%%%%%%%%!%%??%??!!%?%!%%!%?%!%!?%!%%?!%!%%?%?%%%!%%!!??%!%%!!!%%?!%%??!%%%%?%%?!??%%!%%!%!?%%%!!%!?!%%?%!!!!%?!%%%%%?!!!!!?%%%%!!%?!!?!%!!%%%%??%?%%%?!??%!%?!%%%!!!%??!%!%%%%!%%??%%%!%%!%%?%%?!!!!!%%!%%?%?!%??!!%!%%!%%%!%!!!%%!?!!!?!%%%%%%!!?%%!!!%!?!!%!%%%?!?!?!?%?%%!!!?%!%%%%??!%??!!???%%!%%%%?!%%!%%%!%%!%%!!!?!!%!!%!!!??%!?!?!%%!!%?%!%!%?!%!!%%!!%%%!%!!!%!%!?%!!!!!%%%%%%!%%!%%!%!%!%?%%!!%%%%%%%%??!!?!%%%?%!!%?%?!%?!?!%%!!!!!%??!%%%%!!%!%!%!!%?!%%?%%?%!?!!%!%%%!!%%%%!%%!!%?%%!%?%?!%%!!!?!??%%%%!!%%%%%%%%%!?%!!%!%?!!%?!%!%!!!!?%%%?!%%!%%!%%!%!!%!!%!!%%?!!%?!!%%!%%?!%%!%%??!%%%!?%%?!!%%%%!!!!!%!%?!%?!%!!%!%!!!%%!%%!%!%%%!%%%!!!!!%%%!%!%%%!!%!%%%?%%!!%!!%???!%%!%!!?%!%!?%!%%!!!?%%%%!%!?%%!%%%!%!!!%%!?%%%!%%?%!?!%!%%!%!!!?!%!%%%?!%%!!%%!?!%!?%!!?!!!%%%?%%!?!%%%!!%?%%!!!%!??%!%%%%!?%%!%?%%%?%%!!%?%%!?!?%!!!?!?!%!!?!!??%%%!!%!!%%!!%%?%%?!%%%%?%!%%%!!?!%%!!%%!%!!!%!?!!%?%!%?%%%%?%%!%%!%?%%%%!%!!%!?%%!%%!%%%%%%%%%%?!!!%?%%!?!%%!%%!%!%?!%%!!%%??%!!%!?!!%!?%!!%%%?%%%!?!%%!!!!%%%!!%!?%%!?%?%!%!%%!!%!!%%!%%!!%!!%%%%%%%%!!%%!!!%%!%!%!!??!%?%%%%%%?!%%!%!?%?%!?%%?%!%!%%%!!?!!!!%!?%!%!%%?%!!?%!!?!%!!%%%!?%?!?%%%%!?!%!!!%?%%?!%?!%!!%%%!!?%%!!%!%!!%%%!%!??%!!%%!%%!%%!%%??%%%?!!!%%%%!??%%%%?%!%%!%!%%%%?%!%!?!!!%?%!%%%?!%!?%%??!?%!!%%%%%%!!%%!!!%%%?%%!%%%%%!!%!?%%!!%!!!?%!%!!?%!!%!?!%!!!!!%?!%%?!!%!!?%%??%!%!%!!!%?!?%?!%%%%!%!!%%%!%!?!!!?!%?%%%%!??%?%%%!?%!%%%%?%%!!%%%%%!%!%%%!!?%%%!%%!?%!%!%%%%%!!!!!?%?!!%%%!%!?%!%?%!!%%%!%!%%%?!!%%!!??%%%%!%!%%%!!%%!%%?%%!%?!%%?!%!%%?%?%%%!%?!??%!%?%!%!!!?!%?%?%!%!%%%!?%%%%%%%%%?!%!!%%%%??%?!!%%!!%%!!!%%%%!%%%!%%!!%%!%!!%%!%%!%%!!!!!%%%??%%%%%!?!!%!%%!!%%!%%!%%%%%!%?!!!%!!%!%%%%%%%%!!!%%%%!!!??%%!?%%%!!!!%?%%!!%!!?!!%??!!?!%?%?!!%!!?%%?%?!%!%?%%%%!%?%?%!!!%%%!%!?%?%!!??%?%!!!?%%!%%%%!%%%??%!?%!?%%%%?%%!%!!%%!%%!%%?%%?%%%%!%!%%%!%%%%%?%!%%!%!?%?%!?!?!%%%%%%!%?!%!%!%?%%!%%?%!!?!!%!!!!!!!??%%!%??!%%?%%!%%?!?!%?%%!!?%?%!!?%%%!!%%???!!?%%%?%%%?%%!%%%!!!?!%!?%!%!!!%%!!%?%!!%%%%!%%%%%%%%!%%?%%!!!%!%%%%!?%%!?%!??!!!%!%?!!!!%%%!%!!!!?%%!%!!!?!%%%!!%!!%%%%%%?%!!?!!%!%%!%?%%?!!%!%?%%%%!%%%%!%%?!!%!?%%!!!!%%?!%!%%!!!%%%%%%!%%%%!!%%?%%!%!?%%%%%%%!?!!%?%%!%%%!?!?%!?!%%%!%!%!%!??!!!!!!!%!%%%%%!%?!%%!!%!!?%!%%%?%?%%%%%!!%%!%%?%%%%!%%?!!%!?%%%%!!!!%?%%%!%%!?%%%?!!!!%!%%%!!?!%%!!%%%%??!!!?!%%?!!%!%!!%!!%!!!%%%!%%%%%!??%!%?%!!!!%!?!!%%?%%!%!%%!?%%%%%!!!%%!%?!?!!?%%?%?%%%!%%%!%%?!%%%!!%%%%!!?!%?!!!!??%%!?!%%%%?%%%!!%%!%?%!%!%!?%%!%%?!%%%%!!!%?!!????!%%!?%%%%?!?%?!%?%%!!%%%%%%%!%%%%!%?%!!!%%%%%??%!%%%%%!%?%%%?%%%%%!%%%!%!%!%!%%!%!%%??%!!!!%!%!%%%!%!%!?!%!?%%%!%!%%%?%%!%%%%%!%%!%%%%%!%!?%%%%!%%???%!!%%!%%!%%?%?!%%!%%?%%%!%?%%!%%??%%%!%?!?!!%%%?!%%!%%?%%!%!%?%!??!?!!%%!%!!%?%!%!%%?%%!%%%!%%!%!%%!%!%!%%!!!!%%!%%!%%!%%%!%!%%%?!!!!!!%%!!!%%%!!%!%%!?!!%!!%!%%%%!!%!%?%!!!%%!!%%%!!??%!??%%?!%?%%%!%!%!!%?%??!!%%%%?!!?!!!!%%%!?%!%!%%%!??!%%?%%!%%!?%?%%!!%%%?!!%%!!%%%%??%?%%?%?%?%%%?!%?!%!%?%%!?!%?%%%!??%%!!%%!!%???!%%%%!!%!?!%%%%!!%?!!!!%%%??!!??%%!%%%!%?%%!%!!%!!%%??%%!%%?%%!!%?%!%!!???%?%!!%!%!%%%%!???!%%%?!%?%!%!!%!%!?%%%%?%%!!!?!%%%!%?!%%!!?!%!%%!!!?!!!!?!%%?!!!%%!%%!%!%%????%!%%!!%%%%%?!!%!!!%%?!%%%%?%%%!?%!!?!%!%%%%%%%!%!!!!%!%%!?!!%%%?!%!%%!?!?!%??%?!%?%%!!%!%%%?%%%!%!!%?!!%!%%!%%%?%!!!?%?!%%!!!%??!%?%!!!%%!!?%!!!!!!%%!%%!!!!!!%!%%%!%!?!%??!%%?%%!%%!%!!%%?%?!?!%%%%!?%!!!!%%%?!!!%%%%%!?%!%!%%!%%!%!?%!%!!!!%%%%%%!!?%%%?!!???%%!%%%!%%%??%?!%%%%%?%?!?!?%?%%!%!!%%!%!%%?%%!!??%%!!!%%?%!!!!!%%%%?!%%!!?!!%%%%!!%!!!%!%!!%??%!?%?%%%!%!%!%%??%%%%%%?%%%%%%%!%%%%?%%%!?!!?%%%%%%?!!?!?!!%%!!??!??%%!!%?!!%!!!%%%%??%%%%%%?%!!?%%!!%%?%%%%!!!%%?%!!?!%%!?%?%%?%%%%!%!%%!!!!?!%%%!%!%%!%%!%%%!!!!%!%%%%?%?%%!%%%%%%!%%!%??!%%?%%%%!%%%%%%!!!%???!%%%%!!!!%!%!!?%%%%%!%%%%?!!?!%?!?!!!!%!%%%%!?!!%%?%?%!%?!!!%%%!!%%%?!%%%?%%!%%%%%%%!%%%!!%%!!%%!!%%?%??!!?!!?%%!!%%%!!?%%!%%!!%!!!?%%%%!!!!?%%%!??!%%%%%!?!!?!%!%%%?%!!%!%!%!!!%?%%%!?%%%??%?%%%!!!%%%%%!%%!!!!%%%%?%!%!?%????!!!%%!%?!!%%%%!%?%%!?%%!%!!%??%!?!??!!!!%%!!!%!?%?%%!?!%!!%%!?%?%%%%?%%%!!!?!!!%!%%!%%%!!!%!!?!%%?%?%!%%%%%!!?%!!%!%!%!?%?%!%%%%?%?%!%%%!%!%?%%%%!??%!!!%!!?%%%!!%%%%!%%!!?!!!%!?!!?%!%!?!!!!%!?%!!!%%%!%!!!%%!%!?!%%!?%%!%%!?%%%%%%!?!%%%%%!!%%!!%%%!!!!!%?%%%!!?%!%%?!%?!!%%!%!%%?%%!!%%?!%!!?!%%!%!%??%!%%!%!%!!%?%!!%!%%!!!?!!!!%%%%!%!!%!?%%%!%%!%%%!%?%?!%%!?!%?%%?!!!?%%?%!!!!%?%%!!%%%%!!!%%%?%?!%?%!!!!%%%?%??!%%!%??!?!%%%%?!%!%!!?%?%?%!!?%%%!!!%%!%!%%?!%%!%%%!%!%!!!??!?%%%%!%%%?!%%%!!!%%?%?%?%??!!!!%%!%!%%??!?%!?%%!?!%!?%%!!!!%%%!%%!%??!%!%%?!?!?!!!!%%%!!%%!!!%%%!%!!?%%%!!%!!%%!%!!%?%!%?%!!?%!!?!?%?%?!?!%%!%%%!%?!!!%?!%?!%!%!%!%%?%!!%%%?!%%!%%!%%?!?!!%%!!!??%%%%%?!!%%%?!%%%!!!!%!!%!%!?!%!??%!%!?%!!%!%%%%%%?!?%!%!%??!%%%%!%%%%!%!%%%%!%%?%!?%%??!%!!!?!?!%%!%!%%%!!%%%%?!!!!!%!%%!%!!!?!%%%%%!?!!%%%!%%%%!??%%?%%?!%!%%?%%%!%!%?%!?%%%!?%?%?!!!%!%%%!?!!%%?!%%?%!??%%!%!%%!%!!!%?%???%%%!!%?%%%?!%?%!!?%%!!??%%%?%%%!!!!%!%!%%!%!!!%?%?%!%!%!!?!!!?!%!%%?%%%!%!!!%%!!%?!?!!!!%!%%%?%?!!?%%%!??%!!%?%%!%!!!!!!!!?%%!%%%?%?!?!!!%%%!!!?%?!%?!?%!%!!??!!%?%!?%%?%!?!!%%!%!??%%!%!?%?%!?%%?%%%!!?%!%%%%%%!%!!!%%%%%?%%!%%%?%%%%%!!%!?!!?%!%!?%%%!!%%?!%%%%%%%!%%%%!%?!?%%!%%!%%%?!%%!%?!%%%?%!%!!%%?!?!%%!?!?!!?!!%?%!%?%%!%%!%%%!%%%%%%%!%%%%!!!%!%?%!%%%%%%!?!!!!!!!%?%!%%%!%?!%???%%!%!%%!!%!%?!%%!%%%%%%%!%?!??%!!?%%!%%%!?%%%%%%%%%?!%%!%%%%%%!%%!%%%!%?!%%%!??%!%?%%!?!!!?%%%%%!%%?%!!!%?%%%%%%!%%%%!?%%?%?%!?!!?!?%?!!?!%!%!%%?%%%!%?%?!?!%!%!%!!%%!?!!%!!??%%%%%%!!!!%%!%!!!%%?%?%!%%%??%%?!?%!%%?%%!%%%?%!%%%??%?%%%%%%%!?%!!!%%?!%%!!%?%??!?!!!%%%%?!%%?!!%%?%!!!%%%?%!!!%%?%%%!!%!%!!?%?!%!!???%%%%%!!%?!%%!%%%%%%!!%!?%%%%?!%?!!!%%!%??!%%%!%?!!%?%?%%!%%%%?%!%%%%%!%%!?!!!!?%%%!%!!!!%%%??!?%?%%?!?%%!!?!%!%?%!%!%%!!?!!%%%??%!!%!%%%%%%%%!%?%?!%!%%%?%%%%%%!%%!!%????%!!%%!!%?!%%!!?!!?!%%?%?%!%???%!%%%%%!!??%%%!!%%%%%?%???!?%%%?!%?!?%%%?%!!!??%%?%%!?!%%!!!%?%%%!%?!!!!%?%?!?!%?%!%%%%!%?%%%!?!%%!!!?%%%?!%%?!%!!%!!%%%?!%!%%%!%%%!%??%!?%%%!!!%!%%%!!?!!%%%!!!?!%%!%%%%%%!?!??%%%%%?!?%%!??%!%%%?!%?!%!%!%?%%%%?%%%!%%%%!%%!%%!!%?%!%??!?%%!%!%?%!%%%?!!%%%%%!?!%%?!%%%!%!!%!%%%!%%%!!%%?%%%??!%%%%%%%!%%%?%?%!!!%%?%!%%!%!%%%%!%%!%%!!!%?!%!!%%%?%%%!%!%%%%!%?%?!%%%?%%%!!!!!%!!??%!%%!%%?%!!!!%%!!%%!!!%%?%???%?!%%%!%%!??%%!%%%!%!%%??%%?%!%%%%%%!%!!%%!%%!%!%%%!%!!%%%!%?%%?%!?!!%%%%!?!!?!!%?!%%!%?!!%%%%!%%?!!%!%!!!%%%%%%!%???%?!!!%%!?!!%!%%?%?!!%%%!!%%%%!%!?%?!!??!%%!%!%%%?!%!?%!%??%!!%%!%%!%%!!?!%?%%?%!?%?%%?%%%%%!%%?%%%!%!%?%!!?%%%%!%%!!%!%?%!!%!????!%%%%%%!%!??%!%!!%!!%%%%%!%!%%!!%?!!%!?%?%%%%%%!!%%%!%%?!%%!%!%!!%!%!!?!!%!%%!%!%?%!%!%?%%?%!%!!?%%%!%%%!%%%!!?!!?!%!!%%!%%?!!!%%!%%%!%%!%!%%%!?!!!?%!??%!!!!?%?%!!%%%!%%!!??%%%!!!!!?!!%!%%%%%%%?!!?!%%%!!%!%??%?%!%!%!%%%%%!?%%???%%!%?%%%!!!?%%?!!%%!%!?%%%%%%?%?%!%!!%%!%%%?%%%%!%%%!!%!?%%!?%!%%%!!!%%!!%?!!%???%!!%?!!%!%%%!!%%?%!%%?%!!!!!?%?%!?!%?!%!%?%%%%!!%%%!!?%%!?%%%%??!?%!%%?!%!%??%?!%%%%%!%!%%!%%!%!!%%?%!!%%%%?%!%%??!%!?!%!%??%?!??%%%!%%%!??%%%??!?%%?%%??%?!%!!%?!%%?%?!%!%%%?%?%%%%%%%%%%%%?%%%%!%?%?%%%%%%!!!%%%!%!%%%%!!%%%!%%%%!%%?!%!!!?!%?%%%!?%%%!!!!%%%!!?%%!!!%!%%%!?!%%%?%%?%?!!%%%!!%%!!?%%%%!%%%!?%??%!%??%?!!?%!?!?!?%%!!%%?%!!%!!%!%!?%%%?!%!!!!?!?%%!!%?%?!%!?%%%%%!!%%!%%!!?%?%%!!%!!%%%%!%%!!%??!!!%%%%%%!%%?%%!!%!%!%!%!?%%!%%%%?%%!%%%%!?!%!%%!%!!%!?%%%!%%%%?!?!%!%??!?%???!??%!?%?%!%%%!%!!!%!?!%?%%%%??%?%%!!!!%!%%%%%%?!!%%!!%?%%?!!!%%%?!%%!%%%%?%?!%!%?%!%%?!??!%%!%?!?%%!??!!%%!?%%%%%?!%%!!!%!!!%!%?%%!!%!!%!!%!%%%%%%%%%%!%!!!%%%!%!!%?%%%%%%%!!%%%!?%?%%!?%!%!%!!!%%!%%%!%%!?!!%%!%!%!!!%!%!%!!%!%??%!%!%%!%!%%%?%%!?!!%??%%%!!!!%!%!?%%!!!!%!!%%%%!!!!!!?!%!%%%?!%?!%!!%%!%%%%!?%!%!?%?!???!%?%%%%%%?!!%??%%!!%!%%%%%%!%!%%%%!!!!?!%!?!%?%%!%!?!%%!??%!!!%%%%!%!%%%!%???!!%!%%%!%%?!!%?%%!%%%!?!?%!%!!%?!%%?%!?!%%!!!!!%%!%!!%?!%?%%%%?!?!?%%%?!%%!!%%%%??!%?%!!%!?%%!?%%!%%??%%%%%!%%!%!!%!?%%!!!!!%!?!%?!%%%%%%!!?%?!!%%%%!%!%!!!!%%%%!%!%?!%%!%!%%%%?%!%%?%%!%!!%??%%?!?%?%%%%%%%!%%!?!!%%!%!%?%!?!%%!%!%!%%%%!?%%!!!%?!!!!!%!!!%%!%?%?%%%%?%!%%%!%!%%%%!???%%%!%%!!%?%!!!!%%!??%?%!!%%%????!%!%?%!?!%%!?%?!!!%!!!!!%!!%?%!!%%%%!%!?!?%%%%%%%%!?%!?!?%%%%%%!%!%?%!!!?!?%!%%??%%!%?%!%%!?%?!!%!?!??!%%?!%%%%!%!%!!?!%!??%!%%?%%%%%?%!!?%!%!!?%!%%?%!!%%%!!!?%%!?!!%%??%!%?%%%?!%!%%?%%%?%%!!%?!!%%%!!%%!?%%!%%%?!!!?!?!!?!%%%!!?%!%!%%!!%%%%!?!%%%%%%%%?%%%!%%!%?!!%!%??!%%%!%?!%!%!%%?!%%?!%%?%?!%!%%!!%!%?!%%%%!%!%%%%!%!?!!%??!%%%!?%%%%%%%%!%%!%!%!%!!!%%?%!!%!%?!!?!%!%!!%%?%!!%%%%%?%!!?%?%%!!??%%%!%?!?%%!?!!!!!%!!!?%!%!!%%%%!%%%!?%%%%!!!??%%%!!!!%%!%!%%%?%?!%%!!??!%!%%?%%!!%%!!!?!%%%!!%%!!%%!%%%%%%%%%%%!?!?%%!?!%%%!!%??!!%?!?!!!!%!!%%!?!!%!!%?%!?%!!%%%%?!??%!%?%!??%%%%%!%?%!?%!%?%!%%%?!%?!%%%?%!!??%%%%!!??!!!!%!%!?%%%%?%%%?%!?%?%%!%!%%?%%!%%%%%!%%!%!%!%!!%?%%?!%%!!!!!!!!%%!?%??%%%%??!%%!!!!!%%%%!!!%!?!%!%!%?%%!!!!?!!%%%%%%%!%%%!!%!?%%%%??%!%%!!?!%!?%%!%!!!%%??%!!%!%%%!?%!%!%%%!%%%%%!?%?!%%!??!?%%!%!%%%??!%%!%%!%%?%%%??%!%?!%?%%%!%%?%%?!%%%!%%%%!%!!%%%?%!%%!%!?%!%%%!!!?%%!%%!!!!?%!!%!%!%%%?!%!!?%%?%%%!!!%%%!!%!%!?%!%%%?%?%!%!!%%?%?%?!%%%!!%%%%?%%?!%%!?%!%!%?!!%!%%%!??%!%!!?!!%%!!!!!?!!%!!!!!%%%%%%%%%%%%%%?%%?%!?%%!%!!%!%%%%!%!%%!!!%!%!?!??!?%%%!!!%%?%!?%!!?%?!%!%!!???%%%!!!%!!%%%%%%?!%?%%??%!!!%!??%?!!!%!%!!?%!%%%%?!%%%%%%%%!%!?%%%??!!%%!!!!!%%%%%%!!!%!%!!%%%!?%%!!%%!?%%%!!!!?!%%%%%!%!%?%%%%%%%%%?!%!%?%%!%%?%%?!%!!%!!%%?%!%%%?%%!?!!%!%!%%?%%%!???!!%??%!%%%%!%!?%?%%%!%%%!!%%?%%!?!%%!%?!!?%%?!!%%%?!%%%!%%%!?%!%!%!!%!!%!!!?%%!%?%!%??%%%%!!?%?!%!!?%%?%%%?%%!%?%?!%%!!?%%%?%?!??!!%!%%%!!!%!!!!?!!?%?%?%??!%!?%%!%!?%%%!%?%!%%?%!!!%%%?%!%!!!!?%!!!?%%?%!!%!!!%?%%%?!%!%!%?%!!%?!?%?!%!!%!!!?!??!%%!!%%%!!?!%!%%!!??%!%?%%!!!%%!!!%%!%%!!!%!!%!!%??!%!%%%%%!!%%!%?%%%!%!%!!?!?!%%?%%%?%%!%%%%!??!%!%?%%%%?!!!%%%%!%%!%%%!%%!!!!%!!%%?%?%!%%%%%!?!%?!?%%!?%!!!!?!%?%!!%!%?%%%!%!?%!%%%%%%%!!!%%%%?%%?!!%%!?!!%%?%?!?%%!!%%%!!%%!%%%%!%%%?!!%%?%%?!?%!%?%%%%??!%%!%%%%?!%!%!?%%?%!%%%!!?%!!??%%?!!?%%!%%%%%%%?!!%%!%!!%!%%%%!?%%!!%%%!%%%%%%%!%!??!????%!??%!%!%%%?%!?!?%!%%!%%%?%?!!%!?%!%?%%%%!!!?!%!!%!%!%%!%!!%??!%%%%??%!!!%!%%%%%%%%!!!%!%%%?!?%!?%!%?%!%!!!%!%%%%%%%!!%%!!%??%?%!%!%%%%?%?%!???%%??%!?!%?%!!%%!%!%!?%!%%!%%!?%?%?%?%!!%!%!%%?%!%%?!%%!%%%?%%!%!!%!!?!%?%!!%!%%%%%%%%%!%%?!%%!%!%?!!%??%%%%!!?%!?%!!%!%%!%!!%?%%!%%%!%!!!!!!?!!%%!%%!!!%%!?%!!%?%%%%%%%%%!%%!!%?!%!!%!!%!!%!?%%!%%%?!?!?%%!!!!%%%%%!%%%!?%%%%%??%%%!%!!%!%!!!%!%!%!%?!%!%%!%!?!%?%%!%!??!%%!%%!%%%?%%!%!!??%%?%%?!%%%%%?%!%%%%%%?%%!!%%%?%%!!!%?%?!?%!!!!%!!!!%%%%!?!%!%%%%%%?%!?%%%!!%%%%%%%!?!!%%!?!!%!%!?%%!!!?%%!%??!%!!??%%%%%%!?%%%%%%%!!!!%!%!%%%!%%?%?%%!!!%%%!?%?%%%%!%%%!%!%!%%%!%?!%!?!%%%?%!%%%?%%%%!%!?%%!%!!%%!%?%%%?!%%%%!%%%!?!!%?%!%%!?%!%?%%%%!!?%?%%%%%!!%?!!?%%??%%!!%?%%!!!!%%!!!%%!%!%?%!!%!%?%%?!%%%?%%??!%!!%%%%!!!%?!!!!%%?!!%?%%!%?%%!%%!!!?%%?%%?%?!%%%%%%%??%%!!!%%%!%%?!%%!%%???%%!%%!%%%!%%?%%!%%%%!?!%%!!?!!!%!%!%??%%?!%%%%!%%?!?!%%%!%?!%%?%%%!!%%?%!%??!%%%%%!!!%!%%!?%%!%!?!!!!%%%!%%%!%!?!%%%!!%%%%!%!%%!%!%%!%!%%%%%%%%%%%%%?!%!!!!%%?%!??%!%%!!%%!?%%!%%%%%%%!%?!?%%%%!%%!??!!%%?!%%%%%%!!%%%?!!%!%?!%%??!%%!%!%?%!%%%!%!%!%%?!!!?%%!!!%!%!!%?%%!%?!?!??!%!!%?%%%?!%%%%?!%%%%?%%!%!%!!!!%%!%%%?%%%%%%!?%!!%?!!?!%%%!!!%%%??%%?%%%!%%??%!?%%%!%?%!??%%%!%!%%!!%%!%%!%?!%??%!%!!!%%%!!?!%%%%%%!%!%%?!%!%!!!%!??!%?%!?%!%??%!%?%%%%%!%!!!%%?!!!?%!!%%!!%%%!?!?%%?%?!!?%%!%%!%%!?!%%%?%?%%!!%?!%!%!!%%%!!!%!?%!!%%%%%%??%%%%%%?%!%%!?%?!?!%%!?!!%!!%?%!!%?!%%??%%%!%%%%!%?%!%?%%!!?%%%?%%!%!!!%%%%%%!!?%!%!%%%!%?!!%%%%%%%%%!?%!!!%%!%%??%?%!!%%?!?%%?%?%%!%%?%%!%%?!!%%!!?!!%%%!%%%!?%%?!??!!!?%%%%%!!!!?!!%!%%!%!%%!!%!%!%?!??!!!!%!%?%!%!%%%!!?!!%%%%?!!!!!!??%??%%?%%??%!%!%!!%!%!!?%%%%%?%%!%??%!?%?%%%!%!%%%%?!!?%?%!%%!??%!%?%%%%%!!!%%%?%%!!%%!%%?!%%!!%!%?%%%!%?!%%%%!%!%%%!!!!%%%!!%?%%?%%%%?%?%!%%%!!%%%??!!!?!!!!%!%%%?%%??!%!%%%%!!?%%!??%%!%%!%%!!!%%%%%%!%%!?!%?%%%%%?%!%!%%!%??%!%!!!?%?%%!%%%%%!%%%%%%%?!!!%%!%%%%!!%!?%!%?%%%!!%%!%!%%%%%!?%%%!%!%%?!%%!%%?%%!%?%%??!?%%%!!??%!%??!%?!?%%%%!%!!!%%?!!%%%??!%%%!?%!%!%%!%!%%!%!?%%%?!%?%!!!%%%???!!%!!%%%!%%%!!!!!!!%%%%!!!%%!%%?!%%%!%!%?!??%??%%%%%!%!!%??!!?%%?!!%%%!!%!?!%?%?%%!?!?%?!!!%!!%%?!%!?%%%%%%%%!!!%%%!!!?%%%%%%%%!%%%??%%%!?!%!%!%%!!%%%%?%%%?%??!!%%%%!%%%%%%?%??!!%%???%?%%%%?%%?%!?%%%%!%!%%?%?%%%%%?%%!?%!!!%!%%%%%%%!%?%%%!?!%%!?%?%?!!!?%!%?!%%%%%!??%!%%%!!%%%%!??%%%?!%!!?!%????%?%!%%!!!%%?%%%!??%!%!!?!!%!!%!%%?!?!%%!%!%%!!%%!!!!%!!!!??%!%%%!!?!%??!!?!%!!!%%?%!!%%%!?%!?%!%?%!%%%?%!%!?%%!!!%!%%?%%!%!!%!%%?%!%%%?%!%!?%!!%!%!%%%%?%???!%!?%%%%????!!%%%!!?!?!%%!%%%?!%%%%%%!?!%%%%??%??%!??%!%?!%%%!?%%!!%!!%!%%%!??!!%!%%!!%!%%?!%%!%??!%%%%!%%?%!%??!!%%?%!%?!?%!!?!%%%!?!!%!??%%%%%!!?!!!%!%%!!%%!!%%%%?!!%!??%%!%!?!%%??!%!%!%%??%%!%!!%%!%!?%!!!%!%?!%%?!%%!%%!%%%!%%%%!%?!%%?%!!%!?%!?!!!?%?%!!!%%%!%!%%%!!%%!!?!!!???!?%!%??%%!%%!%!%?%%?!%%%!?%%%?%%%%?!!%%?!%%!%?%%%%!%%!!!%!!%%!!%%!%%%%%!?%!%%?%%!!%!%?!%!!!%?%%?%!!%!%%%%!!?%%!?!%%!%%??!%!%!%!%??!!!%!%!%%!%?%%?%?!%%%??%!%!%%!?%!?%%%!%?!!%!%%!!%%?%%%!%%!%?!?%%!%!?%%%!%?!!!%%!?%??%%!%!!!%%%!?!!%%!%%?%!??!?%!?!%!%?%%%!!%%%?%%!!!%??%??!%%?%!%!%%?!%%%%!%%%%%%!%!%%%???%?!!%%%!%%%!!%%!!%?%!?%%!%?%!!?!%!!!%%!!?%!%??!%%!!?%%%!%%?%%!%!%?!%!!!%?!?!%!!!%%%%!?%??%!!!%!%??%%%!?%%%%!?%???%%!%!!?!%!??!%%!!%?%%!!%%%%%%!!%%%?!%%%%%%!%!?!%%!?%??!%%%??!%%%%!%!!%!%%%!?%%%%!%%?%?%?%!!%%!%%%?%%%!%%%%%%!%%?%!?%!!?!%?%?%%%???%!!?%%!!!!%!%!!%%!%!%%?!%!%%!!!?%?!?!!?!%%!%%%%%!??%??%?%!%!%%!%%%%%%%!?%%%!%%!!%%%%%!%!%%!!?!%??!!%!%%%!%?!%!%??%%%!%%?%!!%!%%%?%%%!%!?!%%%%!%%%%!%??%!?%!%!%%?%?%%?%!%!%%!%%%%%%?%!%%%%!!!?!%%%%%!%%%%?%%??!!???!!%!%!?%%%!%?!%!%??%!!%!!?%!%?%?%?%!!%?%!?%%%%%!!%%%%%%%!%%%!%%?!!%%%%%!%%!%%%!%%%!%?%?!?!!!%!!?%?%!%%%%!%%%%%!%??%%!%%%?!%%%!?%?!%%%%%!%?!??%!!!%%!!!!%!!?%%%?!?%%!!!%%?%?%%%%!?%!!%%%??%%%!%!!!?%%%%!!%?%%?!%%!%%%?%%%!?%?%??!%!?%%%?%!!%%!?%%!%?%!%%%%?!%!%!!%%%%%!?%??%?!?%?!!!%!!!!!!%!??%%!%!!%!?!%!%%%?!!!%%!%%%!%%??!??%%!%%!%?%!%%%%!%??!%!??%%%!%?!!%%%!!?%?%%%%?%?%!??%%%?%?%?%!%%!%?%?%!%!?%!%!%%!!%!%%%%%%%%!?!?%?%!?!?!?%!%%?%%%%!???%!!!!?!%!!!%!%%!%%!?%%!%%%%!!%%!?%%!!%%!!!%?!%?!!?!%!?%%%%!%%?%%!!%!!%!!%!?%%%%%!!?%?!??%!%%??%%%!!%!?%%!%??%%?%%%!%?%!!??!!!%!%!%!!%%!%?!?!!%%%!!%%?%%?%?!%!%!%%%?%!%%!%%!!%?%%%!!!!%%%%!%?%?!%!%%!%%!%%%%%%%%???%!%!!%%?!%%%%?%%%?%%%!%%?!!!%%%%%!%%!?!!%%!!!%%!???!%?%!%?!!%!!%%%%%%?%%?%!?%%?%!!?!%%%%%?!!!%%%?%%%%%%%!%?%%%%!!%!%%%%!%?%!%%!!?%!%%%%!%?!%%!?%%!!%%%!%!!%%%!!!!%%!%?!%!!?!??%%%!?%%!%!?!?%?%!%!!%??%%!!!%!!%!!!%!%?%%!%%%%?%!!?!%!?%%?%?!%?%%!%!%%%%?!!%%?%!!%%!!?!?!?%!%!%!?!?%?%%?%?%?%%%!%%%%!%??%!!%!%!?%!%%!!!%!!%%%%%?!!%!%?%%%!?!%!?%?%%%!%%%?!?%%!?!!!%%%%!%!!?%!?%!%%?!%%%!%!!!%%%?%!!%%%%%%%%!?!%%!!!??%%%!%%!%!!???%!%?%%%!%!!!!%!!!%%%%!%%!??%%%%%??%%!%%!%%%!?!%%%!%???%%!!!%!!%%!%!!!%%%?!%%!?!!%%?!!%%%%%?!%!%!%%!!%!!%%%!%%%%!%%%?!!%?!!!%%!%!!!%!%!%%!?%!!?%!%%??%%?%%!!%%!%%!%%%!!%?%%%%!%!%?!!%!%%!%%%!%!!?%!!%%%%?%??%%%!!%%!!!!!!?!%!?!?!%%?!%%%?%%%!?%%!!?%!??%!?!!%!%!%%%%%%!%%!%?%%!%?%%%!%%%!?!!%!!%%%%!!%!!%!%!?%!!!!%%!?!!!??%!%%%%%?%!%?!!!!??%?!?!!%%!!?%!%%!%%!%!??!?!?!!?%%?!!%?%?!??%!!?%%!%?%!??%!%?%%%!%%%%%?!%!!%!%%%!?!??%%!?!!%%!!!%%%?%%%!!?!?!?!%!!!%%%%%%%%%!%%!%%%%!%%!!!?%!!%%%%%%%?!%!%?%!?%!%%%%??!!%%!%!?%?%!%%???%!!%%%%?!%%%%!%!%!%?!?!%%!%%%!%!%!%%%!?!!!!!!??%%%?!!%%!%%?!%?!%%%!!!!?%%%!!?!!!!%!%?%%?%%!%??%!??!%!!%?%%%%%%%!?!%%%!%%?%!?!!%!!?%!??!%!!%!%%%%!%%?!!!?!%!%!%%!?%%%%%?%!?%!%%!%%%??!%?%%%?!%%%%%!!?%!?!?!%!!%%!%%%!%%%!%?%%%%!%?%?%!?%%%!!!%%!%!!%!%%?%!!%!%%!%%%!%%!!%!%%!%%%!%%!!%!%%!!%%!%%%%!%%!!%%%!%?!%!!!%%%%%%%%!?!!%%%%!?!%%!?!%%%!!%?%%???%?%!?%!!%%%%!%?!!%%%?!%%!?%%!%?%?!?!!!%!%%!%%!%%!%!%!!!?????!!?%?!?!!%!!?%!%%%%?!%!%%%!%%!!!%%%!%%%?!%%%!!%%%!!!!%?!%!%%%%!!%%%!%?%!!!!!%%%!%%!!%%?!%%?%?%%!!%?%?!%!!%!!%?!??!%!!%%%%!%!!?!!!%!%%%?!!%%!%!!%%%!!?%%!!%!%!%!!%%!%!!!!%!%%!%!%!%%!%!%%%%!??%%%%%?!%!%?%%%!%!%!!%!%%!%!%%??!%!%!?%%%!%!%!!!!%%?%!!%!%!?%!%%%!%?%%!%%!%%!%!!%?%!!%%!!?%?%%!%%%??%%%%%%%!!%%%!%%!!?!%%??%!%%%%!!%%!!?!?%%%%%%!!!%%%!%%?%!%!%?%!!%!?%%!?%!!!%?%!%?%!%?%?%!%%!?%%!?!%!%?%%%!?!%%%!!!%!%?!!%%%%%!!%!%!%!%%%!?%%%%%!?%%!%%!%%%%%!%!!%!!!%%%%?%%!!?%?%%!%!!?!%?!%%!?%?!%??!%%!%?!%!%!%???%!%!?%%!!!???%!!%%%%!!%%!?!!!?!%!%%%?%%!%?!!!%%%!%!%!%?%%?%!?%!%!%%??!%?%%%%%?!?%!!!%%!!%%?%!%%?%%%%%!%?!!!?!%%!%%!!%%%!%%!!?%%%%%%!%!!%?%%%!%%!%%%%!!!?%%?!!%!%?%?%?%!%!%?%!!%%!!%!%%!!?%%!?%%?!%!!%%??%%%?%?%%!?%%!%%!%?%!%!%%%!?!%!!?%!%?%%%!??!!%%%%!%%?!!%%%%%?!%??!%!%%!%!%%%!%!!!!%!!?%%?%!%%!%%?%%?%!!%!%%!!%%!%!%%%!!?%%!%??!!?%%%%??%%!%%?!%%%!%!?%%%%!%!%%%!!!%?%?%?!?!!%!?%?%!%!%%?%!!%!%!!?%%!%%??%%%?!!!!!%%%%!?!!!!!%!%%%%%%%?%!%??%%%!%%%%%%????%?!????%!%%!%%%!%?!?%%!%%%!%!?%%%!%%%!?!%%%!%!!?%!%%!%???%?%%%%!%!%%%!%!%?!?!!!%%%!??%??%?!!%!?%%!!%%%%?!!!%%!%!!%%%!!%%!!%%!!%%!!!%%!%??%!!%?!%%!%??%%!!%!%!!?%!%%!%%!!%!%%%%!!!!!!?!%%!!!!%??%!!!%?!!?!%!!%%%%?%%?%%%%?%?!%!!%?%%%%!%%%%!%?%?%?!!!%%%!%?!!%%%?%%%%?%!%!?%?!!!!%!!%%?!!?!??%%!!%%%!?!%!?%?!%%%%%?!%%%%%%%!%%!?!%!!!%%%%!%%!!%!!%!%!?%?%!!%%%!%%%!%!!!%!?%%%%%%%%%!%?%%!?!??!!?%%%!%%?%%%!%!?%%%%?!%?%!!%!%%%%!!%??%!?%%%!?!!%%!?!%%!%%%%!%%!%?!%!!!!!!!!%%!%?%?%!!!!%%!!%%!!!?!%%!%!!%%%%%%%!%%!%%%?%%!?!!%%%?%%%?%!%%!%?!?!!???%!!%!%%%?%!%%%!%!%%!%!%%!?%!%!%!!%?%??!!!%%!?%!%!%%!%!?%%?!?%%!?!?!!!?!!!?!%?%!%%%%!?%!!!%%%?!!?%?!%%!%!!%?%%!?!!%?%!!!%!%%%?!??!%%!??!%%%??%!%?!!%%!%?!%?%%?!%?%?%!%%%%!!!%%%?!%%%%%%!%!%!?!!!!%!?%!%?%!!%%%%%!!%%!%%%?%?%??%!%!%%%%%!!??%!!?%%??%%%%?!!!%%?%%!%?!%?!%!%?%!!%!%?!!%?%!!%%!%?!!?!!%%%%?%%%!%?%%??!!%?%!%%%%!!%%?!%?%%?!!!%%%!%!?%%%%!%!%!%!%%%%!%!!%%%%?!%%!?%!%!?%%!!?%!%!!%%%!!?!!?%!?%%!!!%!%?!%%??!!%?!!?!!%!%?%%!%%!?!%?%?!??%%!!!?!%%%%%!!?%%%%%%!%!%!%??%%%!%!%!%!!!!%!%!%%?%%%?!!%%%!!?%%!%%%%%!!?!%!!%%%%%!%%!?%%%!%%%!!?%!%??!!!%?%%%%%!%!?%%%%%!!?%!%!?%?!?%!?!!?!%!!%!!%????%%!!!!!!%%!%!%?!?%!??%?!!!?!%!%%!?!!%%!%%!%!%!%%?%%%!%%%%%?%%%%%?%?%%?%!%%!!%??%!?!%!%%%%%%!%%?%?%?!!%%%!%%!?!%!!%!?!!?%%?%%!!%%%%!%!!%!%?%%%%%!!!?%!!!%%!?!!%%!!?%!%%%%!%%?%%%!%!!%%!%%%!??%%%!!!%!%%!?%%%%%%%??%%%%%%%?!%!!%?%%%%!%!%!?%%!?!?%!!?%!?%!!%%??%!!%%!%???!!!%%?%!%%%!%!%!%%%!?%%!%?%%%!?%?%%!!%%?!!???!%%?%!%?!%%!%!!!%!%!!!%%!!%?!!?%!!%%?%%%!%%!%!!!?%?!!?%!!%!!!%%!%%!%%%%!!%%%%?!!%%!%%?%%!!%??!!%!!!!???%%%%%%%?!%%%%!%!!%%%%%!!?!!!??!!%!!%%%%%!%!!%!!!?!?!%%%!!%%!%?%!!??!%%%?%!%%!?!%%!%?!%%!%%%!?%%?%%?%%%%!!%%!!!?!?%!!!!%%!%?%!%%?%%%!%??!!!%?!?!%!%!!%%!!!!%?!%!!%??%!!%%%?%!!!!!%%?%%!%!%!%%!%!?!!%%!!!%%%%!%%!%!%%!%%%!%%!!%?%!%!%%!?%%%%%%?!!!%!%%%!%%!%%%%?!!!%!%%!!!?%?!!!%%%%%%?%%!!%!!%!!%??!%%?%?%%%?!%!!%!?!?!!?%!%%%?!%%!%%%!%??!?%%?%%!!%%!%!%%%!%??%%!??!!?%%%%!!%%%%%!%%?%!!%%%%!!%%!??%%!%%!%%!?%%!!!?%!?%!%%%%%%%%?%!!!%%%%%%!%!!!%%!%%%??%%%?%!%?!%%%%%%%%!%?%%%!%%%%!!?%%!?!%!%%!?%%!%!%%%%!??!!%!!%!!%%%%%!?%!%!%%!!%?%%%!!!%?!??!?%!%%!%%!%%!%!!%!%!!%%?%%!%%??!%%?%??!?%!!!%%%%%!!%!%!?!?!%%!%%!?!%%%!!%!!%%%%%%?%%!%%%!!!%%%!!%%!%%!!%%%%?%%!!?%?%%!%%!%%%%%!%?%%%!%%?%?!!?!?!%%?!%%%%%%!%!!!%%!%%%%!%!!%?%%%!%%!%?!%%!?!!%%%%%%?%?%%%?%%%%!!!!!%%%%%%%!%%?%%%!%!!!!???%!!%%%%%%!%?%%?%%!%%!%%!%%%%!%!%!%?%!?%%%??%?!%%!%!%?%!?!?!%!%!?!%!%?!%?%%!!%??!!%?%!%!%%%!?%?%!%?%%%!%%%%?%%%%%!!%?!??%%%%%%!%%%?%%??%%!%%%%%!!%!!%%!?%!%!!??!?%!!?!%%%%%?%%%%!%?!%?%%%%!%%%%!!?%??!!%%!!%%%%?%!%!!?%%%%%?!%%%%%!%?%%%!!??%%?!!%%%???!?%%!??!%?!%?%%?%%%%%%%!!!!!%?!%?%??!%%%%!%%!!%%??!!%%!%!%%!%!%%?%?!!%?!?!%!%!!?%%%%!%!!%!?%%!%?!%%%?!%!!!%!%%?!%%!!%?!?%%%%%%!%%%%!!?%!?!!!!%!%%%%%%!?%%?%!%%!!%%!%?!%!%!%!?%??!?%!%?%%%!!?%%%!?%%!!?%!%%%!!%!!%?%%%%%!!%??!!%?%?!!%%%%%!!!!%%!%!??!?%%%!!!!!%%%%%%!%%!!%?!!%!%!?%?%!!%?!%?%!!!%%!%%?%!!%%%??%?%%?%!%%!!%!%%!!%%!%!!%%!?%!?%%%%!?!?!?%%%%?%?!%%%!%?!?!?%!%%!%%%%%?%%%!%%%%%!?%%!!?!!%!%?!%!!!%!%%?%?!!%%%?%?!%!?!%!%%%%!%%!!?%%?%?%%%!%??%%%%!!%?!%?%??%%!%!%!%??%!!!%%%!!%!%!!%%?!!%?%%%%%!!%%%%%%%%?!%%%??%%!?%%%!%!%%%%%!!%%%!!%???!!%%%!?!!!?!%!!%%?!?!!%?%!!?%?!%?%%!%%%!%%?%?%!%%?!%?%%?%%!!!?%%!%?%?%!!%%%%?!%%?!%%!!?%%?!!!%%!%%%?!%%%%!%?%%%!?%??%!!%%%?%%%%???!%!%%%?%!?!!!%%%!%?!%%!%%?!!!?%%%%?!%!%%!!%!?!%!!%%!%?!%?%%!?!?%?!!?!!%!!!!%!%%!!?%%!%%?%?%%%?!%!???%??%%%%!?!%?%?!!%%??%!%%%%%!!%!%%!%!??%??!!!!%%?!?%?!%!!!!!%!!!!%%%%!%!%%!????!!!%%!%!!!??%%%%%%%%?!%?%!%!!%%?%!%!!?%%!!%%!??!!%%??%%!?%!!%!%??%!%%!%!?%%%?%%%!%%%%%!%?!%!%%!!%!%%!!!%%??!!!!%%%!%%!!%!%%?%%%%%!!!?%%%%%!!%%?%%?!%%%%!!!%!?%!%?%%!?%%!???!%%%!!?%!%%!!%%%??%!%!!%%%%%%?!!?%???!%!!!??%%%%!!!!%??%!!%!%!!%%%!?!?%%!%%!%%?%%?%!??!!!%!!%%%%%%?%?!%%!%!!%!%!%%!!%%?%!!%%%%!!!%%%!%%%%!%!%%!!%!%!?%!!%!%%%%%%%!%!!%%%%!%%%!%%%!%?%!!%%?!!%!%%?%%!%?%?%!%?!%%?%!%!!%%!!%%!!%%%%%%%?%!%!%%%%!%%%%?%%%?%!!!%!?!%%%%!!%%%!%%%%!%%?%!?%%?%%?!!!!!%!?%%!%%?!!%%%%%%%?!!%!!?!%%!%%?%!!!%%%%!!%!%!!!%!%%?!??%%%%%%??!!!%%%%%!?%%??!?%?%%!?%!%!%%?!!%!%%%%!?!%%!??%%%!?%%%!?!!%%!?%??!%?%%%%!%%%!?%%%?!%%%%%?%%!%?%%!!?%!!??!%%!%!!%%?%%%%%!%!?%%%%%!%%???%!!%%!?%%%%??%!?%%%!!?%%!%!!%%?%%!%!!?!!!?%%!!!%%%%!%%%%%!!??%%%%%%%%!%%%%!!%%!%%!%!!%%%?!%%%%%%%%%?!%!??%%?%%%?!%!%!%?%?%%!!!!!%%!!%%!%%?%!??%?%%!%%?!%!!%!!???%?%%%%%??%!!%%%%!!!%%%%%!%%?%%%!!%%!!%!!?%%%%%%!!!!!%!???%%!!%?!%%%%!?%!%?%?!%!%%%!%!!%%%%%%!?!!%!%!?%!!!?%!!%!%!%?%%!%%!%?!%%??%%?%%%?%%!!?%%%!%?!%%?!!!!!!!?!%%?!%????!%?%%!%!?%!%%%%%!??%!!!!!%%%!!!%%%!%%!!%%%%%!%%!%?!!?%%%!%%!%!!?%%!%!%?!%%%!!!%%%!???%%%!!!!%%??!?%%%%?!%%!!%%%?!%?%%%!%!!%%%!!?%%?%!%!!%%%!!?!%%?%!!!?%%!!!?%%!%%?%%%%%!!%!!%%!%!!?%%%!?!!%!!%%!%!%%!!%?%!!?!?%!%%%%%%!%!%%!!%%!!!!%!%!%?!%%%%!!!!?%%!!!%%%!!!%!!%!?!!%?%%%!%%!%!%%?%?%%%%%%%!!%%%?!?%%%%%!?%%!%%!?!!!%!%!%%%%%%!%?!!%%%?!?!?%?!%%%?%?%%%%%%?!?%!%%!%!!!%%!%%!?%%%%??%%!!%%!%%%%?%?!!?%%!??!!?%??%%%!%%!%%%%%!!%%%%!%%%%?!!%!%!?!!%!!%!!%%%%!!%%!%!!%?!!%%!??!%%%%!?!?%!?%%%%%!%!!%?!%%%%!!%!%%%%?!!%??!?%!%!%%%?!%%!%%?%%!?%!!?%!?%!!%!%%!?!%%%%%!??%%?!%?%?%!%!%?!%%!!!!!%%?%?%%%?%!%!%!%%%!!!%%%??!%%%%%%?!!%?%%%!!!%%%%!?%%%%%!%%?!!??!!%!!!%!%%!%%%!%!%?!!%?%!%?%!%%%!?%%%%!!%%%!!!%!%%%?!%!%!!%!?!!%!!!%!!??%%?%%!%%%!?!!%%?%!!%?!%!%%%!%%%%%!%!%?!?!!%?%%%%%%%%%!%!%%!%!!!!%!!%%!%%!!%?%!!!%!!%%!!??!%%%!!!?!!%%%!!!!%%!!??%!%%%!!%%!%!!%%%!!%%%?%%!!?!!%!!%%%!?%%!!!?%%?%!?!%!!!!!!?%?!?!%%%%%!%!!%%%%?%%!!%%?!%?%%%!?%!!%%%?!%%%%%%!!!!%%%!%%%?!%?!!?!%%%%%!%%%!%!??%%!%%%!%?%!%??%!!%%%?%!!%!%%!%%%%!%%%%%%%?!%%?%%%%%%%%!%?!!%?%%!%??!%!%?!%%%%%%%%!?%?%%%%!?!%%%!?%%!%%%%%%!!%?!!!?%%%%%%!%%%!!%!%%%%%%!!%%!%?!!!%%%%%%!!?%!?!!%!%%!%!?%!%!!%%%%%!%?!!%%%???!!%?!%!%%?%!!%?!!?%%%%%%%??%%%!!?%%!?%?%!%%%!?%?%%!!%?!!%??%%%?%%%%???%!%%!%!!!%%%%!?%%!%!%???%?!!%!?%%!?%?%!%!%%!%%%%?%%%%%!?!%%%%?!!!%!%%%%%%%%%!!%%?!%!!%%%!%?!!!%!%%??!%%!%??!??%%%%?%!%?%!%?!!%%!!?%%??!%%?!%!%%!%%%!?!%%%%?!%%%%%?%%?!?!?%!%%??%!!!%!?%!%!!??%%%%%?%%%!%!%%%%?%?%!%!%%%%%%%%!?%!%!%!%%!!?%%%!%%%?!!?!%%%%%?!%%%!?%%?!?!?!%!%%?%%?%!!?!%!!%!%%?%?%!!!%!%!%%%%!?%?%%?%%?!%?%?%%?%%?%!!%%!?%%%??%%!%%%?%%%!%!%!!%?%%%%!!%%%%%%?%?!?!??%%%?!?!%?%%!%%!!%!%?%!!?!?!%%%%?!!%!%%%%%%?!!!%?%%%?%!%???%!??%!??%!%!!%!%%%%%!%!%%%!!!%%!?%%?%??%!!%!%%%!%%%%?%%%!%%!%%%!%?!?%!!%%%%%%%??%%%!%%%!%??!%%%%%!%%!!!!?!?!%%%%!%%%!%%!!?%%%?%%%!!!!!?%%!%!!!?!%%!%%!!%%%!!%?!%?!%?!%%%?%?%?%!%%%?%!?%!%%%%!!!%?!?%!!?%!%%!?%%!%!!%%%!!!!!%%%!%?%??%%%%??%%!!?%!!%%!?!%?!!!%!%%!!%!%%!%!??!!!!!!!%%!!%%%?%%%%!%!%%%!!!?!%%%%!!%%%%??!?!!%%!!%%%!%%?%%!%?%!%!%?%%%%?%?%%%!?%?%!%!%%%%%!??%%?!?%!?%%%%!%!%%!%%%!%?!%?!?!?%%%!!%%?!%!%?%?%?!?%!!!!%%!?!%?%%!%!!%!?%?%!!!%!!%%%%%%%?%!!%%%!%??!%?%%!%%%%!!%%?%%%!!%!!?!!%!?%%?!?%%%%%!%!%!%!???%?%!!!!!?!%?%!%!!%%?%?%%%%?%%??!?!%%!%!?%???%!!%!!%%?!%?%%%%%!%!%!%%%%%%!?!%%%%%!%!?!%%?!%%!%?%!?%%%!%!%%?!%%!!%?%%!%%%!%!!%?!!??!%%%?%!%!%%%!?%?%%%!?%%%?%?!%%??%!%%%%%%%%%%?!??%?%%?!?%!!??%!!?%%%!%!%%?%?%!!?%?!!!!%?????%!%%%%?%!!!?%!%?%!%!%!!???%!!!?!%!!!%%!!%!%!%%!!??%!%%!%%!%!?%!!%!%%%%%%!?!?%%!%?!%!%%%%?!!%%%?%%%?!%%%?%%?%!?%%%!!%!!%?%!?!%!!!???!!%%%?%%?%%%%%%%??%?%%?!!%?%%%%!%%%?%%%%!%%%!?!%%!!!%%?!!!!?%??!!%!!%%%?%%%%%?%%%%?%??%!%!%%%!%%?!%%!%!%?%%!?%!%!?%!?!!%!?%?!?%?!%!%%%?%%%?%%%%%!%%!%!%%%%%%?%!%%%!%!%%%%%%!%%!!!%!!%%?!!?%!?%!!!%%%?%%???%?%%%%%!%%?!%%%!%%%%%%?%!%?!%%!%%%!%!%!%?%%%%%!!!!!%%!%%!!%!%!??!!?%!!!?%%%?%%!!%!!!!%%%!?%!%!%!!%!?%?!!!!%!!%!!%!%!%%%!!!%%!!?%?%%!%?%?!%%!?!?!%!%%%%?!%%%%?!%%%!%!?%!!%!!%!%%%%!%%%!!%?%%?%!?!?%%?%%%%%%%!?%%?%%%%%?%!%%?%!!!!?%%??!%%!?%%%%!?%%%!!!%%%%?%%%%!%%%%!!%%!!%%%!%!%!%%?!%?%%%%?%!%!?!%?%%!!?!%%%!!!?!!??%!!!%!!!!!?!%!?%%!%%%!%?%!%%!!!!%%!%!!%%%%!%?%%%%%%%%!?!%!?%%%?!?!%%%?!%%!?%!!%%%?%%%!%!%%%!%?!%%?%%?!!%!%%!!?!%%!%?!!!%%!%?!!%!%%!%!%!??%!??!!%%%%!?%%%%%%%%!?!%!!!!!%!%!!%%?!?!%%%!%?%?%!?%%?%%%!!%%!%!!?%%!!%%!%!%%!%%?%%%?!%!%%?%%!%!%%!%!%???%%%%%????!?%%?%%!!?!!%!%!%!%??%??%%?!?!!!?%!%!%%!%%?!%%%%%!%%!?%!%%%%%!%!!!%???%?!%%!!%!?!???%!!%%%?!%!?%%%%%%!?!%!!!%!%??%%%?%%%%%!!?%%%%!!%?!%%%%%%%?%!?%!%%?!%!%%%!!?!?%%!!?%!%%!%!!!%%%!%!%!!%%!%?%!%%!%%!!!%%!?!%%%%%!%?!!!!%%%!%%!!!!%%%%%%%?%!?!!?!!?%%%?%!??%?%%!%?!%!?!%%!!???!?!%!%%%?%%???%!%%%%!?!??!!%%%!%%%!%!!%?%!%%!%%!?%%%%%?%!%%%!!%?!%%!!?%!%%?%!!%!!%!?!%?%?%!!?%%%!%?%!!!?%%%%%!!?%%%%!%%!!!%%%!!%%!%!%%?%%!?!!%!!%!%%%%%%?%!?!%!%!!%!?!!?!!%!%%%!%??%%%%!!!%%%%!!?%?%??%!?!%%!?!!%%!%!%%%?!!%%!!!!%?%!%%?%%%!?%%%%%?%%%%%??%!%%?!%%%!%%!%%%%!!%!%%!%!!?%!!??%%!%%%?%%!!%%%!!%%%?!?!!!%!??%%%!%%??!??!??%%%!!!%!?%%%%!!%%%!%!%%%!!!%!?%%?!%!!%?%%%?%!!%!!%!?%%%??%%!?!%!%?!%%%%%%%%%!?%%%!%%%!!%!?!%%!%!!!%!%!?!%%%!%%%%%%%!%%!!?!!!!%?%%!!!%%!%?%!%?!!?%!!%%%%!%?%!%!?!%%%%%!%%%?!%%?%!%%!%!%!?%!!%%%%%????%!%?%!?!!%!?%!%!?%!%%!!!?%%!%!?%!!%%%!!%?%?%?%%!%%%!%%%%%!%!!%%%?%%%%%%%%?%%?!%%!%!%%%%!%%%?%%!!%%!%%%?%%%!%%%%?!%%!!!!??%%%!!??!?!!!?%%?%??!!%%!%%%!!?%%?%?!%%!?%??%??!%?%?%%?!%!!?%%?%%?%!%!%!%!!!!%!%%?!!%%%!!%!%?%?!?!%!%!?%!%!!!!%!%!?%!%!!?!%%!%?!?%?%%!?%?!%%!%%!?!%%!%%!%???!?%%!%!%!%?%!??%%%!!%!%%?!?%%%%%%!?!!?!!!%!?%?!%%?!!%?!!%%!??%%!!%!!!!!%!!%%%!%%?%?!%?%%?!!?%?!?!%%!!%!!%!%!!!!%%%%%!!?%!%%%%%%!%!!?%%!!!%%??%%!%!!!!!%!%?!%%??%???%?!!%!?!!%%?%%%%%!!!!%%%%??%%%!!%%!%%!!%%%!%?%%%!%%!%%?!%%%%!!%%%%%%%%!?%!!%%!%?%%%%%%?%%%?!?!%%!%%!?!!!!%?%?!%?%%!%!?%!!!!!%%!%!%%%%?!%!%?%!%!!!?%%?%%%!?!!!!!%!%%%!?!%!%!%%%?%%%!%?%%%???%??%!!%%%%?!?%%%%??!%!!%?%%!!%?!?!!%%%%%%%%%?%%%%%!%!%%%!%!%%%%%%%?%%%!%!%!%%%!%!?!?%??!!%%%%%%%!%%%!%!%%%%%?%%%!?!?%%%%%!?%%?%%?!%!%%%!?%!%!?!!%%!%?%%!!%%!%!!?!!!%%%!!!!%%??%!%%%!?!!%!!!!!%%%%????%!%!?%!%%!%!%?!%%?%!!%%%%?%!?!!%!%!?!%%%%%%%%!%%%!%!!%%!!%!?%%?%%!%%?%%?%??%%%!?!!??%?%%%!%%%%%!%%!?!!?!!%!!%?%%!!%%!%?%%!!?%%%!??%?!!!%%%!%%%?!!!%%%!%?%?!%%%?!%!%%?%%!%%!?%%?%!?%!?%%!%%?%?%%!?%?%%??%%%!%%!%!?!%%%%?%%%%%!!%%%!!%?%%%%!!?%?%!!%?!%!!!!%%%!%%!!%%%?%!?%!%%%%?%%%%%%%%!?!!%%%!%?%%%!!!!%%!%?!%?%%%!!%%%!!%?%?%%%%??%%%%%%%!%%%%%!%%?%!%%!%?!%%%%?%!%%!%%%%!%!%%!!!!?%%!!%%?%?%%?!!%!%%!%%%!%%%?%?%!!?%%%!%!!%%%?%!%!%%%%?!??%%%!%%%!!%%%!?%!!!%?%%!!?!%!%%!%!!!?%%%!%%?!%%!%?!%??%%!%?%%?%!%%?%%!%%!%%%?%%!%%%%!%%%%%%%!?!?%%%!!%?%??%%%??!?%%%!!%!??%%?%!!%%%?%?%!!%!%?%?!%?!%%%%%%%%!%!%%!?%%?!%%%??%%%?%!%%%%%%?%%!?!%%%?%!!?%!%%!!?%?!!%%!%!?%%%%!!%%!%?%%%!%%?%%%??%!?%!%?%%?%!?!%%!%!%?!%!%%?%%%%!%%?%?!!%%%!%%%%!!%%!!%!%%%?%?%?!?!%%%?%%%!!?%%%!%!!%!%%%%%??!%!%%!!!%%?%?????!!%!%%%!%%!%!%%%!%%%!%!!?%!%%??%?%!%%?%%?%!%!%!%?%%%!%!%!%%%%?!%%%%?%%?%!??%%!!%%%?!%!!%!?%%%!%!%!%%!%?%!!%%%%??!%%%?!!!!%!%!!!%%%%%??%%%!!%??!%%?!%%!%!%?!?%?%!%!%%%%%%!%%%%%%%!!?!%%%?%%%?%!!%%%%%%%%!%%%!!%%!!%?%?!!%?%%%%?%%!%!!%%?%%%%%%%%%???%%!%!%!%%%%!%!%!%?!%?%!??!!%!?%%?!%%?!!!!!!??%%?%?%!%%!!?!!%%%%!?%%??!!%??!!%!%%%%%%?!??!%??!%%?!!%??!!%%%%!%?!%%?%!!!%!%%%%%!%???!?%!!%!%%!%%%%!!!!!%%?!?!%!%%%??%%%??%?!%%%%%?%!!%!%!%!%%%%%!%!%%?!%!!!%!%%%!!%%%%??%??%%%%%?!??%%?%?%!%%%!!?%%%%?%!%%%%!%%!%%?!%%!%!?!!%!??!!???%%%%!%?%%%?!!%?%%%%?%?%%!!%%!!!%%!%%?%!!%%!%!??%!%%!%??!%!!%%!!?%!!%?%?!%??%%%%?!%%?%?!%%%%%??%!??%%!%??%%%!%!%%!!!%%!%%%?%!!?%!!%%%%%%?%!%?%!%%!??%!?%%??%!?%%%!%%!%?!%%!%!?%%?%!%!!?!%?%!%?%?!?%?%!%%%?%!?!??%?%!%%!!!?%%%%?%!%!?!!%!%%?!%??!?!%?%%?!!%?%!!%%%%!%%!?%%%!%!!?!%%%!%!!%!?%%%%%%?!%%%!?%%%%%?!!%!%%%?%?!%!%!%!!!?%%%!?!??%!%!!?%%%%!%!!?%%?!!%!%%%!!%%%%!%%%!!%%!!%!%%!%%%%%?%!!?%!!%%!%%?%%%!!%!!!?!!??%%%%%!!%??!?%%%%!?%%?%!!%%?!%%?!%%%?%%%%!!%%%%%?%?%%!?!%%?%%!%%!!%%%%%?%%%%?!?%%!?%%!%!!!%!%%%?%%%%%%!!%?%%!%%%?!!!%%%%!?%%!!%%!%%!%%!!%?%!%!%%%%%%!%!%%?%%%!%%!%!%?%!!%!?%?%%!%!?!!!%?!%!!!%%%%%%?%!!?!%!?%!!%!%!?%%%?!!%%!?!%%?%%%!%%%%?%?%!!!?%%!?!%%!?%!!!%?!?%?!!%%%%?%??%!%%!!%!?%%%%%%!!%!?%%%%?%%%%%%%%%!!??!%%%%!!!?!??!%%%%%%%!!!%%%!%?!!%%?%!!%!?%%%%%!%!%%%!%%%%?!%%%!%!%%!?!!%%!!%%%%%%!?%!?%!%%!%??!?!?%!%%%%%!%%!%!!%!%!%%%?%!?%?!!%%!%%%%%%!!%%%%%%%%%%%%!%!!?%?%!%%%%!%%%%!?!%%%!%??!%%%%?!!!%!!%%%%!!!?!%?%%%!%!!%?!%!!%%!!?%%!%%?%!?!!%%%%!!!?!!??!?%%%??%?%%%!%%!!!%!%%!%%%?%!?%%!%!%!%!%?!%!%?!%?!%%%%%?!?!%%%?%%!?!!!!%%!%%%!!%%%?%%?%%%!%%%%?!%%%%?%%%!%!%?%?%!?!%%!!!!?%!%!%%?!%%?%?!%%%!!%!?!%%?%?%%!%?!!!!%%?%??%!%%%%%%!%%%%???%%%!?%?!%!?%?%%!%?%%%!!!!%!!%%!%%%?!?!!??!?!%!%%!!?%!!?%%?%!?%!%%%!%!%%!!%%?%??%!%%?%?%%%%!%%!??!%?!!!?%!!??%!!%!%???%%%!%%%??!?%!%%%??%%!%!!%%?%%%%?%!!%!%!?%?%%%!!%??%!!!%!%!%!!%!%%%%!!!?%%%!!%%%%?!??%!%?!%!!%??!?%%%?%%%%!?!?!!%%!??!%%%!!%?!%!%%%!!%%%%%%!?%%!%%%?!?%!%!??%!%%!?%%!%!?%%%%?%%!!??%%?%!?!%%%!!?!!!?!%!??!!%!??!%%%%%!!?!%%%?%!!??!?%!%%!%%!%!%%%%!!!%!?!?!??%!!%%%%!%?%!??%%!%!%!%?!!%%%!%!?%!!!%?%?%%%??!%%!%%!?%?%%%%%!%%%!!!%!%%%%%?%!?!?%!%%%%%!!?%!!%!%!%%%%%!!?%?!%!!%!%!%%%!%%%%!%%?%%?!?%%%?%%%%%%?%%%%!!!%%!%%?%%%%!?!!?%??%%%%!?!%!!!!!%?!!?%%!%%%%%%!%%%%!%!!!!!%%%!%%?%%%%?!?%!?%%!%?!?%%%!%%?!!?%!%%%%??%%!%%!?%%?!!!%%?%!!%?!?%!!!!%????!!?%!?%!%%!!%!?%%?%?!!%!!%%%%!%???%%!%??%%?%%!%%?!%?%%%?!%%?%%?%%%%%%%%%!?%%!%%%%!!%!!%!!??%?!!%%%%!?%!!%%%%%%%!%%%%?!!!!!!?!!%!?%%?!!?!!!!%?!%%!!%%%!%%?%!%%??%%%%%%!!%%!%%%!%%%%!!%?%%!%%%?%?!??%%??%%!!%%!!%%%%%%!!?%%%%%%%!%%!!%!!%%%!%!%%!%!%?!!%!%!%%%!%%!%!!!%!!%%?!%%!%!%%%!!%%%%%!%!%%%%%!%!!%%%%?!!?!!?%!!%!!!%%!?%%%!!%!??%%%?!%%%!!%%%!?!?%!%!!%%%!!!?!%%?!!!!%!%%%%%!!%%??%%?%!!!%%!?!?%%?%%?%!%!%%%!%%%??%%%%%!?%%%%?!%!%!!%%?%?!%!%!%%%%!!%%!%!%?%?%!%?!?%%%!%%!%%%%%%%!?%%!?%!%?%%!%%!?!%%!?!%%!%?%!!%%%!%?%?%%%%%??%%!?!%%%!%%!?!?%!%%%%?%??!!!!!!%!%!!%!%%%%%!!!%?%??%%%%?%?!%%?%%%%!!!%!%!!!!%?!!%?!!!%%!%%%!?!%%%?!%?!%?%%!?!%%?%!%%%!!!%%%!%%%!??%!!%!%?!%%?!%%!!%!?%!%?!%???%%!!?%%?!%!?%%%!%%!%%!%%%?%%?!??!%!!%!%%?!%%%%!!!!!?%%!%%%%%?%!!?%!%?!%!%!%%%%!%!!?%%%?%%!%%%!%?%!?%??!?%!!?!?!!%%!!!%%%%%!!!!!%%%?!%!!!%?!?!%%%!%%%!%%!!%?!!%%!%%%%%%%%?!!%?%!!%!%%!!%!!%%%!??%%?!%?%!%%%?!%%%!!%?!!%!%?%!!%%%%%!!%%!%!!!!%?%?%!??!!%!%%%?%%%%%!!%%%!!%!%%?%%?%%!%!!!!?%!!%%%!%%%!%%!%!!%%?!%?%!!%%??%%?%%%!%%?%!%!%%%?%%?!%!!?%!%%%%%!?%!%%%%!!!!?!!%%!%%!!%?%%%!??!!!!%!%%%%%?%%!%!?!??%!?!%%%!!%?%!%!?%%??!!%%%!?%%!%%%%!%%%!%!!?!!?%?%?%??!!!!!!!!!%%%%!%!?!%?%%%!%!%?!%%!%?%%!?%%!!?%?!%?%%!%%!?!%%!%?!!%!%?%?!!!%!%%!?%%!%%%?%%%!%??!?%!%%%%!!!%%!!%%%%%!%%!%%!!%!?!%%!%%%?%%%%%!!%!%%!!!!%!!%%%!!%%%!?!!?%%?!?%!!?%!%!%%!%!%%%!%!%%!%%%!?%%!!!?%!!%!%?%%!!?%?!%!%!?%?%?%!!?!%?!!%%!!%!%%%%%%%%?%%%%%%?%!!?%%?!%!?!%!!%?!%%?%?%%%%?%!?%!%!%%!!%%!%%!!%%%!!!!%%%!?%!%?%?%!%%?!%%%?%%%!?!%!%!?%??!%%!%%!%%!?%%!!%!%!!!!%%%%!%!%%?!!%!!%!?!??%!%?%%%%%!%?%!%%?!%!!?!?%?!%%!%%%%?%%!!!!!%%?%!%%%%%?%%%%??%!!?%!%%%?%!?%%%????%%?%%%!!%?%!%!?!?!%?!?!%%%%!%%!!%!!!%!%%?%%%%!%!%?%%!%!!!%%%%%%%%%%!%%%%?!!%%!?%??%%%%!%%%%%%!!!%?%!%%%%!%!!%!!%%%%!%%?%!!%%%?%!!%!?%%%?!%%%%?%%%%!?%!???%!%%%%%?%%!%%!?%%%%?%%%!%!?!%%%!?!!%?!!%%%%!%!!%%!?%%%!!!%!!%%!%!!%!%!%%%!%?!!%%!%%!!%?%%%%!%!!%%%%%%?%%%?!!%!!%??!!%%?!?%?%%!!%%!!?%?!%%%%?%!%!%%!%%%!!!!%!!!!%%%%%!!?%%%!!%%%!??!%!%%?%%%%!%%%!!%%%!?%%%%!%?!!!%!%%%%%%!%!%%%%?%?%?%%!%!?!??%?%!%%%%%%%%%?%%%!!%%!!!!!!%!!!?%!!!?!%%%%!%!%!%%??%!?%?!%%?%!%!!!%%%%%%?!!%%%%%!!%?%%!??%%!%?!!%!!!%?!!?%%%!%%!?%%%%%!%%%%!!%!%?%%%%!%?%%!%%%%%?!%?!%%?%!?%!?%?!?!!!!%%?%!?%!!%%%!!!?!%%%%!!%!!%%%?!!!%%!!%%?%!%%%!?%%%!!!%!%%%%!%%!%%%?!!?%!!?%??%!%!??%%!??%%?%%%%!??%?%%!%%??!%?%%%%!!!!!%%%?!%%%!?!%!!!!!!%?%?%%!%%%%%?!!%%%!!%!%%!%%%%!%!!!!!?!?!?!!%%??!?!%%%!%!!!%%?%%%%?%%!!%?%%!!!?!%!%!%%?%!%%!%!%%%%?!%!!?!!!!??%!%%%%?!!?%%!%%%!!!!!!%%%%%!!%?%%!?%?!?%%?%?%%%!!!!!?%%%!%%?!?!?!!?!%%%!!%!%!!%!%%?!%!!%%?!%!%!!%!?%%%!!!?%?%!?!%?%%?!?%%%%%?!%%%!!?!!%%%!%!%%!%??!!!%!%%%!?!!%%!!!%%%%!%%!?%%%!!%!%%!!?%!%%!!??%%%%%!!%??%%%!%!!%%!!?!%%!!%%!!%%!%?!?%?%%%%?!!%%!!!!?!!!??%!!%!!%%?!!!??!?%?%!!!!?!%!!%?!%??%!!%!%%????%??%!?%?%!%?%?!%%!%!%!%!!!%?%%!!%%!%%%%%!!%!%%%%!!%!!%%%!%%?%!!!?%!%%?%%%!%%%%!!!%%!%%%!!%%%?%%%%%%%%%%%%%!%%%?!%?%!??%?%??!%%!!%?%!%!?%%?!%!%%%!!!%?!?%%%!%?%!?%%?!%%%!!%%%!!!%%%!%?!%!%%%%%%?%%!%?%?%!%!%%!%!%!?!%%%?%?%!%!!!!%!!!?!?%?%!%!!%%!!??!!%?!!%%!%!!%%%%%%%!!!!%!!%%%!!!%%?%%%!%%!%%%!%%%%%!%!%!%?!%?%!!%!!%%%%%?!%%%!??%%!!?%?%?!!%%%%%!!%%%%%!%%!?!!%!%!%%%%%!%%!%%%!!!?%!!%%?!%%%?%!?%%!%?%%%%%%!!%%%%?!%!!!!%!!!%?!%%!%??%!?%!?%%%%%!%%!%%!%%%%%!%%%%?!?!!!!?!?%!!%!%%%?%!??%%!%!%?%%%!%?%%!%%%%%!%%!!!?!%!%?!%!%%!%!!%%%%%!%?%!%?!!%!%%%!!%%%%?%%%%?%%%!??%!%!!!!?%!%%?%%!%%%!?!!%%!!%%%!%%%!!!%%?%!%%%?%!%?%%%?%%%%%%!%!%%!%%%%!?!!%!!%?!!%?%%!%!?%%!!%%%%%??%%!%%!!%!%?%?%%?!%%%!%!%!!%%???%!%?%!?%%!%%%%%!!%%%%%!%%?%!!%!%%%%%!?%%%?%?%%%!%?%!?!!%!!%!?!!%!!?%?%%!%%!!?%?%!!%%%!%??%%!!!%!?!%%%%?!!!%??%%!%%!%%!%%!!?%%%!?%?%!%%%%%%?!%%%?!!?%%%%%%%!!!!%%!%!%%!%!!!!!%%!!%%%?%??%!%%%?!!%%!%!%%%!%!?!%%%?%!%?%%%!%%?%%?!!%!%!%!%!%%%!%%??%??%!!%!!!%%!!!%%%%%%?!!?!%%!%!!??%!?%%!%!%%?%?!%!?%!%?%%?!%%???!!%%!!%%?%%%?%%!%!!!%%%%!%%%?%!%??%??%%!?!!%%!!!%!!?!%%%%%%%?!%%%%%!?!!!%%%%%%!??!?!%%!!%%!%%%!?%?%%%!!%%%%!???%%%%!??!?!?%%!%%!!%!?%%!!%%!%?!%%?%?%?!?%%?!!?!?%%%!!%!%%%!!%?!!?%?!%!%%%%??%!%%%%%?!!??!!?%%%!!%%!%%?%!?!?%!%%!%!!!%?%!?%!%!%%!!!!%?!%%!!%!?!!%??%?!!?%!!%??%?!%?!%!!%%?%!??%%%%!%%%!?!%!!%!%!%%%%%!!??!!%%?!%%!%!!?%!?%!%%%%!?!%%%!?%!%???!%%?!%%!%!?%!%%!!%?%!!%??%%!!?!!!!%!!%?!%?!%?%!%%%!!%!%!?%??!%%%%!!!!!%!?%%%%%!%?%!!???%%%!%?!%%%%%%%%%?!%%%%%!!%!%??%%!!?%!!!%!%!%%%!%%?%%%%!%%%!%!%?%!%%%%?!%%%%!!%%!%%?!?!%!!%%%%%%??!%%%%!!!%!%%!???%!%%!%!!!%%?!?%%%%!?%!%!!!%??!?!%!!!%?!%!!%%%!!!?%?!%?%%%%%??%!%!%%!!%!%?%%!?%!%!?%!%%%!%%%%%?!?!%%%%%%%!??!!?%!!??%%%%%!%%!%!%?!!%%%!%%?%%%%!?!%!!!!%!!%!%?%!%!%%?%!%?%!!!!!!%?%%%%!!%%!?!?!%!%%%!%%!%%??!!%!?%!!%%!%%?%!%???!?!%%%?!%%%!!!!%?!??!%???%!?!%%!%%!!!%%!!?!%!!%!%!!%%%?!%%%!!%%?!!%%!%!%!!?%%%?!%?!?!!%?!!%?%%%!!%!!!!%%%%%??%%!%%!!?!??%%!!!%!!!?%!%!!!%!%?%%!!!%%%!%%!%!?%%!%!!%%!!!!!!%!!!!!%?%!?!?%!%%%!!?%%!%!?!!%!!!?!%??%!?!%!%!?!%%!!?!%%%?%!?%?%%%?%!%%!!%!?%%!%%%%%!%?!!?%%!?%%!%!%!?!!%!%%!!%!?%?%%?%!%%!%%!!?!%%!%?%%%?%%%!%!!!%???!%%!%?!%!%%!%!!%%%%!%%!!!!?%!!?%!!?%%!!%?%?%%!!%!%!%!??!%%?%!!!??!%%%!?%!?%!??%!%!%!%%%?%%%!!!!%%!%!%%%%%?!%!!??%!!?!??%??!%!!!?%%!?!?%!!%!?%!!%%%!?%?!?%%%%%%%%%!%%%!%%!!!!%%%%%!%?%%%?!%??%??%!!!?%!%%!!%?!%%??!%!!%%!%!%%%%!?%?!%??!%?%%!?%%%%%?%!%?%%?%!!%%%%?%%%%!!??%!%%???%!!%!%%!!!%!?%%!!%!!!%%%%!!%!!%%%!!%?%%?!%%?%%%!!?!%%!%!%%!%??!?!?!%!!%%%%??%%!%!%%%%%!!!!!!?%%??%%%%%%!%%!%%!?%%%?!%!!%!!%?!?%?!%!!?!%%%!!%!%%!!?!%%?%!%??!?%!%%%!%%!%!!!!!!!?%!%%%%!%?%%%%!%%??!!?%!%!!!%!%?!!%?%%!%%%?%!??%?%%?!%%??!!%%%!%?%%%%%?!%!?%!%?%%%!!%%%%!%%!%!%%%%!!%%!%?!%?%?%%?%%%%!?!?!?%?%%%%%!%%%%%%%%!%!%%!%?%%%!?%%!!!%%?%!%%!%%%%%?%%!%%?!%!!?%%%!!%!%!!!!!?%!!?%!?!?%!%%?%%??%%%%%%%%?%%!%%%!%%!?%%%%!?%?%%!%!%%!%?!%%%%?%%?!!!%%!%%%!!%!!!%%%!?%%!!!!!%%?%%%%!!%%%!?%?%?%!?%%?%?%%??%%!%%%!?!%!%?!%%%%%%%%%!!!!!%?%!?%?%%%?%%!%%!%%?%%!!??!?%%%%??%%%?%!!%%%!!%??%%!!%!!!!!!!!?%?%%%%%%?!%!%%!%!%%%!%??%!?%?%%%%%!%!%!!!?!%%%?!%?%%!%!%!%!%%?!%%%%%?!%%?!!%!%?!!!%!%%?!!%%!?!%%!!!%%%%%!!?%!%%%!%!?%?!?!%!?!!?%!!%!!%!!%%?%?%%!%%!?%%%?!!!?%!!%%%!?%%??%%!!!!??%%%!?%??%!%%!%%?%%?!?%!!%!%%!!%?!??%%!!??!%!??%%!!%%%!%%?%!!?!%!!!!!%%%?!?%!?!!!!%%%?%%%!!?%%!!%!?%!?!%!!%??%%%?%?!%%%!!%!%!!%!%%%!%?!!%%%%!!%!%?!%%!!%?%!%%!!%%%?!%!%%%!!!??%%!!%!%%%!%!%%%!!!%!%%?%%!%?%%??!!?!!%?%!?!!!%?%!!%%%?%%%??!%!%!!%%%!%%%%!%%%%%!%%!!%?!%!!!!%!!%%!!%%!%%!!%!%!!!!!%?%!%?%%?!?!%%%%%?!!??%%!%?%%%??%%?%!%%!%?%%%!%%!%??%%%%%%%!%?%?%%!%!%%%%%!%%%%!!%%%%%%??%%!%%!!%??%!!%%%%?!%%%%%!%!!!!%%%!%%%%?%%?%%%%!!!%%?!%%%%%%%!?%%?%%%%!!!%%!!!!%!?!!!!?!%%%?%%%%!%!%%!!!%?%%%??!%%%%%!?%%%%?!?!%%%%!%!%!%?%!%!%!!%%!?!%%%%%%%%!%%?!%%!%%%%%%!%%!%?%%??%%%%%!!%!!%%!!%%!%%%%%%%??!%%%!%!%??!%%???!!!!!?%!!?!%%!!%%%!!!%!!!!%%??%%!%%!!!%!?%!%%%%%!%!%!!?%%!?!!??%!!!%%!?!%??%%?%%!!?%%?%!%%!!?%?!!%%!%!??!%%?%%?!%%%%?%?%%%!%!%?%%?%!%!!!%!!%%%!?%%%!%?%!!%%%!!%%%!%%%%%%%%!!%!!?!%%%!!!%%!?%%%%%%!!!!!%!!%!%%!%!%%!?%%%?!!%%%%!?!!!%!!%!!!!%?%!%%%?%%%%%??!%?!%%?!!%%%!!%%!%!%%%%%!%%?%?!!%?%%!%!%!%%?%%%??%!!!??!?%!!%!%%%?!?!%%!?!?%%?%?!%%??!!%%?%%!%%!!%%%%%?%%!!?!%%%%%%%!!%%!?%%!%%!!?!!!?%%!!?!%??%!%%!%?!%%%?%%%%%?!%?%%%?%!?!!?%??%%!%%?!%%!!%%%!%?%!!%%%?!%?!%%%!?!%%%%?%?%!%%%%?%%?!!%!%%%%!?!%%%?!%%%!!%?%%%%?!%%%!!%!%!!!%%%%%!!%%?!%%%%!%?!!?!!%%?%%!%%%?!%!%%%!!!%%%?!?!!!!%!%!!%!%%!?!!%%%!!?!?%?%!!!!?!%%!!!%!%%%%!!??!!!%!%%%%!%!%!!%!%%%%!!!!??!!%%?%!%%!?%!?!%!%%?%%%%!?!%%%%!!?%!%%%%?!%%%!%%%%!!??%%!%!%%%!%?%%??%%%!?%!!%%%%%%?%!%!%!?%%%%!!%??%%!!%%%??!?%?!%%%%%?%%%%!?%%%!!!%%?%%%!!!!!!!%%%??%!???!%!%%%?!?!%%!%%!!%!!?%%%%!%%%!?!%!%%?%?%%%!??%%%%!?%!%!%!%!?%!!%%%%!!?%!%!!%%!%%%%%%?%?%%%!!!!!!%!%%!%%!%!!!%%!?%%%?!%!%!?%!!%!%!?%!!!%%%!%!!%%%!%?%!!%!!%!!%%%!?!%%!%!%!%%!%??%!!!%%!%!%!!%!!%!?%!?%%?!!?!!!!%%%%%!%%%%%%?%!%%%%%%%?%!%%??%?%!%%?%%!!!!!%%%?%%%%%!!%%!!?%??%%%!%!??%??%!%!!%!!!?%!%%%%%!!!!!%?!%%!%!!%!%%!!!!%%%?!%%%%%%?!!%%%%!%%%!%?%!%%?!%%?!%%!!!%%%%%!%%%%?%??%%!?%%??%%%!?!!!%%!?%%!?!%!?%%?%!!?!!%%?%!%??!!!%%?!!%!?!%?!!%!%%%?%?!!%%!%!!!%%%%%%!%%%%!%%%%!?!%!?%%%?%%!%!!?!???%%%!??%!!!%%%%!%%%!??%!!%!?!%%!%?%%%%??%%?!?%%%!%%%%%%!%%%!!%%%??%!%%!%%!!%?%%%%!%%!%!!%!!?!!!%%%%!!?%!%!%%%%!%%?%%!?%%!%!%%!%%!%!!?%!?%%%%%!!!!!%!%!%!%!%?%?!%%!!%%!%!!!%!%?%%%%%%?%%%%!%%!?!?!?%!!%%%%%%!%%%!%!??%!!%!!!%!%%!%%%%%!%%%%%!!!%?%!%!%!%?%%?!%%!%%!%!?%?%!%%%!%%!%%!!%!%!%!%%%%!?%!%%%?!%!!%?!?!!!!%%!?%!%%%?%!%!%%!%%%%!%?!!!%!%%%?%??%!!??!%%%!%%%?%!%%?%%!!%%??!!!%%!!%!?!%?%%%%!%?%!!?%?%?!?!!%%!?%%%!!%!%%!%!!!!%%%!%%!%%?!?!%?!%!?%%!%%%?%!!%%%???%!%??!!%!%%%%%!!%?!?%%?%!%%?%%!!??!!%%!!!!!?%%%!!!!!!!!!%%?!%%?%%!?!!!?!!%?%%%!%%%!!!??!%!!%!!!%!%!!??%%%!%%%!%?%!!%%!%!%!%!??%%%!!%%!%%?!%!?!!!!!?!%!%%%!%?!%!%!%!!!!%!%%%%!!!!!%%%??%%?%!%%!!!???!%?%!%%%%%!%%!?%%%!%!?!%%%%%!!%?!!%!%!%%%%%!!%%%%%!%?!%!?%%!?%?%!%%%!%!?%?%!%%?!%%%!%!%!%%%!?!%!%!%%%%!%?!%?%%%!!%%%!%!!%?!!!!!!%!?%%!%!!%%!?!!%!!??!!%%?%!!?!?%%%?!%%??%!!!%!%%%%?%!%%%%!!%%!!!!!!%%?%%!!!%!!??!!!%!%%%!%%!!%%?%?%?%!?!%?%%??%!?%%%!%%%?%%!!?%!%%!%%?!%?%%%%?!??%%!%!%%%!%?%!?%%%%!!%!%!?%!!?!%%!%!%%%?!%%%!??!%%!!!?!%%?%!!!!????%!%!%%%%!%!%%?%%?%%%!%!!!%%%%!!%%%!!!!%%!%%%!%%%%!%%?%%!%%%%!?%%!%%!%%%%?%%%%!%%?%%!!?!??%!%%%%!%!!!!%!%%%%??%%!%?????!!!?%!?%!!%!?%%%%!!!%%%!!%%%%?%%%?%!!%!?%!?%!?%!?%?%?!%!!?!???!?%!?%%%%!%!?!%?%%!!%%?%!%%%!!??%%%?%%!%%!%!%%%??%%!%%!%%%!%!%!%!%%?%!%??!!?%%%%!%%!%??!!!!!!%%%%%!%!%%%!!%%%%%%%!!!!!%%%%?!?%%%!!%%%%!!%%!!!%?%%%%%%??%%%%!!!!!%%?!%!!!%%%%%%%!%?%%!%%%!!?%!%%?%!?!!%!%!?!!!%%%??%%%!%%%!!%%%%%%??%!??%%%??%??%%%!%?%!?%?!%%?!!?%%!!!?%%%%%%!!!%%%!!%!!!!!!?!%!%!%!!%%?%!%%!??!%!%%!%?!%!%%!?%%!%?!!!%?%!!!%%!%%%%?!%?%%%!!!?!?!%%!%!!!%%!%?%!!%%%%!?%?!%!!!!!?%%%%!%!!?%!!%%%?%%??%%%!%%%%%!!!%!!%!?!%!!%!!!!?!%?!?!%%???%!%!%!!!%!%!?!!!%!!?!?!!!%?%?!%%%%!%%%%%%%!!%!%!%??!!?!!?%%%%!%%%?%%?%%%%%%%%!!!%%%!%!%%%%!%%!!!%?!%!?!!!%%!%%?%!!!%%%%%!!?%?%%%?%!%%%%%!!%%%%%?%%%%!!?%!!??!%?!!%%?%!%?!!%%!!%%%!%?%!%!%%?%%%%!!%!%%!!%?%%%%!%%!%%!%%%!?!?%%!%%!!!!%%%%!!!?%%%!!?!!%!%%?%%%%%!%!%%%%?%%%!!!?%%%?!!%!!%%%!%!!!?!??%%?!%?%?!!?%!%!%%?!%%%!%!%%%!%!%?!%!!%?!%?!!%%%%%?%?!!%?%%?%!%??%?!%%?%!%!%%!%%?%???!!?!%!?%%%!?!!%!!%!?%!!%?!!??!?%!?%%!!%%!%!%%%%!!%%%%%!%%%?!?%?!%%!%!!%%%%%%?%!%%!??%!%!?!??%?!%!%?!?%%!?!%!!!%%%%?%%%%!%%%?%?%!%%%%%%!?!%!!!%%%!!!%!?!!%%%?!%!?%%!%!??%!!%!%?!!!!!!%!!%%?%?%!%!%%%??!%%???%?%!!%%!?%%!!%%??!?%%??!!?!%%!%!?%%%!%?%%!%!!!!%!%!?%%??%!!!?%%!%!?%%!!%%%%!%%??!!%%!%!!!???%%!?%%?%!%%!?%%%!%!!!%%%%?????%%%??%?!?%!!%!?!%%!%%!%!%!%%?!%!!%%!%!%?%%?!%%%!??!%???%!!??%%!%%!!!%!%!%??%!!!!%?%?%%?%?%%!%%%!%%!?%!%?!%!%?!%%!%%%%%%%%%%!!?%%%?%%%%!?!%%?%?%%!%?%?%%%!%?%%!%%%%!%!%!!%!?%!%?%%%%%!?%?%?!%%%!%!%%!!!%!!%!!!!%%%%!!%%?%%?%!%%%%%%!??%!%?!%%!!%?%%?%%!%!!%!%%!!!!?!%!%%%!!%?%!!!!!!!?%!?%%%?%!!?%%%!%%!%%!%%%%%!!%?!%%%!%%%%!%%%%?!!?%??%%!!%!!%%%!%!?%%?%%%!!?%!?!%%?!?!%%!!%%%!%%%%!%%%!!!%?!?%!%%!%%%?%%!!?%%??!%%%!%%!?%%!%?%%!%%!%!!%!!!?%%!!%%%%?%?%!%??%?!%!!!%%!?!%%%!!?%%%%%?%!%%!%%?!%%%%%!??!%%%!%!%!!?!%%?!!!%%?!%!?%!!!?%%!??!!%?%%%!%%!%?!%!%%?!%%%!!%!?%!%!?!!?!!%!!%!%!%!?!!!%%!%!%!%!%!%!?%?%!%%%%%%%%%%%%%%?!!!!%!%%%?%?%!%!%!%%!!!?!?%%???!%?%!%!%%%%%%!!?%!%!%???%%?%!?!%!!!%%!%%%!%%%?%%%%%%%!%%%!!?!?%%%!%%%?%%%%%%?%!%%??!%%%%!?%%!!%%%??!%%?%?%!!?%!%%%?%%!!%!%%%%!!?!!%%!!!%!%%%!!?!!!!%??%%%%!!!%%!!%!!%?!%!!???%?!?!%%!!!!!!%%%!!!%%%%%??!%!?!%%%?%!!!!%!%%%%%!%?%??!!?!%??%%!%%!%!!%!!!%!!%!!?!!!!%%%?%%%%%!?%%!%?%!%!?!!???%?!%?%?!?%%!%%%%?!??%!?!%?!!%%%%%!!%%%?%%%%!%!%!%!!!??%!!!?!%??%%%%%%?%?!%%%%%??!%??%!%!?%%%%%?%!%!?%%!%!!?!?%?%?%%%!%?!?!%%!%!!!!%%!%%%%%%?%!%!??%!%!?%!%!%%%%!!%%%%!%%%%!%%%!%?!%%%!%!%??!!%!%%?!!%!%?!!?%%!!!%%%!!%!%!%!%%?!%!!??!!!!%?%%!%!!?!%%%!%??%%!%!%%?!!%!%!%!%!!!?!!%%%!?%%%%!%!?!%?%%%!!!%%!%!?%!%!%%%!%%%%?%?%!!%%%!%%%?%?%!??%%?%?%%?%%%%!?%!%?!!%?!%%%?!??!%%!%!%%!%%%%%!???%%!%%%%!%%%?%%%!!!%??!%%!!%%%%?%%??!!%%%!!!!%???%!%??%%!%!!!%%!!%%%!%%%%%?!!!!%%?!%%%%!%?%?%??%%%%%%!%%?!!!!!?%!%%%%!!!%!%%%?!!!%%%%!!%%%!%!%%!%%%!?!%%%%%%%!%%%!%!%%%?%%%!%%%?!%%!%%%!!%%?%%%%%%%!%%%!?!%!!%!%%!!!%!!??%?!!?!!!%%%!%%%?%?%?!!%?%?!!!%!%%!%%%%!%%!%?%%%%!!!?%%!%?%%%!%%?!%?%%%%%%!!!%%%!%%!%?%!%%%%%?%!%!%!%%%!%%!!%?!%?%%!%!%%%!!%%??%%???%%%!!%%!%!%%?!!%?%?%!!?%%%%!!%%%!%%?%!%%?!!%!??%!???!%!%%%!%!%!!!?%%%%%%%%?%!%%??%%!!%%?!?!%%%!!!?%%%!!!%%!%??%!!%%?%!%%!%?!!!!%!%%????%!???%?%!?%!%?!!!%%!%?%!?%?%%%?!%!%!%?!?%%%%%%%%%%%!!!%%%%?%?%%!%%!!%!%!!!!!%%%%%%!%%%%%?%%!!!!%!!!%%%!%??%%!?%?%?%!%%?%!%!!!!%%%?%!%%!%!%%%%!!%??!%!%%!%??%%!%%%%%%%%??%?%%%%%%%!%???%?%?%%%?!!!%%!!%?%%%%%!!%!?!!?%?%%%%?!%!%%?%%%%?!?!??%!??%%?!?!%!%!?!!%!!%%!?%%%!!%%!!!%!!%%??!!!!%%%%?!%%?%%!!%!!%!!!!%%%%?%%!%!%!%!%%!!%%%%!!%?%!%?!!%%%%!%%??!%!?!!!!?!%!!%%!%%%%!?%%!%%%%%?!%%%!!%??%%%%!!%%%%%%!?%%%?%!!%%%%!%??!%%%?!?!%%%%%?%%!%?%%%?%!%%%!?%!!%%%%%!!%%%!%%%%!?%%%%!!%%!!!%%%%%%?%!%!!!%%?%??!?!%%!%!!!%!!%?%!!!!%!%%%%!%!%%?%!%%!%%%?%?!?%%!!?!?%%!%%!%%!%?%%?%?%%%%%%%!!%%!!%!%%%%%!!?!%!%%!!%!%!%?%?!%%!%%!?!!%?%!!%%?!%%%?!%!!?%%!%%%!?!%%?!%?%%???!!?%?!%%%!!%%!?%%!%?%%?%%%%!!%%%%%?%%??!?%!%%??%!%!%??!%!%!%%%%%?!%?!!!?%%%?%?!%!!%!%%%!?!%%!%%!!%%!!%!%%!%!%!%%%?!?%!%!!!%!%%!!!%%%?%?!%!%%%%!!%?%%%%!!!%?!%%!%!%%!%%!?%%%!!%!!!%%%%%%!%%!??%%%!!%!!?%!!!%%%%%!%%?!%%!%%!%?%?!%%?!!%%!?%%?%%%%!%!?%%!?%%%?%%!%%%!%!!%!%%%!%%?%!!%%%!?%%!!!%%!%%??%%%!%?%?%!?%!%!%%%!!!!!!%!%!!!%???%!%?%!%%%%%%%!%%!%%!%%!!%%%%%%!!%!?!%!?%?%%?!!%%%%%?!!%!??%%%!!%%%!!?%!%!%%!%?!%%%%%%%?%!!!%!!!%!%%%%%%!?!%?%%%?!%%!%%%%%%%%%%!%%%!%??%!%!?!!%!%!?%!%?%?%%?%!%%!%%!%%%%?%%??%?%%!?%%?%?%%%%%%?%%%!%!%%?!%!%?%!!!??%%%%?%!!%!%%!!%%%%%%!???!!%!!%???!!!!!%???%%?!!!!?%??%%%?!%%!?%?%%%%!%?!%!!!%!%?!%%!%!?%?%%!%%!?%%%!%???%?!!%%%!%!%?%%%%%%?!%%%!!%!%?%%%%!%%!!%%!?%%?!!?!%!!!?!??!!%%%??%!!??!%!!%%%%%!!?!?!%?!%%%!!%!!%!%?%!%%%%!!!%%%!?!!!%??%%?!?%!!%!!%%%%%!%%%!!%%?!%%!%%%!%?%!?!!%%!!%%!%%%%!!!%!%%%%%%%?%%?!?%???%%%%%?!!%?!!!%%!%%%%%!!%%!%%%!?%%!%!!%%??%?!!!%!%%!%%!!%!?!%%%%%%???!%!?%?!%%?!%!???%!%%%%%!%!%%%!%!%%?!%?!!%?%%!%!!!!%%%%?!%%?!!!!!%%%!?!?!%????!?%%!%??!!!%%%%!%!%%%!%%!!%!!!%%%%%%%!!!?%%!%%%!!!!%%?%!?!!%!%%%%!%%%?!%??%!%??!?%%%??%%%%%%??%!?!?!?!%?!%???!!%%!!!%%%%%!!?%!!%??%?!!!?!%%?%%?%!!?%!%!%!!%!%%%%%%?%%%??%%?!%?%!!%?!%?!%?%??%%?%%%!?!%%%%!%%!!!%%!%?!??%%!!%!%!??!%%!%!!!?%?%!%%%%!!!%%!?%!%%%%%!??%??!!%%!%%!%?!%!%!%%%%!%!!%%!%!%%%%%?%%%%?%%!!!%%!!%!?!%!%%?!%%%!%%!!%!%!%!%?%%!%!?!%!%?%?!?%%%%%!%!%%!%?%?!!!!!%%%!!%%?!??%!!%%?!%!%?!?%?%%%?%?%!%!%!?%%!!!?%!!!%!!!%!!%%%!!??!%%?!!!!!!%!%?!%%%%??%!%%!!!%!%%%!!%?!%%%?!%%!?!?%%%!%%%%%!!%?%%?%%%?!!%%?!%!%%%?!!!%!%%%%%%!%!?!%!%%%?!?!?%?%%%%%%?%??%%%??%%!!%%!!!!!%%%??%%!!%?%!!!!%%?!!%%!%?%%%?%%!??%%???%%?%?%!!%!?!%?%??%%!%!?%%?%%%!!!!%?!%???%?%%%%!!?!%%!%?!%?!!?%?%%%%%%%%%!%%%%!!%%%%!!%?%%!??%%?!%%%??%%!!%?!!%!!!!%!%!?!!!%%%!%!?%?%%!%!!%!!!%%!!?!!!!%!%!?!%!!%!?%%%!!!%%%!%!%!!!%%!%%!?!!%!%!%!!%!%%%%%%%%?%!%%%!%!%%!!%%?!!!%%%!%!!!%%!%%?%%!%%%%?%!%!%?!?????%%%%%%!!%!%!%!%?!%!%!!?%%!%!?%%!%!!!%%%%!?%%%%%?%%%%!%%!%?!?%!%%%?%%%?%?%!???!!%?!?%%!!%%?!!!!%!?!?%%%!%%%%%?!%!!%!!%%%?%%!%!%?%!!!!??%!!?%%!!!!?%%%!%%?%!!??%?%%!!%?!?!!%!!!%%%%%%??!%!%%!?!!%%!?!%!!%%?%%!?!!%%?%%!?%%?%!%!%!??%?%!??%%%??!!%%%??%?%?!!%%%%!!%?%!?!?!!!??%%!?%?%!%!!%!%%!%%%%%!%!!??%?%?!%%!!??%%%%%%!%!%%%!??%%!!!?!?!?!???!%%%%%%%?!%!!%!!%%%%!!!%!%%%!!!!!%%%%!!?%!%!%!%%%!?%%%!%?%!%%%%%%!!!%%%!?%!!?!%%%!%%!?%%%?%%?!?!!%%%!?%?%??!%!!!%%%%!!!%!%%?!?!%%%!!!%%%%!%%%????%%!%%%!??%?%%%%%?!%%!%!%%%%!!!!%%!?!%?%%%%%!!!%?!?!%%!%%!!!%!!%%%!%!!%%!%!!%%%?%??%%%%%%%%!?%%??%?!%!%!!%%?%%?!%?%!!%?%!!%?%?!%!!!!%!!%?!%?!!%???%%!!%%%!?%%%%!%%!%%?%?%%%!%%%%%??%%%%%%?!!%%!!!%!!%!%!?%%?!!%%?%??!%??%!%!%!!!!%%!%!!?%!!!%!%!!?%?%!%%?%!?%??!%%?!%?%%%%%%!!%%!%%%!!??!!%%!!!%?%!%?%?%%%%%!%%?!?!!%?!%%!??%%?%!%%%%%%%!%%?!%?%?!%%?!%%?%!!!!%%!%?%!?%%?%%%!%%!!%%?%%!?%!%%%?%%!%?!%!?%%%%%%%!!%%!%%%!!%!%?!!%!!??%?!!!%%%?%!%!%?!%%%!%%!!?%!!%%%!?%%%%!%!%!!%%?%%%!!!%?%!%?%%%%%%%?!%%%%%%!%%!!%%!!!!?%!%%%!!%!%%%%%%!%?!%%!%!??%!%%%!!%%%!%!!%?!!%!!%%%?%%%%!%%!!%%%%%?!!!!!%%%!%%%???%%?%%!%%!!%!%%%%%%%%!!%!%!%??%%%?%%?!?!!!!!!%?%!!%?%!%!%!!?!%%?!%%!!%%%!!%?!%%%%?!!!%%?!%%%?%!%%%%!!?%!%!%%%?%%%!?%?!%!??%!%%%%%%!%%?!??%!%!%%!%!%??%???%%%%!%!????%!%!?%%?%!%?%%?!%%%!%!!%!?%%!!!!%!!%%%%!%%???%!%??!%%!!%%%?!!!??%%%%%%%%%!%?%%!!%!?%!!%!%%%%?%%?%%?!%%!%?!!?!!%!!%!%%!%?%%%??%%%%%?%%!%??%??%!%!%?%!!%!!%?!?%!%?%%!%!?%%%%?%%%??!%%!%!?%%!%%?%!%%?%!%!%!%!%?!%%!!%%%%%!%%!%??%%%!%!%!!%%%!%%?!%%%%%!!%%%!???%!?%%!%??%!?%!%%!%%!%%?%%?%%%?%!!?!!!!?%%%!%!!%?!%?!!!%%%!?!!!!?%%%%%!!!%%%%%%%!!!????%%%?%%%%!%!!%!%!?%!%?!!%???%%%!?!%%%!%%%!!%%%!%?!%%?%!!%%%%!!?%%%%%?!%%!%%%!!!!%!??%?%%?%?!%%%%!%!!!?!%!!!!%?!!?!!?%!%?%!%%!%%?!!%!%%%%%%??%?%%%?%%%%!!%%%%?%%%%%?%%!%!%%%!%%%!!%%!%%%%%?!%%?%?%!!%%?%%!%%!%??%%!!!%?!??%%%????%!!%?!%?!?%%%%!%!!%%!%?!!!!?!%%%!!%%?!%%?%%!!??%!%%!??!!%%!%%%%%?%!!%%!%!?%%!!%%%%!?%%!%%!!!??%%?%%!%%!!%%?%%%!?%%%%!!%%?!%%%!%%??%%%%!!%%%!?%%%?%!!%?!%%!%???%?%!%?!!%!%%%!%!%%%%%%!?!%??%%?!%%%?%!!?!%!!%!%!?!%!%%!%??%!!!?!%!?%!%%%?!%%%%%%%%?!%!!?!!!%%!?%!%!%%!%?%!%!?%?!!??%%%%!%!%?%??%!!%%??%%%%!%%?%%!%%?!!?%!?!!%%!%?!??!%!!%?%!!%!!!!%!!%!?!%??%%!%?!%?%%%!!%??%!!%!!%%!!%!!!%%%%!?%!!%%?%%%!%!!!%!!?%!???%!%!%!?!%!?!!%?%!%!%?%%%%%%%%%!%!%%!%!%?%%!?%%!?%!!%!%!!%?%?!!%%%%%%!%%%?%!%!%!%%!!%?%!%%!?!!!!!?%%?%?%??%?%!%%!?%%!!%!!%%?!!?%!%%%%%%!%?%%%!%?%%???!!!!?!?%%%!!%%%?%%?!!%!?%%%!%%?%%%%!?%%!!?%%%%?!%%!!!!!!%!%!%%!%%!!%??%!%??%%%%%%!%!%?%%!!%%?!%%!%!%%??%?%!%%%?!!%?!%!!!%%!%%%%!!%!?!%%?!%!%%!!%%!%%?!%%%!%%%?%%%!%%!!%???!%!?%%!?%?!%!!?%!!!%%%?%??!!%%%%!%%%!%!?!%!%!%?%%!%??%!!?%%%%!%%%?!%!%%%%%!%%?%!?%!!?!?!%?%!%?%%!%%?%%%!?!?%%%%%!%%!!!?!!!%?%%%%%!%%%?%!%%%!%!!%?%%?%!?%!!%!!!?%%?!!%%%?%%!%?%?!%%!%!%%%?%!!?%%%%%%%%%!?%%%!%%!!%!%?%%??!??%%!?%!%!%%%!%%?%%??%?!?%?!%%??!!?%?%?%!%%%%%%!%%!?%%!%%%?%%%%?%%!?%?%!!!%?%%%!%?!!!%%%!!%%%%%%?!!%%?%%!!!!%%%%%%%%!%?!%%?%?%!!!%!!!?%!!??%%!%?%!!%!!%%?!%?%%?%%!%!!!!%%%?%?%%%!!%%?!%!%%!??!%!!%%?%%%!%!!%!!!%!%!%?!%!?%%%!?!%%?%?!?!!%%%%!%%%?%%%!!%%%!%?!%%%??%?%??%!!!%%?!%!%!!!?%!!%!%??!%?%%%%!%%?%%%%%%%%!%%%!%%%%!!!!%!!?!!%!%?!!?!%%?%%%?!!%!!%%!!%%%%??!%!%!?!%%%!!!%???%%!%!%!%%%?%%!%%%?!!%%%%%%%!?%!?%!%!?!%%%!%%!%?%%%%?!!%%?%%!%!%!%!%!!!!!!!%!?!%!%!%%!%?%%%!!!!%!%%!!%?!!!!!%?!!?!%!?!%%!!%%%%!%!%!?!?!!!%%!!%%%!!!%%%!%%!?!?%%%%?!%%?%??!!%%%!%%%%%?%!?%!%!%%%!%!%?!?!!!??%%%%%%!%%?%%!!!%%%!%%??!%%?%!%!!%!!!?%%!?%!!?!!?%!!!!%%!%!!!%%?!%%%%!!%!%!%!%?%%%?!%%%!!%%%!?!??!?!!%?%%!!!%??!!!%%%%!!%!%%!%!%?!%%?!%%!!%%!!!%!%%%%!%!%%!!%!?%!!%!??!%!%%%!!%!%%%%!!!!?!%%?!!!!!%!!!?%%%!%%%!%%%?%%!!%%%%?%%%%?%%%%!!!!%?%!?%%%%%%%%%%!!!%%!!%%!!??!%%!%!!?!!%%%!%!!!%!%!%!!%!%?!!%%!%!%%?%!!%%%%!!!!%%??%%%%%%!%%%%!?!!?!%%%?!!?%%%%%??%?!%!??!!%!%%!%!%%%%%%%%%!?%%!%%%%!!!!?!!!!?!!%?%%?!!?!%%%!%!!!%?%?!!!!?%%!!?%??%!%!%!!!%%%%%?%%%%??!%%!!!%??%%!%!%%?!%%!%%?%%%%!%!!%%%!?%%%%%!%%%%!%%!%!%!%!!%%%%%?%!?%%%!%%!%%%%%%%%!!%?%!?!%%!%%%!!%%!%%!?%%%%?!!?%%%%%?%!!%!%!?%%!?%!%!%!%!%%%!%!%%!%%%!!!!!%%!%??%%!%!%%%%!%%!!!??%%!!!?%?!?%!!!!%%%%?%!!%?%%?%%!!??%!%%%!%%%%?!%%%%!!%%%!?%??!!!%!%!?!%?%?%%!!?%???%%%?%!%%??%%?%!!?%%%!!!%??!!%!%%!??%?!%?%!%?%!!%%?!%%!!%!%%%%%%%%%?!!!?%%%!?%!!%%%!??%%?%%%%!%%!!!!%%!!!%?!%!!?!!!!%%%!!%!%!%!%%%%%%!?%%%%!%!%%!%!!!?%!!!%%!%!!%%%!!%%%!!%%%?!!!%%%?%%%!%!!!%%!!%%%%?%!!?%%?%%%%!%%?%!?%%%!%%!%!!%%%%%!!?!?%!%?!!!!%%!%%%%?%%!%%?%?%!%%!%?!%%%!?%!%?%!%!!%%%??%%%!%%%%%%%!%?%!!?!%??%%%%%!%!%?%!!%!%?%%%%!%!%%%%%%%%?!%%%%!?%!%!%!%%%%!!?%%?!?%!%%%%%%!%%?%!%%%%%??%%!%%%%!!%%%%?!!!!%%!??%!?%!%%%%%%??%?!?%!!!??%%!!%?%!%!????!%!%%!!?%%%%%??!%!?!??!%?!!%%?%!%%!%!%%%!!!!%%%!%%??%!!!%?%!!!!%!%%%?!?!%%?!%%??%?%?%!!%%%!!!!%%!!%!%?!%%?%!!?%!%%%%%%%???%%?!%!!%%%??%%%%%%%??%?!%%%%%%!!%%%%!!%%%%%?!%!!%%!?!!?!%%?%!?!%%!?!%%!??%%?%%%%%!%?%??%%%%%!!??%%%!%!%%%??!%!%%%%!%!%?!!%%!?%!?%%%%%%%?!%!%!?%?!!%%%??%?!!?%%%%?!%%%%%%!%%%!%%??!%%??!!!%%!!%%?%%?!%!!%%?!!%?!%%%%??%%?!!!!%!%%!!%%%%%!%!%!%%?%%%??%???!%%!%%%!!%??!!!%?%?%%!!%%?!!%??!%%!%!%!?%%?%!%%?%%!%???%!%%%!?%!%%!%%?%%!!%%%!%??%?!??%%!%%!!!!%!%%%!%%%%!%!!%%!!%??%?%%?%!?%%!!%%??!!%!!!%?%?%!!%%!!!%!!%%?!?!!%%%%%?%%!%%%!%%%!?%?%%%%!!??!%%?%%%%?%?%!%%!%?%!%%%?!!?%%%%%!!??%%%!%%!!?%??%?%%%!%%%!%!%%%%%%%%%%%%!%%%%%!%?%%%%%!%%%!?!%!!%%%%%%?%??%%%?!!%?%!%%?%%%%%!%!%?%!?%%?!%%%%%%!!%%?%!%!%%!!%%??%?%%%?%!%%%!!?%%???%!!%!!!!%%%%%!!!%?%!!!!??!!%!!?%%%%%!%%%?%!!?%%?%%%!%?%?%%%%??!!!!%!%?!%%%%!%%%!?%%!?%!!%%%%%%%!%%?!%%%%??%!!!!%!!%?!%%%%%?%%%!?!!%%%%%??%%!%!%!!!%!%%??%???%!%!???%??!!?%!%!?%?%%!%!!%%?%?!!%%??%%!%%%%%!?%%%!%%%!!%!%!?%?%%!!%%?%%%!%?%!%%!?!!%!?%%??%!???!%?%%!%!%%?!%!!%!%%%%%%!!?%%%%%%?!%!?%?%!%%%?%!!%%!!!%!!!!?%%%%%%!?!!%?!%%!!%%%?%%%!%%??%%?!%%%!%%%?%?%!%?%!%?!?%!!!%!!?!%?!!!!?%!!!%%%!!%%%!%%!%%?%%!%!%!!%%%!??!%!%?!!%%?!!%%%%?%!%??%%%!%!%%%!%!%?%%%!?!!?%%!%?!!!!%!%%%%!%??%!!!%?%%?!?!!%%%%%!!!%%!!%%!?%%%!!%?!!%%??%%?!%%%!%%%%%%%!%!%!%!!!%!%!!!!%?%?%?%!%!!?%%%%%!%!%%!!%??%%!%%!??%!%!!%%!%%%!%%%!?!!%?%%!%%?%!!%!!%??%%?%%%?%!?%%%!!!!!!?!%?!%%!?!%%%!%%%!?%?!?!%!!!?%!%?%!%%!%!%!!!?!!%%%!!%%!??!%%%!%%!!!%%?%?%%%%%%%!!%%??%%%%!!!????%!%%%%%!%%!%!%%%!?%%%%!?!%%%?%%??%!?!!%?%%%?!%!?!%!%!%%!%%%%??%!%?%%!%?!%%!%!!%%%%%%!?%%%!%%%%?!??!!!%%%!!??%%%?%%?!%%%!%%%!?%%%!%%%!!%!%%??%!!!!%?%%%%%?!%%??%??!!!?%%%!!?%?!%%!!%%!%%!%%%%%%%%?%?!%%%%%%?%?%!%?%%%%!!!%?%!%??!%%!%!%%??%!%!?%%%%?!!%%%%?%%%?%?%%?%!!!%%!%%!%!%!?%!!!%!!%%%!%%%%%%!!!%!?!%%!!%!%!%?!%%%%%??%?!!?!%%%!%%%?%%!%%!?%%%%%!?!%?%????!!%!!%!%%?!!%!!!%!!!%%!!?%?!%???!??!%!!!!%%!%!%!%?%%?!%!!%!!%!%%!!!!?!%?!!%!!%!%!!%%%%!!%!%!%%%%%?%!?%%%!!%!%!?%%!%!%%%!?!!??%?!%%%!%?%%!??%%%%!%!%%%%%!!?!%%%!%%%!!!%%%!%!!!!!?%%!!!!?%??!!???!%!%!%?%%%?%!!????%%%?!%%?!%%?%%%%?%%?%?%%!???%!%!%%!%!!%%%%!!%!!%%!%?%!%??%%?%%???!??%%?%!?%%!%?!!!%%!?%%%!%%%%%!%!!%%!%?!%!%!%%!%?!!??!%%!!??%!%!!%%!%!!!%!%!!?%%!%%%?%%!%%!%%%!?!!!%%!!?%!%%%%!!%%!!!%%%%!!!%%%?!!%%!%%!???!%%%%%%%%%!!!%!%!!??%!%%%!!??%%%%%!%%%?!!!%%?!%%!%%!!!%?!!!%%!!%%%%!!?%!%%%!???!%?!!?%!%%??%%%%?!%%?%!%%?!%!!?%%!%!?%!?!!!!?%!!!%%!%%%!%%!%??%!%?!%!??!?!?%!%%?!%?%!!!%%%!?!!%%?!?%??%?!%!%??%%%%%??%%%%!!!!%!%%!?%!%%%%%!?%?!%!?!?%!!!%?%%!!!!%!%%!??!%%%%!%!%%%?!!%!%%%%?%!!%!%%%!%!??%?%!!!%!%!?%%%%?%%!!!!!!!%%%!%!?!%!?%%!?%?!%%!%!!?%%%%?!%%%??!!!%??%%??%!%%?!%%%?%%%!?%%%%!%%%!!!???!!!%%%!%?%%?!%%%!!!!?!%%!%??!%!?%%%!%?%!!%!%%%?%?!!%%%%%%%%?!%%!%?!%%%?%??%?%!?!?%??!%!%!%!%??%!!!%%%?%!??!!!?!!%%!%%%!!%?%%%!%%%%!!%?!%%!!%?%%!?!!!%!!!%%?%!%%!%!%%!%?!%%%%!%%%%!%!!?%!!!!%??%%%?!%%!!?!!%%%%?%!%!%%?!?!%!%!%%%%?!!??%%!%!!!?%%!%!%%??%!!?%%%%%!?!?!!%%%!%%%%%%%%%!%%!%%%%%%%%!!?!%%%%%!%!%%%%%%???!!%%%?%!!!!?!%!%%%%%??%!?%!!%!%%!!!??%!?!?!!%%!?%!%!!%?!%!%?%?!%%!!??%??%!!%!!!%!%!!%%%%!%?!!%!!%%!!?!%!%%%?%%!%?%%!%?%?%%%??%%!%!!%!%%%%!%%%%%%%%%!%%!%!%%%%?%%!%!!!%!%%!%%%%%%%!%%?%%?!%?%!!!%?%!!%%?%!%%?!%%!!?%!?%%!!%%!!?%!!?%%??%!!%%?!%%%!!!?!%%?!%%!%%!%!!%%!!??!%%!!!%%%%%%!%!!?%%!!?%%%%%!%!%%%?%%%%%%%!?%!%%?!%!!%%!!!!%%%%%!%?!%!%%%%%%!!%%%!!%%%%!!!%%%%%%%?%%!%%?%???%%!!?!%!%%?!!!!?%%?!%%!%%%%%%%?%!!?%%%?%%!!%%?%%%%?%%%!%%!!?%!%?%%!!!!%?%%!!!%!?%?%%%!%!!%%?!%%%!%!%%%!!%??!!%?%!!!%!%%%?!?%?%%%?!%!%!!!!%!%%!!%%%%??%???%%%!?!?!%!!!%!!!!%!%!!%!%!%%%?%%!!%!!!%%?%!??%!%?!%%!?%%!%!!%?!!!%!!!?%%%%%%!%!%%!!%??%?!%!%?%!%%!%%%%%%!!%!!%?%?%!%%%?!%%!!%%%!?%!%%??%!??!%%%%%%!%?!%!%?%%%!%%%%%%!!%!!!!%?!%%!%!!!%!!%%%?%%!!!!%??%?!%!!%%%%?%%!!%?%?%?%%%????%%%!%!!?!%%%!?%!?%!!%!%!%??!!%%!!%!%%?!!?%%%?%!%%%%!!%?%%!%!%%?%%?%!!%%!!%!%?%%%?%?%%?!%!%?%?%%%?%!!%?%?%!!%%%%%%!!?!!%%!%%?%?!!!??%%!!%%%!%!!%%???!!%%!%%%?!?!%%!%??!?!%!%!?%%?!%%!!?%%%!%%%?!!?!%%!!%?%!?!%!%%!%!!?!%!%%%%!%!!!%!%%%%?%?%%%!!%!%%!%%!%!?!??!!!!%?%%???%%%!%??!%!!%%%!%!%%%!??%!??!!?!?!%%%!!%!?%%%!%%!?%%!!!%%!!%%%!!%%?%%%%!?%%!!%?!!?%?%!%!!!%%!%!%!%%!!%%%!%%%?!%%%%!!!%%%?!%!%?!%%%!!%!?!!!%%!%%%!%%%%!%%!%!%?%!!?%%!!?!%!%!!??!%%%%?%?%!%%???%!%%%%!%?!%%%!%%?%?!%%!?%?!!%!?%!!%?%%%%?!%!%!%!%!%%?%%!?%%%?%%!%%%?%%%%!%%%!!??%!%!%!%%%%%??!!%%%?%%%!?%!??%!%%??!%!!!%%%%!!!!%%%!!%!%!%!%%%%%%?!%??%!%%!!?!%!%?%!!%!!!!!?!%%%%!%%!!%!%%%!!?!!%%%!%!%%!%!!%?!%!!?!?%?!?!%%!%%%%%!%?%%%!%!%%?!?%!!?%%?%%%%%!!%!!!!%%?%%%?%%%?%%?%%!!!%!%??%%%%%%!%!?%??!%!%!!%!%!!!%%%!%%!?%!!%!?%%???%?!%%?%!%%%!?!??%?%%%%%?%%!%%%!%%!%%??%?%%?%%%%%%?%?!?%%%%!%%%!%%%??!?%!%%!%%%%!%%%!!!%%%%%!!!%%%%%?!!??%!%%%!!%!??!%%!?%%!%%%%!%?%!%%%??!!!?%%!%%!%%%%?!!%!??!?%%%?!%?!!!!!%!?%!!!!???%%!?!%!%?%?%!?%!%!%?!!%?%!?!?%!!%!%%!?%%%!%%%%?%!%!%!%!!%??!%%!?%!?!%!%%!!%!%%!%?!?!%%!?!%?%%%!%!%%!%%%%%%%!?!%!!%!!!?%!%%%%%%%%?!%!%%%%?!!?%!!%!%?!!%!!%!%!%!!%!%?!?!!!?%%?%%!%%!?%%%%?!!?%%%%?!%%%?%%%%?%%%%?!%!!!???%!?%?!%!%%???%??%!%?!%!%?!????%?%%!%%%%%%!!%%%%%%?%!!%%%%!!%%%%%!%%?!!!%!!%%%??%!%!!!%!!!!?!%!%%%%%%!?%%%!%%%?%%!%%!%?%%%%%%%?%%!!!%%%!!%???!%%!%%!!!!%!%%%%!%%?%!%%%!%%%%%!%?%?%!!!%%?%%%!??%%!%!%!!%??!%?%%!%%%!?!%%%?!!%?%!%%%%!!%%%%%?%!!!%%!!%!%!!!%%!%?%!%!%%!%%%!?!%!!%%!%?!%!!?!%!!%%%%%%?%?%%%!%%!%%%%!!%!!!%!%%!??!%!?%?%%!%!%%!?%!%%%%!!!!%%%!%!!%!!!!!%!%%%!!!!!%!%?%%!%%%?!%?!!%%?%%%!?%%?%!!%%?%??%%!!!!%%%!%%?%!!%%!?%%%!%%!!!%%!?%%%!%?%!%%!%%%!?!%%%%?!!%???%%%%!%!!%%??!%%%%?!%?%%%%%%%?!%%%!%?!%%%%!!%!!!!?%!%%!!%%%%!!%%%!%%?!!??!!%!?%%%%%%?%%!%%%%!??!!%%%!?%%%!%%!%%!!?%!!%!!%%%??%%%%!%%%%%%%!%%%%%%%!%!%%%%%%%!%!?%!%%!!%!%!!!%!!%!!!%!?%?%!%%!?%%%%%%!%%%!%!%%??%!!!?!!%!%%!!!%%!%!!?%%%%!%%!!!%!%?%%!?%!!%%!%?%!!!%?!%?%%%%!!%%%!%?%!!!%%%!!%!!!%??%!%%?!?%!?!?%%!?%%%%!?!%!!%%!??!%%%%!%%%%!%%!!!%!??%%!!%%!%!!%%!!%%%%?!!%%%%!?%!%%%%%?%!!?!!%!%!%%!%??%!%%%?%!!%?%%?!%%%!%??%%%?!%?%?!%%%!!!!%%%!%%%!!?%%!%%%!%%%!%%%?%%%%%?!%%%%%%%%?%?%!%%%?%%?%?%?%%??%%!!!!!%%!%%%!!?!%!?%!!?%%%!!%!%%%!%%!%%%?!!%!!!%?!!%?!%!!%!!!!%%!!%!!!!!%%!!%%!%%%!%%?!!%?!?%!%%%!??%%!!?!%%%%%!!%%%?%!%%?!!%%?!%%!%%?%%%%!!!!%%!%!%%%!%%!!!??%%%%%!!%%%!%!?%!!%%%?%%%!%!?%%%?!!%%%%!%%%!%%%?%!%%!%!!!%%%!?!??!%%!%?!!%!%!%%%%!??%?!!!?!!!!%%%!%%!!?!%!%%%!%!%%!!!%?!?%%!%%%!%%%%!?%%!?%!!%!!??%??%%%!?%%?!%%!!?%%!%!%%?%%!%%%%!%?%%!?!?%?!??%??!%%%%%!?????!?%?!?%!!!!??!?%?!!%?%%??!!%%?!%!!!!%!%!!%%%!%?!%?%%%%%%??%%%!!?%!!?!!%%!%?%!%?%%%%%%%!??%!%%!%%%??!%%!%!%%%!?%?!%%%!!!!!?!!%%%!!%!!%?!!?%%%!%%!!%%%%!?%%?!!%%%%?%%%%!??!!%?%!!?!%%??%!??!%!%%!?!!%!%%!%!!?%%%%!%%?%?%%%?%%!!?!!!%!%?%%?%?!%%?!%%%%!!!%!!%%%%?!!?%%%?!%%%%%!%!!%%%?%%!?!%?%!?%%%!%!!!%!%?!?!%%?!??!!??!!%%!%!!%%!%%!!?!%!?!%!!%?%%%%!?%!?!%%?%%%!!?!%??!%%%%?!%%!!%!!!%!%?%%!!%!!%%!!!?%!?%??%%%!%!%%%!?!%%%%?!%%?%%!%?!%%%!%!!???%%%!%%%?!??%!!%!?%!!?%%%%!%!%!%%%%!?%!%%?%%%!?%%!%!%?!%%!%!%!!%%?!%%?%?!?%%?!%%%%%%%!%!%!!!?!!!%!%%?!?%!!??!!%%%%%!%%%!!?!!!!%?!!?%%!!%%!%!?%%%!!%!!%?!!!?!%%!%%%?%!!%!%%%%%%!?!!%!!??%%?!%?%?%!!%%!?!!!?!!%!%%!%?!%!%%%%%!%%%%%%?!?!!!!?!?%%%%!?%!?!!!!%?%!!!%!!%?!!!!!?%!%%%!%%!%??%%%!!%%%?%%!?%%??!!%%%%%!?!!%!!??%!%!%?%%%!%%%!!?!!%%?%?!?!%%!!%%%??!!?%?%%!%?%!!??!!?%%%!!!!!???%%%?%!?%??!?%!%!%!!%%!%%?%%!%!%%!%?!?%!!%%!!!%!%!?%%?!%!%%!!!%%?!%!?!%!%%%!%!!%%?%!!!%!!?!!%%%%!%!%%!!?%%?%%%%%%%!!%!%%!%!%%%%!%!%!%%?%%!%!??%?%%%!??%!!%!!??!?%?!!%%%?%%%?!%!%!%%?%%!%%%!!?%%!%!%!!%!%!!!?%%%%%%%%!?!!!????%?%%%%?%?!%%%!%%%%%!!?%?!!%%!%!?%?%%%%%%!%?%!%!%!%%!%%%%!%!!%%?%%%?%%!%%%%!!%!!%%?%%!?%%%??!%%?!%%%!!%%??%%%%?%%?%!!!?%!%%!%%%%!??!!!?%?%%%%%%?%!%!!!!%?!!!%%%!!?%?%%?%%%!!?%!??%%?%!!%!%!%!%!%!%%%%%%!%%!!!!??!%?%!%!%%%!%!!%%!!%!%%%%%?%%!%?!%%%!?%%%%%?%%%!%!%!%!%%%%%!!%!%%%??%?!%?%!%??%!?!?%?%!!%!!%%!%!%%%?%!%??%%!!%%%!??!%%!?%%!!!?!%%%?%!%%!!!%%%%?!%%?!%!!%!??!?!%%?!%%%?%!!%!%%%%?%!%%!?!%!?%!%%%!%!!%%%?%!%!?%%!%?!?%!%!?!!%%%%?%!?!%!!%%%?%!!%%!%?%%%%??%?%!?!%!%!!%!!!?!!%?%?!%%!!%!!!!%!%%!%%%!!%%%%%?!%!%%!?!?!%!%%?!!?!!?!%%%?!!!!%%%%!%!!!?!!!%%!%%%!%%!!!???%??!%%%!%!!%%!?!%%!%%%%%!%%!%?!%%!%%%%%%%?%%?!!!%!%%%!?!!!%%%!?!%%?!!!!!!%!%%%%!?!!%%!!!!%!?!!%!!!%%!%!?%??%!%%%%%?%??!!%%%?!%%%!%%%%%%!!%%!%%?%!!%%!%!%%%!?%!!!!!!???!%!%%%!%%%%%?%!%?%!%%%%?%%?%%!%%%%??!%%!%%!?%%%!!%%%%%!!?%%!%!%%%!%!?!%?%!!%!%!%%%%%%%!!%%!!%%%!!%!!!%?%%?%%%!%%!%%?%%!?!%!!%!%%%%?%%%!%%%%%%!%%%!%!?!?%%??%%!!%%??%?!%?%%!?%!?!%%%%%%%%??!!%%!!%!%%%?!!%!%??%?%!!%%%!%!!!%%!?%%%%%%%%!??%%%%%%!%!%?%%%%%!!!%%!!%!!?!!%%!%!%%!!%?!%%!%%%%??!%%%!%%!%?!%!!!?%!%?%?!%%%%%%?%!!?%!!%?!%%%%!%??%%??%%%?%%%!?%%%%%!%!%%%!!%!!!?%?%%!?%%%%?!%%?%?%%%!%!%%%!%%!%?!!%%%!%%%!%%%!%%?%%!%!%%!%?!%%??!%%%%!!%?!!!!%!!%%?%%?%!?!?!?!%%%%%!%%!??%!%%??%!%!%?%!%!%!!%!%!%%!%!!!?!%!!%?%%!%!!%!%!%%!?%%%?!!%!?%%%%%%%%!?%%!%%%!!!!!%!!%!%!!!%%??%!%%!!%%%?%%??!%%?%?%%%%!%!?%!%%%%%!%%?%!?!?!?!!%?!%!!%!?%?!!!%%%?%%!%%!!%!%??!%!%%?!?!%%!?%??%%%%?%%!%%?!!!!%!%%?!%%%%%?%?!!!!%%?%!%?%!%%???%%%%%%%!%%%%%%%%%%%?%%!%%!%%!%%%%!!?%!%%!!!!%!!%!%%%?%!?%?%%%?!!%%!%!%?!?%?!%%%%!!%!%!!%!!%?%%%!!%%%!?!?%?!%%%%%%!!!%%%!?%%%%?%??%!?!!!?!%?%%!!!!??%!%?%!!%%!%?!??%%!!%%?%%%!!%!%!?!?!%%%%!!%?%%%%!?!?%%!%!!%!!%%!%!%%!%%%%!?!%!%!%%%?!%%!%%!%!%??%?%%%!!??%?!?%%%!%%!%!!!%%%%!%?!??%%%%!?%!%%%%!%%%%%%?!%%!%%?%!%%!%%%%%%!!%%!!?!?%!!!%!%?!%%%!!!!%?%%!?!?%!!%%!!%!%!%!%%%!??%%?!!!%!?!%!!!?!%%%!!%!!!?%%!%%%%%%!!!???!?%!%%?!%%!!?%?!%%?!%%!!!%%!?%%%!%%%?%%??!!%?%!%%%?%??!?%!?%%%?!!!%!?%%!!%%?%!%!%?!%%%?%%!%!?!%!!%!%%?%%!!%%!!!%%%%!!??%!!!!%?%?!!%%%!%%!%%??%!%!!%%%%?%%!%!?!!%?%!%!%!!!!%%!!!?%%!!%%%!?!%%!!!!%!%%%%%!!!%???!!!!%%!%?%!%!%!%?%%%!!%!!%%%%%%!%!!%%%%%%!%%??%?%%%%?!%%%%%%%%%%%%%!!%!%%!!%%???!%%%!%%%%%!!%%!?%!%!%%%!%!%!%?!%%%%%%!!%%!%%%!%%%!!%!?%%%%!!%%!%!%!%?!%%!!%!%?%%%?!%%!%%?%!!?!%!?%!??!!!!!!%!?!%?!%%%!!!%!?!!!%%!??%%!!%!%?%!!?%%%%%!%%!!?%%!%!!?%%!!%?%%%%!??!!%!!%!%?!?%!?%!?%%%%%!!%!?%%%%!%!!%!%%!?!%%%%!%%!!%?!%!%!!%%!%??!!%!?%%!%%!%!%?%%?!%%%!%%%!!%%%?!%%!%!%!%%%%%?%%!!%???%%%%!%%%%%!!%%%%%%%%!%!!?!!!??!%!!%%%%!%%?%!%!!!%%?%%%!%%%%%%%?!!!?!??%%%%%%?%??%%%%%%!%%!%?!%!%!?%!%!?!%%??!!!!%!?%!%%!?!!%???%?!?%!%!!%%?%!!%!?%%!!%!%%%%%%%!%%%!%!!%%!!%!!!?%??%%%?!!!%?!%??!%%!?%%%?%%%%%?%!?%%%!%%!%!%!!!%?%!%%%?%!!!??!%!%!%%!!%%?!%?%!%?!%%%??%?%%?!!!!%!%?!!%%!%%%%%%!?%!%%!%%%!%%%!??!?%!%%%%%!%%%!?%!%?%?%!!%?%??%!%!?!%!%%%%?%%%%%%%%%!%%%?%?%?%!?%%%!%?!!?%!??%%?!%%!!!%!!!%!!?%%!!%!!%%!?%%!%??!%%%??%!!!!!!%!!!??!?%%%?%!%%%?%?!?!!%%!!?%%%!%?!%?!!?%!!%%!%%!!?%%!?%%?!%%%%%%?%?%?!%?%?%!!?%?%!%!!%%%%%!%%%%%!?!?%!%%%%?!!%%%?%%%?!!?%!!?%%?!%%%%!%%!!%%%!?!%%?!!!%!?%%%?%%%?!!%!?%%?!%?%%!??%!!!%%!%%%!%?%%%?!!%!!!??!%%!%?!%%%!!!%!!?%%%!%%%?%%%??%%!%%%%%!%%%!%?%?!!%!?%%%%%??%!!!%%%?!!!!%?%!%!%?%!!%!!%!!%!%%!%%!!%%%%%!!%%%!!%?%!%!!%!?!!?%%%!!!%%%!%%!%!!?%%!%%%!%%%!??!%!?!%!!!!%?%?!%!%%!!!?%%%!%%%%!%??%%!%!??%!%?!!%%%!!!!?!!!%%!!!%%!%!%%%%!%%%%?%%%%%%%!?%!?%!%%%??!%?%%%!%%!%%%%%%!?!?%!%%?%%%!!%?!%!%?!?!%%!%!?%%!!!!!%%!!%%%%!!?%%%!%?!!%!!%?!%%%??%%?%%?%%!!%%!!%%!%!!!%%!%!%%!?%%%%!!!%%??!!%%%%!??!%!!!%!?%??!%?%!%%!?!!?!%?%?%?!%%%?%??%!%!!!%!%%%%??%%!?%!?!%!%%?!!!%%%!?%!!%!%?%%%%%%%!!?!!%%?!%%!%%?%%%%!???!%!%%%%!%%%?%%%%!%!!!?%!??%%%!!?!%%?%%!!%?!??!%%%%%!%??%?%!!?%%%!%%?%!%%?%!???!!%!!%!%!%!!%!%!!%??%!?%?%%?%?%%!!?!%!?%?%%%%!!%%%%%!%%%!%?%%!?%%?%%%!!!??!?%?%!!?%%%?!?%%!%%!%!%!%%%?%%!!%!%?%!!?%!%?%%!?%%%%%%%!!!?!!%%%!%!%!%%!!!%?%%%%%%%%%%?!!%%!%!%%!!%%%!%!!%?%%!?!%%!%%!%%!%%%%?%!!!%?%?%%!%%!%%%!?%!!?!%!!!%%?!?%!?%!!!%?!!%!%!%%%??!%%?!!%%%?%%%??!?!!%!?%%%%%!!%%!??!%%%%%?!%!!%%%?!!%%!?!%%!!!?%!%%%%%!?%%?%!%%%%!?%%!%?%!!%%??%%!!%%%%%%!!!%%%%!!!%!%%!%!%%%!!%??%!?!%%!!!!%!%!%??!!%%%%%%!%%%!%?%%?%%!!!?!%%?%!%!!!!!%?!!!?%!?!%!%?%??!%!!!?%%!%??%%%?%!!!!!!!!%!%%!%?%%!!%!%!!%?%%!!!%%!!%!!%%!%%?%%!%!?%%?%!?!%%!?%!!%%%%%%!%%%!%?!%%!%!!!%%%??%%%!%%?!!!%%!?%%!%%?!!!%%!!%!!%!%!?%%!%%%%!!!%%%???!%%!!%!%%!!%!%?%%%!%%%!!%%?%?%!%%%%%%!!!!!?!!!%%?!%!?????!%?!?%%%%??!%%!!?%%%?%%%%%%%?!%%%%!%?%!!%%%%!%%!?%%%?%%%!!%??%!%!%%!?%!!%?%!%%?%!?!%%?%!%!!%%%!?%%!%%%?%!%%%%%%%?%!%!%%?!%%?%!!!!!!!?%%!%!%%%??%%?!%%%%%%!??%%%!%%!!?!!!%!!!%%%!%!!?!?%%!?%!?%!%!!%!%%?%?%%!%%%??%!!?%?%%!??%?%%%%%%%!%%!%%%%%%?%!%!!!%!!!!%??%!%!!%%%!?%!%!%%%%?!!!%%%?%!%!%??!!!%%%%%!!!?!%%!?%??!%%??%%%!!%!%?%%%%!%%%?%!%?!!%?%!%%%%!?!%?%?!%%?!?!%!!!!%?!%%%!!!%%%?%!!%%%%%%!!%%!%%%%%!?%%%??%???!%%%%%%%%%!!%!%%!!%??%%%?%%%%%%%%!!??%!!!%!%!%?!%%%!%%?%%?%!%!%%!!%!!%!%%%%%?!!%%!!?%!%?!!%!!%?%?!%!!?%!%!!%%?%%%%!!?%!%%!%%?!!!!%%!??%?%?%!%!!%?!%!%?%!?%!%!?!%%!!%!!%%!!!%%?%!%%%%!!!%!%%!!??%%??%?!!%!%!%!%%%!%?!%!!!%?%%%?!%%?%!%%%?!!%!%%!?!%?%%%!!%!!!%!%?!!!%!!!?!?%?!%!%?!!?%%%%%!%!!%!!?%?%???!%%%!%%!%!!??!%!%!!%%%%?%!%?!!!%!!%!!%%?%%%!!?%%%!%!!%%%!%%!!%%?%%%%%!%!%%!%?!!?!%%??%%%%?!??!%!!?%?%%!%!%%!%?%?!?%!%%?%!!%%?!%%?%%!?%%%?!!!%?%?%!%!?!!%?%?%%!%%%!%%?%!%!!?!?%!!!!!%!%%%?%?!%??%%%%?!%%%%%%%%%%%%!%%%%%%%!!!!%%%%%%!%%!?%!!%?!!!?%%%%%%?%?!%!!?!?%%?!%?!!!%?%!!?!?%%!%??!?%!!!!%%?%?%%%??!%!!%%%!!%?%%%%%%%%!%%%?%!%!%?%!%!%%%?!%%%?!!?%!%%!%!!%%!!%%%?!%?%%?%!%%%?!%%%%%?%%!%?!%%!%%!%!%%?%!%??!?%%%!%!!!%%%%!%!????%!!%?!%!%!%??%%!!%%!%!%%?!?%%%%?%%?%%%!%!!!%%?%?%?%%!?%%%%!!!!?%%!?!?!%%!!!!%%!%???!%%%%%%!%%?!!!%!%%%?%!?!!%!%!%%%%!!!!?%%!%!%%%%?!?!%!!%%%%!%%%???%%!!%!%%%!%%!%%!%%!!%!!?%??%!%?!%%%%%!%%!%!%!!%%!?!?!%%!%!%%?%!?!%!%%?!!%!%!!%%!%%!%?%?%%%%%?%%%?%!%!%?%%!%!%%??!!%%?%%!%%!!%%?%%!!!!!!%%?!?%!%?%!%%%%!%!!!!%?!%??%%!%!!%!%%%!!%%%%%!!%!%%%%?%!!%%%!%?%?%%!%%%%!%%!!%%%!%%??%??%?%%??!%%!%!%%%?%?!%%%%%%%?!?%%?!!!%%%!%%%%!!?!%?!%?!??%!%%!!?%%?%!!?!!!!%%?!?%!%?%%!%!!%?%!?%%!!!%%!%!%%!!%%%!!?%!!%%%!!%%%?!!%%!!%%%!%%%%%!%!%!%!!?%?!!%!%%%%?%!!!%%%%?!?!?%?%!%!!?!%%%?!???!%%%!%%!!%%%!!%%!!?%!%!?%%%!!%%%!%?%?%?!%!!%%%%%????%??%!%%!%%!%!?%!!%!%!%!!%%!!%%%?!!?!!!?%?%!%%%%%!%?%!!%%%!%%%%%?!?%%%%%%!!%%%!!%!?%!%!%%?!?%?!?!%!%?%%%!!!!%%!?%%?%%%%!!%!!%%%!!%?!!%?!!%!?!%%!%!!!!%%?%%?!%?%%!!!%!%%?%?!%?!%!%%%!%?%!%?%?!!%!%!%%!%%%%!%%%%%!%!%%!%%%!?%%%%%!%!%%!%%!?!%%?%?!?%!!%??%?!!%?!!!!%%!%!?!%%?!!!!!!!?%%%?%!!%!%%!%%?%!%%%!??!%%!%?!?!%!%?%%%%?!!!?!!%%?%%%%!??%!?%%?%!?%?%?%%!?!?!%!%!!!!%%??!!!!?!%!%%!%!!!?%?%!%!!?!!%%%!%%%%!%!!!%%%%?%%?%!%!!%%%%%%!%!%%%%%%%%!?%%%?!?%%?%%!%%!?%%%%%!%%?%%?!!?%%!!!!%%!%%%!?%%!%%%%%!%%?%!%!%!!??%!?%%!%%?%%?!%%!%%!%!%!!!!%???%%!%!%!?!!?!!%%!%%%%%%%%?%?!!?!%!%!%!!?%?%?!%%!%%!?!%???%%!%??%%!?!%!%!!?%!%!!%!??%%??!?!!%%%!??%!%%%%%!!%%%%?!!!!%??%!!?%%%%!!%?%!!!?%%!!?%!!%!?!!%%??!%%!%%%!!?!!?%!%!!%%!%!%%!%%!!%?!!?!%%!?%%??%!%%!%%!%!?%!!!!?!?%%%?%!?%?!%%%%%!%?!%!%%!!%?!!!%!%?%%%!%??!!!%%?%%%?%%!%%%?%!??%!%%?%%!!%%!%%!%%!%!!!%%?!%!%!%%%%%?!!%?!?%!%%%!%%?!%%%!!!?%%%!%%%?!%%!!%%%%%?%!%!?%?!%!%%!!%%%!!?%%!%%%!%!%!%!%%%!!!!?!%%%%%!!%%!!%%%%%???%?%!%!!?!%%%%%?%?%%%!%%%%%!%%?%!!%%!%%%%%!?%%%%!?%!?%!%?!??!!!!%?!%%%%?%%!%%%!%!%%%!!!%!?%%!%!?%%??!!%?!?%%??!%%!!!%%%%!%%?%%?!!?%!!%%?%!?%%?!!%!!%%?%?!!!!%!?!%!%%%?%%%!!%%%%%!!%%%!!!%%%%%?%?!%%%!?!?!%!!%!%%?!!%?%%%%!!?%?%%!%!?%!%%%%?!%%!!%%%!%%!%%?%%%%%!?%%?%?%??!%!%%%%?!!!%%?!%%%?!%%%!!%%?!?%!?%!?!?!%!!!%??!?%%%!%!?%!!?%%%%%?%%%%%!!%%!?%!%!%!!%?%!%?%!%%!?!?!!!!!%%?%%%%?%%!?%%%!%!?%%%!%?%%!%!%%??%!%!%%%!?!?!?%!%!%%?%!%?%!??%%!!%%?%??%%%%%?!!%%!%?!%??%%%%%%%%?!?%%!!%?%!!?%?!%%%?%%!%?%%?!%%%%%?%?%%%!?%!%!!!!%?!!%%!!???%%%!%%%%!!!!?%?!!%?%%?!!?%%%%%%?!%!!!%%?!%%?!!%!!%%!%!??%%%!!%%!!%!%%%!!%%!!%!%!%%%%!!!!%%!%%%%%?%?%!%%%?!%%%%%!%%!?%?%!%%%??%%%%%%%%%?!%%!%%%!%%%%%!?!!!%!%%!!!%%%%%!!!?%%%%!!!!!%!!?%%!%!?!%!%%!%?%?%!?%!%%!!%%%%%?%%%?!%%!%%?!%%!!%%!!?%%%%%%!!%!%!!?!?%!!?%!%%%?%?%!!%!!!!%%%???!%%!!??!?%%?!!?%!%!%%%%%!!!!%?!!%%%!%%!%%%?!!?!%?%?!!%%%%%!%??!!?%%?%!!!!!!%%%%?!%!%%%!!%!%!%?!%%!?!%!%!!?%!%%?%%!%!%%%%%%%!%%!%?!!%!!?%%%??!!%!?%%%%%!?!!%?%!!!!!!%?%%%?%%%%!%!?%%?%%!?%!!!%!!!!%%%!!%%%!!%?!%!%!%%!%%%%%?%%!%?%%!%!!!%!?%%%!!!%?%%?!?%!%%!??%!!!!!%?%%!!%!%%?%?%%!%?%%!%%!%%!%%%!%?%!%%%!%%?!%!%?!!%%%!?%%!%!!!!!%!!%!?%%%%?!!?%!?%%%%%%!!%!!!%!?%%!?%%%%!??%?!?!%%?!?%%%!!%%%?%%%!%%?!%%?%%%!!%?%!%!%!?%%!%!%!!?!%%%%%!%!%%??%%%%!%!%!%!%%???!%?%!%%%%%%!!?%?%%%%%!!??!%!%!%!!!%??%!!!%!!%%!!!!%%%??%%%?!??%!?%%!!%%!%%!%%%%?%%!!!!%?%!??!!%%!%?!%!??!%?!%%%%!!!%!%%!%%%!??!%!%%!%!!%%%%%?!?%!!%%!%?!%%%%%%%!?%%%!!%?!!!%?%!%%%%%%%?!%!%!%%%?!%%?%%%?%!%!%!!!!%?%%??!%!?%!!!!!!!!%%%%%!%!?%!%%!!%?!%%?%%%%?%!%!%%%!!??!!!??%?!!?%!%%%?%%%%!%?%%!!!!!%%%!!!!!%!!!%?!%!!!!?%??%%!%!!!?%%%!?!%!!!%%%%%%!!?%?%%!%%%!%%%%!%!?!!!%%!%!%??%%!?%%?%%!?!?!!!!!%!!!%!%%!!%?%%!%%?%%!%%!!!?%%%!!%!%%%??%!!?!!%!%%%%%%?%!%%!%!!%??%!%!%%?!!%%!?!%!!%!%%!??%%??!?!!!?!???%!%!%%!%%%!%!%!%%!?%%!%?%%%?!%%!?%%%%%%%!%%!%%%??%?%%!!!!%%!!%?!%%%?%!??%%!!%%!%%!%%!%!%!%%!!%%%!!%%%%?%?%!%?%%?%%!%!%?!!%??%?!%%!?!?%%!%?!!%%!%%!%%%!?%!%%??%%!!!%?!!?%!%%%%!!!%%%%?!?%!!!%%%%%!%%!%!??%?%%%%!%%%?!!?!%%!?%!%?%!%%!%!%%!!?%?!!!%%%%%!!?%!%%?%!!%!%%?%%%!%%%%!!%!%!%!%%%%?%??%?%!!%%%%%???%%%%%%!%%!!!!%?%!!%%%?!%?%%!!!!%%?%!%!!?%??%!?%?!%%%%!?%?%%??%%%%%!!!%!%!%%?%?!!%!%%?!!%%!%?%%%!%?!%%?!%!%%%?%!!!%%%!!!%??%%%?!%?!%%?%%%???%%!%!%%%!?!%%%!%%!%?%!%%%!%!!%!!?!%??!%!?!%!!??%!%%!%??%%%%?!%!%%???%?%!?%%%%%%??%!!!!%?%?%!!%!%%%%?%!!!?%!%!%?%?!!%!?!!%%?%?!%!%%?%!%!?%%?%%!%!%!!!!!%%%%%%??!!!%%!!!??!%%?%%%%!?%!%?!%?!%!%?!%!!!%%%%!%%%!%?%%%!%%??!?%!?%?%%?%%%%!%%?%%!!%!!%!!%???%%%?%%%!%%%!!?!%%%!%%%?%!%!!%%%?%%%%?%!?%!?%!!?!!?%%??!%!!%!!%%!%?%?!!%%%%%%!%!?!??%%%!%%%%!?%%%!%%??%%%?%%?%%%!?%!!?!%%%!%!?%!!%!%!%!!??%!!%%%?%%!!?%!??%?%!%%%%?%%%%?%!%%!%!!%!?%?!!!%!%%%%!?%!?%?%!%?!!%?!%!!!%%%!!??%!!?%%?%!%%%%??%%!??%!%%%%%!%!%%%%??%?%!!!!?%?%!?%?%%%%%%%!?%%%%%%%%??%%!%%?!%%!%%%%!!%%!%%%%!!%%%!%%%%%%!!?%%%!??%!%!%%!%!%!%%?!?!!%%%%%%%!!??!%%%!%%%%%%%%%%!%%%!??%%%%%%!?%%%%%!!!%%%?%!?%%!!!%%!!%!%!!%%!%!%?%!%?!%!!%%!%%%%%!%%%%!%%!!%%%?!!%?!??%?%%!%!%!?%???%%%!%??!%%!!%!!!%?!!%!%!!%!%%!!%%?%!%%%%?!???%?%?!%!!??%%%%!!?%??!%!?%!%%%?%!!%%!??!%!!%%!%%!%???%%!%?%??!!%!%!%%%%%%%%!!?%?!!%%%!%%%?!%!!%%!%?!?!%!%%?%%!!%!%%%!%%%%?%!%!!!%!%%!%%!%%%!!!%%?%!?%!%?%?%!!!!?%%%%!!%!%!!%!%!%!%%?%%!%?!%%!%?!!%?%%?%%?!?!%!?%%%!%?%!%%!!%!?%%%%!%!!%?!%!?%?%%?%%%%!%?!%%!!??!%%!?%!!!%%%%?%%%!%!!??%%%?%%?!%%%%%%%%!!%!??!%%%%!!?%%?!%!?!!%%!!%%?!%?%!!!%%?%%%?%?%%!%???%!%!%!!%?%!??%%%!!%!%?%%%%%%!%%%?%%?%%%%!%%?%?%%%%!!?%%!!%%%%%?%%%%%%%%%%%!%%??%???!%%%!%?!%%%!%!%%!!!%!%%!%!%%%%?%%%!!%!%!%%%!??%!?%?%%?%%?%!%%%%%%!%?%%?%?%%%%!!??!!!!%!!%%!?%%%%%!!!%%%!%!?!%%?!%%?%%%??!%%%%%?%!%%%%%%!!!%%!%?%%%%%%%!%%%%!?%!!%%%%%%%?%?%%%?!!!?%!%%!!!!%%!%!!!%%?!??!!%%!?!%%%!%!??!%%%%%?!%%?%!!!???%?%%%!!??!%%!?!!%!!%!%%%%%?!%?!!%!?!?!!%!?%%%%?%?%%?%%%!%%!%%%??!%!%%%?%?!%%%!%%??!!%!%%!%%%%!%?%?!%!!%%!%%?%!%%?!%%!%!??!%%%%!!%%%%?%!%!!!%%!%!%?%!!%!!%!!%!!%?%!%%?!%!?%!%!%?%%?%%%!%%!%%!%%%%?%%?!!!%%?%%?%%%%?!!?!!?%!?!%%!%%%%%!!!%%%??%%!%%?%%?!%??%%!%!!%!%%%%!%!%%!%%%!%?!?%%?%?!%?!?%!%%!!%!!%%!%%%%?%%!%%!!?!!?!!!!%!!%%%?%%?!%!%?!%!!%%%%?!!!!%!%%%%%%!%%%??!%?%!%!!%?!%?%%%!!%!!?%!%%!?%%%!!%%!%?!%!%!?!%%%!%%%%%!!%%%%??!!!%!%??!!%%%%?%?%!%%!?%??%!!?%!%??!%!%!!%%%%!?!%!!!%?%!%!%!%?!%!!?%%?!!?%%%?!!%%??%%?%!%?!!%!%%?%!%%??%!!!%%!%%%!%%%%%%%%%%!%%%%%!%?!!%%%!!!!!!!%?!%?!!%!%!%%!%%!?!!%%%%!!!!?%%?%!!?%%!?%%%%!!%?%!!?%%%%!%%%%%%%??%?%!?!!%???!?!!!%!%%%%!%?%?%?!?%!!!!!!%!!!?%!%??!!%???%%?!!!%%?%!%!%???!???!!%?%!!!!!!!%!!!%%%?%%?%?%%?%%%?%?%%%%?%%!?%!!%%!!!!!%%%!!!!?!!%!%%%%%%%?%%!%%!%!%!!!!!%!?%!?%%!%?%!!!!??!?%?%?!%!%%!!!?%??%!!%!!%%!%?%%%!%%!!%?!%%!%!??%%%!%!%!?%?%?%%%%!%%%?%?%!%!!?!%%!!!!!%?%!?%!%?%?%%?%!!%%!%???%%%%%%%%!%%!!!!?!%?%%%%%%!%!!%%!%?%!?%%%!!%!?%!%%!?!%%!!!!%%%%?!!!?%!!%!?%%%?%!%!%!%?!%%%%?!??%!%%%!%?!%%%?!?%%%?%%%%%!%%%!%%%!!%%%?%%%?%%%%%?%?%%?!!%%!!!%%?%!%%%!%%!%%?!!?%%?%?%%?%!%%%%!?!!%?!?!%%!%!??!%!!%%!?%?!%%!?!!!?!%%%%!!?%!!!!?%!%%%!%%??!%!?%!!%%!!?%%%%!%%!%%?%?%!!?!%!%%%%???!%?%!?%%!%%%%%!!%?%!%%%?!%!?%%%!??%%%!%!%!?%%%!?!?!%%!!!%?%!?%!!??%?!%!%%%%?%%!?!%%!%%%%?!?%%%!!?!!!!%%!?%%%%!?!!%!%?!%!%%%%!%!%%!%?!%%%%%!%%%%%!!!!%!%?!%%%%!%!%!%!!?%?!%?!%?!!!!%?%%%%!%!!%%%???%%?!!%!%?%%%%%!!!!%?!%??%!%!!!!%!?%%%!%?!?%%%!!!%!%?%%!%%%%%%%%?%%!%%!%%!%?%?!!!!!%!!%?%?%%%%!%%!!%%!?%%%!%!?!?%?!%!?%!%?!%%!!!%%%?!%?%%?!%%%%%??!!%!%!%%%%!?%%%%%!!!%%%%?%?%?!%%!!!?!!!!%%!!!!?%!%?%???!!!!%%%%!!%!!%%??!%?%!?%?%%!!?%%%%!%!%%??%!%%?%%%!??%%!%%!%!!!%%%!%%%!%!%%!%?!?!?%%%%?%%??%%!?!!!!%%%%??%%%%%!!%!?%??%%%?%%%%%%%!%%!%!%!!!%%!%?%%%%%?%!?!%%%%%!!?%%%!%%%!?!%%%!%%!!!%!!%%!!!?!!?%!!!??%%!%%%%!%!%!!?%?%?%%%!!%%?%!%??!?%!???!%!%%%!?!%!!!%%%?!%%%%%%%%!%%?%?%%!%%%!%%%!?!!%%%!%!%%?%!!!!%%!?%?!%%%%?!!!!!%!!%%!!%%%%!!%%%%%%!%?%!%%??%%%%!?%%!!!%%!!!%!%!?!%%%?%!!!%?!?%??%!%?%?%!!%!?????%!!%!%%!%%%%%%%?%%!!!?%!%%%!%%%?%!%%!!%?%%%%?%!!%%%%?%!!%%!%?!%%?!?!%%%?%?!!?%?%?!?%!!!%!?!%!%%!%!!%?%%!%%%!?!%!?!%%!???!%?!%%%?%%%%!%!%!!!%%!?%%%%!%%%!%%%%%!%%%!%!%?%%!%!?%!%!%!!??%%?%?%!%?!!??%!%%%%%%%?%%?%%%!?!%!!%!%%%%!%?!!%%%?%?%?!%!%%%%!%!!?%%%!%%%!%?%!%!!%!??!!!%!!%!%%%%?%!!%!%!?%%?!!%!!!%?%!!%?!?%!%!%%!!!%?!%?%%!%%%%?!%%?!%%%%!%%!%!%%!%%%%%!!%!!%%??!!%%%%%%%%%%%!%%%%?%!%%%!%%!!?%%?%%%!!%%!!!%!%!?%%!%%?!?%!!%?%?%?!%!??!%%%!!!%!%%?%!%%%%%!?%!!!!!%%%!?%%%!%%!%%%%%!%%%!%!%?%%??%%??!!%%%?%?!?%!%%!%?!%%!!?%%%%!%%%!?!!%%%%%?%%!?!!!!%!?%%%%%!!%!!!%!??!%%%%%%%%%!!%!?%%%%?%?%!%%?!%%!%???!%%!!!!%%%%!!%!%!!?!!%!%%?!?%!%%%%%%?%?!%%%%!%?%%%%?%%%%!%%%?%%%!!%!?%!%%%!!%%%!!%!%!!?!!%%!!!?%!?%!!%!!?!?%%%%%%%?%?!?%%?!%%%%%?!?!!!!!??%%!%!!?!%%%!%!!%?%%!%%%%%!?%%!%%%%??%%%!%!!%!%%%?!%?!%?%%%!!!!%!?!%%%%?!%!%!?!!%%?%%%%!%?%!??!%%!%??!!%!%??!!%%%?!%%%%%%!?%??!%!%?%?%%!?%%%%%%%!%!!%!%?!!!%?%!%?!!?%?%%%!%%%?%%!%!!!%%%%%!!??!!?!?%!!%!%!%%%%%%?!!%%%%!%%%?%!%!%!%!!???%?!????!%%?%??%!%??%%%%!%%?%!!%%%%!!!%%%%%?%?!?%%%%?%!%%%%!??%%?!!%%?!%!%?%!?%%%?!%!?!?%!%%%%%!%%?%!?!?%%%!%!?!%!%!!%!%%!!!!%!%!%%!!%%%%?!%%%!???%%%%%!%%%%%??!%!??!??%%!?%!!!?%??%%!?!!%%?%%%?!!%%!%!!!%%!!!%?!%%?!!!!%%%%%%%%?%%%!%!!%!!!!%%!%!!?%?!?!%???%%%%%!%%%%%!!%!%%%%%%!%%!?%?!%!%?!%%!%!%!%!%!??!!%?%!%%%%!?%%%%!%!!!%!%!%!%!!!!!!%?!%%%%!%%%?!!?%%!!!!%!?%!%%!%!!!?%!%!%%%?%%!%%!!%%%!%!??!%?%!!%!??%%%%!?!???%!!!%!?%%?%!%%%!!!%!?%?%%%%%!!%!%!%%!!%!?%%!%?%!!%%%%?%?%!!!%%%?%%!%%%!%!?!%!%!!?%%??!?!!%!%?%?!!%??%%!%!!!?!!!%%?%%!%%!!?!!!%?%!??!%!%%%%%!!%%%%!!%%!%%!?!??%!%%??!?%?%?!!%%!!?!%!!?%?!?!??%!!%?!?%!??!!!%%%%%!!???!%%!%!%!!%!%%%?%!!%%%%%%%%!!%?%%%!?!!%%%!%%!!%??%%!!!%%!%%?!%!?%%%???%%!?!%%!!%%%%%%%!%%!!%!!!%%?%%?!!%!%%!%!?%%%%%?!%!%%!?!!!!%%!?%%!%!%%%?%%%?%%!!%!!?!%%%??%%%!!%%%%%%%%%%%%%?!?!%!%!!!!%%!?%%%%%!%!!%%%%%%%%%?%!?%%%!%!!%!%%%%?!!?!?%%!!%!%!?%%%%?%!!%!%!%!!!%%!!!?!%!%?!%%%?%%%?%!%%!%%!?!!%!!%?!%%%%%?!??%!?%!!%!?%%?!?!%%!%%?%%%!%?%%%!%%!??%!%??%%!%%!%!%!!?!!!!!%!%!%!%%%%!!%%!%?%%!!?%%!%%!!?%%?%?!%!%%%%?%!%?%?%???%?%%!%?!%%?%!?%?%?%?%%?%%?%!%!%%!!?%%?%%%%?%!%%%!%%!!?!!%%%!!!?%%?%!%%%!??%%?!%?%??%%?!!%!%!%%!!%?%!!!%!%%%%%!%%!%??%??%!%!?%!?%%%%%%%%!%%%%%%%?%?!%%%!?%!!!!%!!??%!%?!!?%%!%!!??%!%?!?!?%?%?!!%!%%%!!!!%?!!%%%!!!%%!!!??!%!%%%!!%%!!%?%%?%%%!%%?%???%?!%%!?%%?%%?%%??%!?!!%%!??%%%?%?!%%!%!%%!%%%?!%!?%%%?!?!!!%%%!!!%!?%%%%?!!!!%%%!%!%%!!!%%%?!?%!%!%%!%%?%?!%!?!%%!%!!%%%%%!?%%?%!%!!%%%%!%%!!%%?!!!%%%%!%%%%%%%?%??%%!!?%%?!!%!??%!%?%%!%%%!%!!%%?!%!%!%%%%!%%%%%!!%%!%%!!!!!%%!%%!!??!?!%%!%??!!??%?!%!%%!?%?%!%!!?%!%?%%%?!%?%?!%?!%%!%%!%%%%!%%?%!%?!!%%!%%%%!?%!!?%?!%%!%!%!%?!!%%%!?!!!%?%%%%%?!!!?!%%%?!?%!?%!%?%!?%?%%%!!%!!!!%%???%!%%??%!%%%!?%!%%!%?!%!%!%?%%%!??%%%%!%%?!!%%%?%%!%%!%%%%%?!%%%!%?%%!!!??!?%%!?%%?%!?%%%!%!!%%!!%!?%?!%%!%!%%%!!%%!%%%%%??%%??%!!!%%%%%%%%%!%?%?%%%!!!%!%%!%?!!?%!%%%%%%%!!%??%%!%?%?%%%%%%!??!?%%!%%!%%?%!%!!!!?%!%%!!%%?!!%!%%!%%!!%%!!!%%%%%?!?!%!%%!%!%!%?%!?!%%!%!%?%!!!??!%%??!!%?%%!%%!%?%!%!!%?%%%?!%?!?!!!!!?!!!%%%%%%!?!?%%?%%!!!!?%%%%%%%%%?!%%!!!!%%%?!%%%!%!!%%%%%?!%!%!%!%%%%?!!!!%%?%%?%!%?%!!??%%%%!%%!!%%!!!%?%%!!!%%!!%%%!%%%%%%%!%%%!?%!%%%!%?!%!%%%%%%!%%?%!%%%%!!!%!???%%%%%?!%!!%!%!%%!!%%!%%%!?!%!%%?%%!?%!%!%!!!!%?%?%!?%%!!!%%%%%%?!%?%%?%?%%%%?!%?%%%%!!!?!%%!%!%%%!%?%!?%%%?!%%!%%%%%!%%%!%%!%%!%%%%%%%%?!%?!!!%!!%%!!%%%!%!%!?%%%?%?!%!!%%!%%%?!!%!!%!!%?%%%%%!!!!!%%!%?!%%!?!%?!!%!%%?%!!%%?!??!%!%%%!?%%%%%%!!?%%!!%!%?%%%%?%??%%!%%??%%%%?!%!!!%%?%%%%?!!%!!?%!%%%?%%?%%%%%%%%%!%!!!%%%!?%%%%?%%%!%%?%%%%!?%%!%?%%%?%?%!%%!?!%!%%%%!!%!!%!%%?%?!%???%%!%!%?%?!!?%!%!!%%%%?!!%!?%%!%%!!?!%%%%!%!%%%?%%%!!%%?%%?%%!%!%?!%%%?%?!!?!%!%%!%!%%%%!%%%!!%!?%%!?%%%!!%!%!%!%?%!?%?!!%!!????%%%%%!?%!??%%?%!%%!%%%%%!?!?%%!%!%?!?%!!!%%!!%%%!!%%%%%!?%?!%!!%?%%%!%?%?%%??%!%%?%%!?%%%%%!!%%?!!%%%%??%?!%!!!%%!%!%%%%%%%?%!?%??!%%%?%!%??%%?%?!%!!%!??%%!!%!!!!%!%%%!%!%%!!!!??%%?%%!!?!?%?!%%%?%%%!%%%%%%?%???!!?!%!%!%%!%?%%?!%%?%%!!%?!%%%!%!%!%??!?!!?!%!!????!??%!%%??!?%??%%%?!?!%%?%!?!!%?%%!?!%%!!%%!??%?!?!%!!%%%%%%?!?!%%?!%%?%%?!%%!%!!!!?!?%?%!%!?!?!!%%%%!%%%%!%?%?%%%%?!%%%%!!%?%!%%?%%?%%%??%%!%!?%%%%%!%?!%%%!!!?%!!%%%%%%!%%!!%!?!!?%!%?!%?%?%%!%%!?%%%%%!%%%?%!%!!%%%!%%%!%%!?%!!!%%!%%?%!!?%!%%?%!%!!%%!%!%%%%??%%!!!!%%!?!%%?%?%?%%%!?%%!%%!!%!%?%%??%?!%%%!?%%%!!!!?%%%%%!?%%%!!%%!?%%%%%%%!%!!??!!!!%!%!!%%!?%%!??!!??!!%%%!!%!?%%%%%!??%%!!!%%%%??%?!%!!%%%%!?%%!%%%%%!%!!%%?%?%%!%%!%!%!%?%!!?!?!!??!!%%%%%!%!%%%%%%?%!%!!%%??%%?!!%%%!%%%?!!%!%!!!%%!%%?%?%!!%%%?!?!%%%!!!%%%%!!%%%!!%!%!%%%!!%!??%%!%%%!?!%%?!%%%%%%%%%%%%!%%?!%%%%?%%%?%?%!%%%?%!?!!!%%!%!!%!%%%%%!%?%!%%??%%%!%!%%?!%!%%%!%?!?%%!%?%?!%!%%%%%!!%!?%%%%%?%?%%!!%??!!%!%%%!%%!!?%?!!%!!!%?!%?%%%?%?%%!!%%!?!!%%%?%?!%%%%%!!%!%!!??%!!%%??%%%%%!%?!!!!!!%%!%%!%%????%!%%?%%?%???!%!!%?%?!!!?%%!?%%?!%%%%!%?!%!??!!?!%%%!!!?%!%!%!%?%!!!!!!%%!%!?!!!!?%?%!%?%!!!%!!%!%!!%!!?%?%%%??!!%!!%!%!%?!%%%!!!%%%%!!!!%%%%!?!!%!%%%%%%!%%%%??!!!%%%%%!??%%!%%!?%%!%?!!!!%!!%!!%!?%?%?%%!?%%!%!%!!?!!%?%!%?!!%%%%%!%%!%%%!%%%!%%%!%!!%!!!%!%%!?!!%!?%!?%%%%%%%%?%!%!%?!!!!%!%%!?%!!%%%%%?%!!%%???!%!!?%%?%!!!%%%!%%%%!??%!%!%?%%?%%!%%%%?!%%%!!%%!%!%?%!!!%!%%%%?%%!%!%!%??%%?%%!?!%%!%%!?%?%!%?%%?%!%%!!%!%%%%!!%%!%?!?!!%%%%%%%!%%!!%!%%!!!%!!%!!!!!!%?!%%?%!!%!!%%!%!%%?%%%%%%%?%!%!%%%%!%%!%!?%%?%!!??%%%!!?%%?!!!!%!!%!!%%!%%%%%?!%!?%????!?!?!!!!?%%!!??!!%%%%%%!%!%%%???%%!%?!!%?%%!%%!%!%?%?%?%%%!%!%%%%!!!!?%%!%!!!%%!%%!%%!%!!!%%!!?!%!%!?%%%?!!%??%!%%!%!%%!%!!!!??!%%!?%%%%!!%?!%?%!%??%%%?%%!!!!%%%!%%%%?!!!%!%!%!%%%!???!%%%%%%%%???%%%!%%%%!%%%%??%%%!!!%%%%%!!%!!!%%%?%?%%!%?%!%!!?!%%%!!%%?%%!%%%?%%%%?%!!%?%%%%%%%%%??!%%%%!%?!!%%%%%!%!!%?%%%!%!%%?%%!!!%%%??%%%%!!!!%%%%%%!%!?!!!%%??%!!%%!!%%!%%!%%?!%?!%%!%%!%??%%%?%%%?!%?!?%%!%?!%%%%?%%%%!!!!%%%%?!%?%%!%%!%!!!!%?!??%!%!%!%%%?%%!?%%%%%!!?%%%!%%%?%%!?!!%?%%%%%!!%?%%%!%?%%!?%?%!?!!%%?!%!%!%%?%%%%%!%%%!!%??%?%!??!!?%%%!?%%%%%!%%!%!%!!!%%?%%%!?!%%%!%!%%?%!?%%?!?!!%!%!!!?!!?%?%?%%%!!!%%?%%%!!?!?!!!%!!!%%?!?%!??!%?%?%%!%?!!%!!%%!%%%?!?!!%!%!%!?!%!%%!%%?%%%!%?!?%?%%%!!%%%%!%%%!!%!!!%!!%%%!?%!%%!!%!?%%?!!!!%!!!%%??%?%%?!%%%?!!!!%!!%%%%!%%?!!%!!%%%?%%!!!?!%!%!%%%%?%!%!!!%%!?%%?!?!!!%!?!%!?%!!%%??%!!%%!%%%!%!%%?%%?%%%?%%!!%??%%?%?!%%!!%%!!!?%%!!!!?!!%%?%!%%?!!%?!?%%!?!!!%?!!%%?!%!%%%%%?%%%!!%?!%?%%%%%!?!!!!?%?%!%%!%?%?!?!%?!%%%?%?%?%!%!%%%!!!!%!%%!%%%%%%%%%!!%%%!!%%%%%?%%?%%!!%!!%!%!%!!%?%%%!!%!%%%!%!%?!!%!!!%%%!%?!?!%!%%?%%%?%!%!!!!?!%%!!!%?%!!%?!%!?%%!%?!%!%??!%%%??!%?%!!%%%%%!!?%%!%%%??%?%%%!!%%!%%%?!%??!%%%?%?!%%%%!!!%%%%%!%!%?!%!%!!!?!?%?%%!!!%!!!%%?%%?%%%!?%%%?!!!?%%!%?%%%%%!!%?!!!!!%?%%%%%?%%%?!%!%%%!!!?!%!?%???%!%!%%%!?!%%%%!%?%%%!%%!%!!%!%!%!!?%%%!%%%%?%!!?%%!%%!%%?%%!%!%?%%%%%!!%?%%%%%%!?%%?!!?%!?!%!%%%%%!%!%!%%%!%%??!?%%?!?%!!!!!%!!%?!%!%!%!!!!!!!?%%!!%%!!!!%%!!%%%!%%%!!!?%%%%%!?%!%%%!%??%%%%%??!%%%?!%%%!!%%%%%?!%!%%??%?!%!%?!?!!%!?!!%!%!%%?%%%%%!%?%%!%???!%!%%??%%?%%!?!?!%!%%%!%??!%!%%!%!!%%!%%%%!%%%!%%!%!?%%%%!!%?!%%%!!?!%!%?!%?!?!%?%!!%!%!!!%%!%?!%??%%!%!%!%%%!?!!??!%!!!%?%%%%%?%%?%%%?%?%%%!%!%!%%????%%!%!%%?!%%%%?!%%%%%!!%!%%!?%%!%%%%!%!%%!%%!%%%!!%%!?!?!?%%%!%?%%%!%!!!%%%%!%%!%!%%?!!!!!%!%%!%%%!!%%%%?!?%%%%%?!%%%%%%%%!?%%%%%!!??%%!?!%%?!%%%%%%%!!%%%!!!%!?%%%!%?!%!%!%%%%%!!%!!!?%%%%!%!!%%!%!!%!%!!%%%%!!%%%%%%!%%?%!?!!%%!!?%!%!?%%%?%?!%?%%%%!%!%%!%%??%%!?!%%??%%?%?%!%%%%%%%%%%%%!?%?%?%%!!?!!!%!%%%!??%?%!%%%%%?%!%%?%%!?%%%!!%!%!%!%%?%%%!%%%!?%%%??%%%%!??!%%%%%!%!!%!!%?%???!!%?!!%!%%%!%!!%%!%%%%?%%%!%??%%%%%%%!?!!%%%?!!%%?%!!%%!!%!%!!!!%%?%%%!!?!%%?%!%%%??!%%!!!?%?%?!?%%%??%!%%?%!!%!%%%!!!%%%!%!?!%?!%?%%%??%!%?%%%%%!%%!!!!%!!%??%!%%%?%%!%!%!?!%%?%%?%%?!!!?%%!!%!%%%!?!?!!!??!%%%??%%!%!!%?!%%%%?!?!!!!!!?!?!%%%!?%%?!!%?%?!!%%!%%%!%!%%!%%??%??%?%%%!!%!!?%!%?!!?!!!%!%!?%!%%%!?%%!!?!%?%!!%%?%%%%!!!?%%%%!%%%%?!!%?!?!%%!%%!!%!!%!%%%!!%%!%%%?!!!%!!%%%%?!!%%%%%!!%!%%!%%!%%%%?%%%%%%??%%!!%!%%%%??%!%!%%!!?%%??!??!%%!?%%%%%%?!%??%%%%!%!?!?!!!??%%!!%!%!?%%%!%%!%%%%?%%!%%!%%%%?%%%??!%!!?!!%!%!!!!!?%%%!??%?!%!!%%%%!?%!????%%%?!%!!!!!!%!!!!%%%%?%%%?%%!%%!%%!!%?%%!?!%%!%?%?%?%?!?%?!%%!?%?%!!%!!%?%!%!!%!?%%%%%%%%!%%%!?!?%?%%!%!%%!!!!????%!%%!?%%??%!?!?!%!!%%%%%%!%%!?!!!%!%%?!!%%%!!!!!!??%!%%!!?%%%%!%%%%%??%!%%!%?%%?%%%%?%%?%%!?%%%%%?%%%!%!%%%?%!%%%????!?%!%%?%?%!!%!%!?%!?!?%%%%%!!!?!%?%%%%%%!%%?%%?%!!%?!%!???%!%!%%!%!!%!!?%%!!?%!!!!!%!!%%?%%%!%?%!!?%?%%%?%?%!?!??%!?!?%?!!!%!?%!?!?%?%%!%!!!?%!!!%!%%%%!%%!%!!%%%!!%!%!!!%!%%%?!%%%%%%!?!?%%%%!%!!!%!!%%!!!%?%%%?%!!?!%?%%%!!%!!?!?%?!?!!!!%%%??%%%!%%%!%!!?%!!?!%!%%%?!?%%%!?!!!%%!?%%%!!%!%%%?!%!%%%%%!!%%%%!%%!!%!%!%%!!!!??%?!%!%%!%?!%!%!%!%%%%?%?%!!!%!%!%%%%%%%?%!%%!?!%!!%?%%%!%%?%!??%!%?%!%%%%%!%!%%%!%?%%!%%%%%%!%?!%%!%%?!%!%!!%%!%!?!%%?%?????%!?!??!!!%%!!?!%%!%?%%%%?!?%!%%!!!!?!?%%?%!!!%%%%%%?%?!!%%%%%%!%%%%%%?%%!%%%!%%!%%%!%?%!%%!!%%!!%?!%!%%!%%!%%!%%?%%?%%%%%%!%%%!?!%??%!!%!%!!!%%!%?%!!%!%!%%%??!!%%%%%!%%!%%%!?%?%%%%%!%%!%!%%?%%%%?!!!!?%?%!?!!?!%%??!!!%!?%!%%%!!%!%%!??!!?%%%%%?%%%!?%!?%%%!%%%!!%!?%!%%?%!!??!?%!!%%??%?%!%!!%??%!!%%?%%%!%%!%!!?%!!?!?!%!%?!%!!%%!%%!%%!%!%%%?%!%!!?!%%%%!%%%!%%??!%?!%%?!%??%%?%%?!!!%%%%%%!!!%%%%!%%%%???%%%!%%%!!!?%?%!!%%!%!%!!!?%??%!%?!!%%%!%!?!%?%!!!%!!!!%!%?%%%%%%!!!!%%!!??%?!%?%%!%??%??%!%!%!!%??%!%??%%!%%!%%%!%?%?%?%%%%%%!!%%!!!!%!!%?%!%%!!%?!%%!%!%%!!!!??!!!!?!?!%!!%!%?!?%%!?%%%%?%!%%?%%%!%!%%%?!%%%?%%%%%!?%!%!?%!?!!!%%%%!%?!!!!%%?%!%!%%!%!!%%!%%%%?%!!!?%%%%%%?!!%?!?%!%%!!!?%%!%!!%?%%%%%%!!!%!!%??!??!%%!!%?%%%%!!%?!%%%%!?%!%!!!!%%!!?!?%%!!?%!?%!%%%%%%!!%?%%!%%%!%!!%?!!%!?%%!!?!!%!?!%?%%%!?%!%%!?!%!?!??%%%%%!!?%!!%%!%!%%%!!!!!%!!%%!%%?%%%!!?%!!%%%?%?%!%!!%!%%%%%%!!!%??!!!!%!!?%%!!%!??!!%?!%??%%%!%?%%!%%??%%!!!%??!%%?%?!%%!%!%!%?!!%?%%%!%!%?!%!%%!%?!!%%%%!%!%!%%%???%!%%!%%%?%%%%??%!!%!!!!%%?!%%%%!?%%%!?%%%%%%%%%!!%!!?%!!%%%!??%!%%%!?!%%%%!!!%!%%%!%?!!%%%!?%%%!%?%?!%?%!%%?!?%!%%%!%??%%!??%%!!?!!%!%!%!!%%%%%!%!%!!!%!%!??%%?%%%%%%!%%!%!%!%%%!!?!!!%%%?%%?!?%!!%?!%%?!%%%%!!%!%!%!%%%!!%%%%%!!%!%!%%%!!%?%%!!!%%%%!!?%!%?%%%?%?!?%%%%%!%%%?%!%!%!!%%%%!%%!!%?%%!!%!?%%%!!%!!!%!!!?!!%%%%!?!%%!%%!%?%!%%???!!%?!%%!!%?!%%%!!!?%!%%%!%%%%!?%!!?%!%?%%?%%!%!%!%!!%!%!!!??!%%%%%!%%!?!%%?%!%%%!!?%!!?%!!%!!??!??!%!!%!%?%!!!%???%%%?!%%?!!!?%!?%!%%!%%!!%%!%%%%!!!!!%!!!?%%%%%!!?%!%%%?!%%!!%%!?%?%%%%%%%%%%!%!%?%%%!?%%!%!%%%%%!%%%!?!??%!%%!%?!!%!!%?%%!!!?!%?%!!?%!!!%???!?!!!%?%?!??%%!!!%!%?!%??!%!%%%?%!!?%!%%%%!%!%!%%%?%!!?%?%%%!!%!!?%%!!!!%?!!?!%%%?!!%%?!%?%%%%!%%%%%%!?%!!%!!%!%!?!!%!%%%%%%%!??!!!?!%%%%!!%%%?!???!%!!%%!!!!!%!!%%%%?%??!%?!%!?%%%!%!!!?%?%!!%%%?%%?%%?!!%%?%?!?%%%%%%!!!!!!%%?%?%!%%%%?%%%%%%%!!%%?!!!!!!?!!?!%%!%%!%!!%?%%%%!%?!!?%%?%%!%%%!%%!%!%!!%!?%?!!?!!!!!!!%???%%!%%!%%%!?!%?%!!%%%%%%?%%%%%%?%?%!%?%%%%%%%!?%%?%%%!%?%%%!?!%!!%!!!!%%?%!!%%?!!%%%!%!%?!!!!%%%%!??!!!%!%%?!%%%%%%!?!!%%!%%!%!%%?!??!%%%?%%!!%??%%%%%%%%!%!%%!%!?%%%??!%!!%?!%%%%%!%%!%!!%%?%%!!%%%?!%!%%%%%%%%??!%!!?!?!%!!!!!%%%%%%%!%!%??%?!!?%???!?!!%?!?!!%!%%%%?%?%%!%%%?%!!!%%%?%??%%%%%%%%%%??%!%%!?!!?!%%!!?%!%!%%?%%?!%%%??!%%!%%!%%?!%!%%!%?!%?!?!%?%%%%!!%%%%!!?%%?%%?%!!!%!%!!%%%%!?!??!%?%%!!!%!%%%%!%!%%%%%!!%%!!%?!!%%?%%?!!%%!%%%%!%%?!!%%%%%!%%%%!%!!!%%?!?!%%!!!!!?%%%!%%!??%%!%%!%?%%%%!?!!!%!%!%!?%%!!%%%%%!!%!%!!!!%!!!%!%?%!%%%%?!?%?!%%%?!%%%?%!?!%%?!%??!!?%?%%?%%!!%?!!?!%?!%%?!?%!%!%%%!%%?!%!%%%!!?!%%%?%!?%!%!???!!!?!%!!?!%%?%!!?!%%!%!!??%!?!%?%??%%%!!%!%!%%!%%%!%?%?%%!%%!%!%%%%?%!%!%!?!%?%!%!%!%%!!%?%%!!!%%%?!%?%?%!%%!%!%%?%%!%%%%%?!?%?%%?%%!!!%!?!?!!%!!%!!!%%?!!%!%%!?!!?%!!%?!!!!!!%!!??%!!!?%%!%!%!?!%%%???%!%!?%!%?!%?!%%?%%!?!!%!%?%%%%%%%%!?!%%%%!%?%!!!%!%%!?%%!%%?%%%%!%!%!!?!!%%?!%!?%!!!%!!%!!%??!%%%%!%?%!%!%!?!!%!%?!%!%!%%%%!??%!%%!!!!%!?!%%%%!!?%?%?%!!%!%%%?%!%!!?%%%%%%%!%!?%%!!!!?%!%%%!?!!%!%%?!!!?%%%!!!%!!!!%%?%?%?%%%%!%?!%?%!!!?!%%!!!???!%%%%%!%%!!%!%%!!!%?!??%%?%%???%?!%!?!?!%%%%?%%%!!%%%!%!%%%!!!%!%!%?%%%!!%%!%!!!%%%!!!!%!%%%%%?%?%?!!%!!?%%%!?%!%%%%%?!%??%!!%!%%!%%%%%%%!!?!??!%?%!?%%!!%!%%!%%%?!?%!?%??!?%!%%%%!?%%%?%%%%%%%?%?%?!%?!!!%%!%%!!!%%!%!%%%%%?%%%!%!%!?%%??!%%%?%!%!%%!??!!!%%??%?%!%%%!%!!!!?%%!%%!!!%%%!?!!%%?%!!?%!%?!!%%?%%?%%!%%?!%!%!?!!%!!!!???%%?%%!!?!%%?%%%%%%%!!!%%?!%?%%!%%!%!!!!?!%!!%?%%?%!!?!%!??%!!%%%!%?%%%%%%%!!!!%%!%%%%%%%%!!%!%%%%%%%%%!%?%?%%%!%%!%%%!%%%%?%%%%%?!%%?%?%!%%!%?%%?%%%!%!!%?!?%!!!!!%%%?!%??!?!%%%!%%%!%!?!!?%%!%!!!%%!%%%!%!%!%%%!?%%?!%%%%%%!!!%!%?%%??%%!!%??%!!!!%!?%?%!!%?%!!%??!%%%%???%!!%%%%%!!%!?!%%!?%!%?!%%!%%!?%!!?%%?%%!%%%%!?%%%?%%%??%?!%%%?!%?%?%?!??%%!!!%?%%?!!!%!%%%%?%%?!!%!%%!?!?%%%!%%%%%!?%!!?!%?%!?%?!%%%?!%%%%%%!%?%%%%!%!%%?!!?%!%!!!!!?!%%!!!%!!%%?%%!%!!%?!%??!!!!?%%!!%?!%%?%%?!!%?%%%!!%%!!!!!%%!???!%!%!!!%%%%!%???%%%?%!%!%!?%!!??%%%%!%??%??%%%%!%%!%!?!?%!?%%%!%%%%?!%%?%%%%%!!%?%%!??%!%%%!%%!!!%%!!%%!?!!?!!%??%!%%%?%%?!%%%%!!%%!%%%%%!%%!%!%%!%%!!%%%!!!!!!%?!%!%%!!%!!%%!!%!!!!%!?%??!%!%!?!%%!%%%!!!%!!?%?%?!?%!!%%%%%!%%?%!!!!%?!%!!!%%!%%%%!%?!??!!%%%!!%%%%%!%%!!%%%?!!%!%%%%!%%%%?%!!%%%!%!%%?%??%%!%%!%%!!%%%%!?%?%?%?!%?%%%%%!!%%%%!!%%!!!%%!?!%?!%!?!%?%%%!%?%!!%%%!%?!%%!%?!%??!!%?%!%%%!%%%%!%%!!%!%%%%?!??%%?!!!%%?%!%?!!%?%%%%?!%!!!!!%!%%%%%!!???%???%!%!%%?!!!%%!%%!%%%%!%%!%%!!%%%%%%%%%%?!%!%!!%?!!?%!!!%!!%%%?!!!%%??%?%!?%!%!%%%%%?%%%%!%%%%!%%?!!!?%%!%!%?!%!!%%%?!!%%!%%%%?%%%%!%%%!%!%!!%!!!%%!!!!%?%!%%!!%%!?!???!!%?!!!!%?%%!?!%!!??%%%%?!%!%!!!?%?!!!%%?%%%%?%%%%!!??%?!%%?%%!%%?!?!?!%%%%!?%%%!!!%!%?%%!!!!!%%!!%%%%%??!!!%%%!%%%%?%?%!%%?!%%!!?!?!!?%!%?%!%!!%%?%%!%%%!!%!?%%%???!!%%%%%%!!%%!%!%!!?%!%!%%%%%%?!!%%!!%%%%?%%!%??%!?!!!%%!%%?!%??%?%!!!!!!%?%%%?%%!%?!%%%%!!%%???%%?%%!%%%!!%%%!%!%%!%%!%!%!?%%!?!!??!?%?%%?%%!!%%%!%!!%%!!%?!??%%!?!%!%%!%?%!%!%!%!%%%!?%%%%?%%??%!?%%?%%!%%%%%!??!?!!%!?!%%?!%%!%%!%%!!?!!??!%%%%%%%!%!?%!%%!!%?%%?!%%!!!?%?%!?%%%%%%!%%?%?!?%%%!%!!!?%%!!!%%!!%%?!%%%%%!%%%!%%!!%!%!?%!%!%!%%!%!%%!!?!%%%%%?%!%!%!%%!!!%%%?%!!%!?!%!%?!%!!??%%%!!!%!!%!?!!!!%%!%%%!%%!%?%!!%%%%???!?!!%?%%%!%%%%!!?%%!!!??!%%??!%!%%?%!%!!!%%%!%!!?%%!!!!%%%!%?!%%!%!!?%%%!%%%!%%?%%%!!%%%%%???%%%%%%!!!%!%!%!!?%%%%?%%?!!!%%%%!!!%!!%!?%?!%?!!%%%%?%!%%?!?%%!%%%?!%?%%%!%%%!!?%!%?%%!!%%!?!!%!!!%%!%?!%?%%%%%%%?!%%?????%!%%%?%%%?!%%!%%%%!%%?%!%%!%!%!%%!!!%!?%%!%!!!?%%!%?%!?%?%?%%?!?%!%%%%!!!%?%%%?!?!%?!!!%!%%!!???!!%?%!%!!%%!%%%%!?%!!%!!%%%%!!%%%!!?!%%%%%!!%%?%?%%%!!%%?%!%%%%%!%?%%?%!!?%?!%!%%?%?%?%%%%!?%?!?%%???!%?%!%%!??%%%%!!!!%%!%%!%%?!?!!%???!%?%??!!%!!!!%%!?%!?%%!?%?%%?%%%%%%%%%%%%!??%%?!!!!!%!!%?!%?!%%!?!%?!%%%%%%%%%%%!%!!!!%%?%%!!%%!!!!?%?%!?%!%%%!%%%%?%?%%!!!%%%!!??%!%%%!!!!%%%%!!!%!%%!!!!!!!%?%%%!%%!%?%%%%%%%%%%%%%%?%!%?!?%%!%%??!%%%%%%??!!!%%%%%!%%%?!%%%%%!!%%!?%!%%%!%???%%%!%!%%%%!?%?!?!%?%?!%!!%!%%%%?%!%%%!%%!!%!%!!%%!!?%%%!%?%!!%%%%?!!!%!%!!%%!!!!%%!!!%%!!!!%!%%!!%??!?%%?%%%!?%%?%%!!%?!!%?!%!?%%%%!%%!%!%!%%%!!%%!%!!!%%%!!%%%?%!!!!!?%??!??%!%!!!?!%!?%?%?!?%%%!!!!!!?!?%%?%%!%%%%!?!!%!?%!%%!%!%?%?%!%?%%!%?%%%?%!!%!!%%!%??%!!%%%??%!%%!!%%%?!??!!%!?%!%?!!?%%!%%%%?!!%%?!!%?%!!%!%%%%%%%!!%!?!!!%!%%%%%%!%!%%%?!%%%!?!%!%%%%!!?%%%%?%!%?!%%%%%%%%%%%%%!???!%%%%%%%%!!!??!!!%!%!%!?!!?%%!%%%!%!%%?%?!!%%!%!!%!!!%%!%!?%%%!!%!!%%!%!%%!!?!%!!?%%!?!%%%%%!??!!%?%??%?!%%%!!%!%%!??%%!%%%?!?%%%?!%!%!?!!%%?%?%?!!%!%!?%%%?%%?%!%%%!?!!!%%!%%!!%%%?!?%%%%%%!??%!%%!!!!!%?%%%%%!%%!!?%!!!%%%%%%%%!!%!!%!?!!?!%!%%%?!!%!!%!?%?!%%%%?%%%!%%?%!!%%!!%!%%%%?%!!%!%!?%?!%!%!?!?%%?!!!%!!%%%%!?%%%%%%!%%?%!?!%%%%%!%%??!!%!!%!?!!?%%%%%%%?!%%!!!?!?%%%!?!%!%%%%%%%%??!!%%%!?!%%!??%%?!!?%?!?%!%?%?%!!%!?!%%!%!%?%%%%!!%??%%?!%?%%!!%%%%!!!!!?%%%!!!%!!%%%%%!!!%!%!?%?!?%!%!?!!!?%%%!%%?%!!?!?%%%!%!%%!!??!%%!!%%!%?!%%!!?%!%%!!!!?!!??%!%!!%!%?!%%!?%??%%?!!!!!!%%%%%?%!?%%%%%?!!%%!?%??!!!!??!!%!%%!%!!!%!!%!!%!?%%%!%%%%?%%%!!!?!%!!!?!!!??!!%!%%!%?!%%!%??!%!%%?%!%%%!%?%%??!%??!%!!%!?!!!!%!%!%%?!?!%%%?%%%?%!%!?%!%?%%%?%!%!!!%!%%%%%%!%%?!%!%%!!%%%!%%%?!%%%%%!%%%%%!?%!!%%!?!!%!%%!%?%!%%!??%!!%?%!!?!!%%!?!%%%%!?!%!%!%!!!?!!!%!!!%%??%?%??%!!?!!%%%?%!%%%%!?%!!?!%!??!!!%%%!%%!%!!%!!%%?%%%!%%?%%%%!%%??!%%!!!?%%%%!%%!!%!!%%%%!!!%%%%%!%??%!%%!%%?!%%!%%!%!%???%!%!%!!!?%%!!?%!?!%%%%%%%!%%%!!!!?%%%??%%!?%%!%?!!%%!%%%%%!!?%%!!?!??!!!%!?!!%?%%%!?%%%%%%!?%??%%%!!?!%?!%%%%%%%?%!?%?%%!%!%%?%%%%%%%!?%%!!%?%%%%%?%%!!??!%%??!%%?!%%%!%%!%%!!%!!%!%%%?%%%!%%!?!???%!?%!?%%%%!%%%!!%%%!?%!%%%?!%%?%?%?%%??!%%%%%%!%%!%%%%!!!%!%%!%?!!!?%%!!?!?%%!%?!?%%!%!!!?%%!%??!%!?%%%%%%?!!!!%%!%!?!%!?%%%%!?%!%!%!%%%!!%%!!%%%%%??%%!%!%?%%??%!?!%!?%%%!%%?%%!%!?%%!%%%%%!!?%%!%!!%!!?%?!%%%%%%!?%!!%!!%%!%%?%%?%!%%%%%%%?%?!%!%!%!!%%%!%!%!%%?%%%%?!???!!%%%%%!?%%%?%%!%?%%!!%!%%?%%!!%!?%!%%?%%%%!%?%%%%%!!?!%!!!%%%!%!%%!%!%%%?%%%%%%!!?%?!?%%!!?%%!%?!!!%!!%?%??%%!%!%!??%%%%%!!?%!!%?!%!%%%%%!%?!%%%!%%?%!!!!??%!!!!!!!%%%?%%%%!%%?%!?!!%%%!%%%%!%%%?%%!%?!?%%%%!!!!?!%!%!!?!!!?!%?%!%??%!!%?%!%%!%%!%!%!?%%?%!%?!%%%%%%%%!!%?%%%%!!%%%!%!%?%%?%%%?%%%!?%%%?%%%!%%!%%%?!!%%%%%%%!%%??%?%%!%%!%%%!%?!?!%%%%??!?%!?!!%%%%%%%!%%??%%%!%!%?%%!%!!%?%!!%?!%%??%!!%%!!!%%?%%!%%%!!?!%?%!?%!!%?%!!!!!%%?%!%?%%%%!%%!%!!%%%?%%%!%%!%?!%%?%%%%%%?%?%%%!?!?%%!%!%%?!??!?%!%!!!!!%%%%%%!?!%?!!%%!%!%!%%!%%%%%!%?!%?%%?%%%!%%%!%?%%??%!%!!%!!%!%!?%?%%!%%!%!%!%%%%%%!!%%%%%!?!%!!?%!!%%?!%?%%?%?!!%%!%%%!!%%%!%%!!!!!%%!!%%!%%?%%%?!%!%!!%??!%%%%%%!%%%!!!%%%?%!%!%!%%%%%%%%%%%!%!?%%!%%%%!!%%!?%%%!!%??%!%!!%%%!!?!!?!%%?!%!%!?%%%?!%%%%!!!!!%!%%%!%%!%%%%!%%%%!%!%!!%%!!!!??!??!!%%!!!%%%!??%!%%%%%!%%%%%%!??%%!!%%?!%??!%?!%%%%!??%%!%%%%??%!?!%!%!!?%!%!%!?%?!%%?%?!%?%%%%%??!%%%%?%%!!!%!!?!?%%%%%!!!!?%%?!!!%?%?%!!%!%%%%?!%%%%!%!%%%?%!!%!?!%?%!%%?%%%%!%!%!%%!!%?%%%?%%%%%%%%!!?!%%?%??%%?%%!%%!!!!!?%%%%%!!%%%%%?!?%%%!%?!%%%%??!!%!%%?!%%!?!%!%!!%?%!%??%%%!!!%!???!!?%?%!%?%!!%%!!!%!%%%!??%?!%!!%?%!!?!!?%!!!%!%%%!%%?!?!%!%?%%!!!!!%%!?%%!%%%!%!!%%%%%%%%%%%%!!!!!!!%%!%%!?!!!%%!%%!%%!%%!%?!%%%%%%?!?%!!%%%!?!%%?!!%%!%%!?!%!?!%%!%!%%!%%%!?%!%?%%%%!!?%%?%?%%?!!%%%%!?!!%%%%%%%?%?%%?%%%%?!?%%%!!%!!%!%%!%%!!%%!!%%%!?%%!!!%%%!%?%!%%?!!!!%%?!%%?%!?!?!!?!!%!!%?%!!%?%%%!!?!%?%!!?%?!%!!%%%%%%%!%%!!!%%?%!!%!%!!%??!!%!!%%%%?!%%%?!%?%%%%%!%!?!%!%!%%!%!!%?%%?%?!??!%%%%!%%!!%%%!!%?!%!%%!%%!%%!??!!!!!!%!%!!!!?!?%%%%%?!!!??%!!%?!!%!!!!?%%!!?%!%%%!!!!%!%%%!!!%%!?%%%%!!%!?!%!!%%%!%%!!%!%%?!!!%%?%!!?%!%??%%%%%!%%%%%!%%!!?%?%?!%!%!!%%?%%!%%!!%%!!%%%%!!?%%%%!%%%!?!%%%!!%%!!!%?%!!%%%%?%%%!!!%%!!%!!!?!%%?!%?!%!!!%%%?%%?%%!%?!%%%!%??%%?%?%??!!!!!%%%%??%%?%%?%!!%%%!?!?%?!?%%%?%%!!?%!!%!%%?%%!!%%!!%%?!%!%%%??%!!!%??%%%%%!!%%!!%!%!%%?!!%%!?%?%%!%!!?!!%??%%%%%%%%%%%%%!!%!!?!?%%?!%?!%?%!!%%%!%!%%??%%!?!!?%%!%%?%%?%!%%?%?%!?%%?%%?%!?%%%%%!%%%!%!!!!!%!!%%%%%?!???%%!!%!%%%!!%%%%%?%?%!%!%?!!%!!!!!!!!%%?%%!%%%!%?%%%%%%%%!%%!%?%%%%!%%%??!%?%%%!%?%!!%!%%%!%%%%?%!??%!%%?!%%!!%!%%%%!!?%%?%%%%!%!!!!%!%?%!!%???%%?!!!!!%%!?!%%%%%!!%???%%%!%!%!%%??%%!%!%?%%!%%%%%!%!%%%!?%%!!%??!%!%!?!%?!!%!!%?%%%!!!!!%%%%%!?%?!!%%!%!??%!!!%!!!%%%%?%%?!!!!!!!%!%%?%%!!%%?%%!%!%%!%?%%!%%%%%?%%%%!%%?!?%%%?!?%!!%%!%!??%%%?%?%!%!!!!%%!%!%!!?!??%?%!%!%!%!%??!!???!???!%!%%%??%!%!%%%???%%!!%%!%!!?!!!%!?%%%%%%%%??%???%%%%%??%!!%?%%%%!%?!?%%%%%%%!%!!!%%!!%%%%%!%%%!?!!?%?%!%!%%%%%%%!?%%%%%%%?!%%??%%%%?%!!?%!?!!%!%!?%?!!%?!!!!!?%%!%%%!??%!?%?!%%!?%%!!%%!%%%%%%?%!%!!%%%%!%??!!!?%?!%!%%??%!!%!!!%!!%%!%%!%%%%%%!?!?%!%?!%%!!%%%?%!%?%!?!%?!!!!?!?!%%%%!%!!?%%%%?!!?!!??!!%%!%!%%%%%?%%%??%?!%!%%%??%%%!%!%!!!!%%%!!%%%%%?!%!%%%?%!!!%%%%????!%!!?%!%!%!!%!!?!!!!?%!?!%??%%%%!?%?%%!%!!!??%%?%%%%%?%%%%?%?!?!%!%?%!%?%!%!!%%!%%%%!%!%!!?%!%%!!%%!%%%!%%!%!%%!!%%!%%?%%%%%%%%%%%%%%!%?!%!!%%%%%!?!%%!%%!%?!!%%!%!!!%?%%%?!!%%%%%?!!%%!%%?%!%!%!%%?%!!!%!!%!?%%!%?!%%!!%%%%%%?%%%%???%?%?!%?!%?%%%%%%%%?!?!%!%!!%!???!%!!%?%!%%!%!%!%!?%%%%%!!%%!?!%%%%%!%%?%!%?!%?%!!!%%%!!!%!!%!!!!%!%%!%%%!%!!%%%%!!%%%!%?!%%???%%!%%!!!!%!!%%?%!??%%!%?%%%%!%!!%??!%!!%%!!%?!%%%!!??%%!%!%%!?%!!!%!!%%%%?%%!!!??%%!%%!!%%%%%!%%!%%%%%%!%?%?%?%!?%?%?!%%%?%!%?!?%%%%%!??%!%??!%%%%!%?%%%!!?%!%!?%%%!!%?%%!!?!%%%%?%!%%?!!%!!%!%?!%!?!%!%%!%%??%%%!!!?%%!!%%!%!%?%??!?!%!?%?%%%!!%!%%!!!!%%%!%%?!%%!!%?%!%%?%?%!%%%%%!?%%!%!!%%?%%%!!%!!%%%%%!!??!?%%%?!%%%%%!%!%%%!!!!%%%!!!?%%%%!!%!%!?!%?!%%?%%%%%!%%?!%%%?%%%%?%!%!!!?!%!!%?%%%!!%%%!%?!%%!%!!%!%!%%!%%?%%%%?%%??!!??!???!!%%?%!?%!%!%!!%???!%?%%%%%%!%?!%!!!%%%%%?%%?!!??%!%%%!%%%%%%%!%%%%!%?%?%%!%!%!%%%%%%!%!!%!%?%???%!%%%%%%%?!!!%!%%%%!%!%!!%%%%%%!!?%!%%!%??%%!%%%!%%%%?%%!%!!%?%??%%!%!%%??%!%%!?%%?!!%%%!%%!!%%?!!%%?%!!??%%%%%!?%!?%%%?%%%%?%?%!?!!???%%!?%%%%!%?%??!!%!%%!!%?!??!?%%%!%%!%!?%?%??!!%!%%!%%!%%!!!%!!%?%%%!!!%!%%?%%%?%!%?%%!?!%%%!?!%!!!%%%!%%!!%?!%%!!!!%%%?%!%!?%%%%%%!!!%!%!%%!%!%!%%%%%%?!%!?%!!?%%?%?%%%%??%%!%!!!%!?!?!%%?!!%%!?!%!%?%??%!!?!?%%!%%%%!%%%!%%??!%%%!%%%?%!!%?%%!!%%%%%?!%%%!??!!!%%%%%%%?!!!!!?!!!!!?!!%%%!%%%!%%!!%%!!%%%%?!%!%!%?%%!!%?%%?%%%!!%!!%!!!%%%%?%%%!%%%?!!%!%%%?!!%?%!%%!!!!%!%?%%!!!?%%?%!%%!%%?!%!?%%%?!??%%!!!%%%?%%!%?%!!%!%%%%%%?!!%%!%%%%!??%%?!%!%!%%%!%!%!!!%!!!?!!??!!!!%%!!!!%?%!!!?!!?!?%?%%!!%%!%%!!%%%!?!?%%%%?!%%%!!???%%%%%%%%!%!!!?%%!??%%%%!!%%%??!%%!!%!%!%%!?%%?%%!%!%%%%?!%!!!!!%%?!%!!!?!%?!!%%!!%%%!!%!%!%?!??%!%%%?%!%!!%%!%%!%%%?!!%%!!%%?%!%!%%%%??!%%??%%%!!%!?%!%!!?%?%!%!?%!!!%?%?%%%!%!?!%%?%%%!%?!???%!!%%!!%!%%!!?!%?%%!?%!!?%!%!!%%!!?%!%%%!%?!%%!%?%%!!!%%!%%!%%%%?!%!%%?%!%!%!!%!%%%!%%!?%!!!%%%%%%%!!%?%?!!%%%?%!%%%%%%%%%%!%%%!%!?!?!%%!?!!?%!%!%%?%!!%?%%!!%!?%!?!!%%%%%%%%%%?!!%!%%!%!%!??!%%!%!!%%!%%!%!%%%??%%%!%%!!%%%?%%%%!%%!??%%?%%%??%??%%%%!!%%?%%%?%!%%%?%?!!%!%%%!%!%!!%!??!?%!!!%%%%%?%??%!%%%%!!!!%?!%?%%!!%%%!%?!!?!%%%%!%%%!%%!%%%%?!%%%!!%%%!!!%!!!!!%%%!%%!%%!!!!%%%%%%?!?!!%%???%%%?!!!!%??%%!!?!%%?!%?%?%?%%%?%?%%?!%%!!!%!%??%?%!%!!!!%!%%%!?%%%%%??!!%?!?%!!!%!!%?!!%!?%!%??%!%!!%!%?%!%??%%%%!%%?!!!%%?%%%?%??%%%%%%!??%!%%?!!%?%%?%!!%?!%!%%%%%%%!??%%%!%%%!?!%!%!?%%%!%%%!%%?!%%%%%!!!%%%!!%%%?!?!?%%!!!%%%%%?%%%%%!?%%!?%%%%?%%%!%%!%%%%!??%!%%!!!!?!%%%%%%%%?%??!?%%%%%?!!?!?%!%%%!%!!!??!%?!%%!!?!?!!!!%!!%%!??%!!!!!!!%%?%?%%%??%?%%%!!%%%!?%!!!%%!!!%!!%!%%?%%%%%!?%!%?%%!!!%?%!!!%%%?!?%%??%!?%%%%!%%!%%%%!??!!%!%%%!%!%?!%%!%?!%%?%!?%%%%?!!!%!%%%?%!?%%!!!?!%%%%%?%!%!%!!!%!!%?%?%%%!%%?%%!%%!!%??%!!%!%%%??%!%%%?%!%%??%%!%%%?%%%%%%!?%%%!!?%%?%%!!!????!????%%%?%%%!?!!%?!%!!%%!!%!%%%%%??%%!%!!?%%!!!?!!!!!%%!%%%?%%!!%!!%%%%%%??!!%%%%!!?!%%%!%%??%?%%!%%!!!?%!??!!?!!!?!!?%!!%%%%%!!%!?!%!!%?%!%?%%?!%?!%!%%%%%?%%!%!%%!%%!%%%?%!%?!??%!%!!%!%!%!!%%!!%%!?!!%%%?!%?%!?%?!!!!%!%%?!%%!%%!%%?%%!%%%!!!!%!!%!!!!%!%?%%%!%%!!%!!?%%!?!?%%!%%?%!!!?%!!%%%!!%?%?%!%%%%%!?!!!%!%!?%!%?!!%%%?!%!!%%!!%%%!%%%?!%%%!?%%%?%%?!!!!!?!!%%?!?%%%!!!%%%%!%%%%!%%!%%%%!%%?%%%?!?%%?%!%?%?%!!%%%%!!!%!%!!%?%%!!!%?!!!%%%%!%%%!?%%!!%!!!%%!?%?!?%!%!%%!!!%?%%%!%%%%?!%%!%%%%%!%%?!%%!!??!!%%?!%?%%!%!!??%%%%?!%%%!!?!%%%!!%?!?%%!!%%!!!?!%??%%%%%%!%!!?%%%%?!%%%%%??%!!!?!%!!!%!!?%%?%!%%%%!%!!?%!%??!!%%%%%!%%%!%!%%%??!?%%!%%%!%?%!?%%%!?!%?%!%?%%%%!!!%?!%?%%!!%%%%!%%%%!%%?%%%%!!??!?%?!?%%%??%!%!!%!%%!%%%?%%?!%%?!???%!?%%%?!!%%%??!?%%!!!%%?%%!%%%!%!%%?!%%%!!?%%%%!%?!!%%!!?!??!%%%%!!%?!!%?!!!%!%!%%%?!!%!%?!%?!!%!!%?!!?%%??!!%!%%%%%?!%%!%%??%??%%%!%!!!!%!!!%%%?!!%?%!%?!%%%!%!!!%?!%%%!!?!%?!?%!!%?%%?!%!?%%%!!%%!!%%!%!?%%%%?%!%!%%!%!%!%?%%!%!!!%!%%!%!!!?%?%%!?%!?%!?!?!!%%%%%!!%%%!!!%%?!%%%%!%%%?%!%???!!%%%%%%%%%%!%%!?!?%%??!!%!?!%?%!%%!!?!!!!?%%!%%!?!%%?%!?!!?%!%!?!?!!%%??%??%?%!!%%?!%?!?%!%%!%%!!!!!!%?%!!%%?!?!!?%!??%!%%?%?!!!!%%!%%!!!!!!!!?%%%?!%!?%?%!!%%%?!?!?!!!%%%%!!!%%?%!!?%%!%!?!!!%?%!%!!%!%?%%!%?!?%!%%?!!??%!?!?%!%??!!!%!%%???!%%!?!%%!%!%?%!!%%%%%!%?!%%!%?!%!?%%%%!%%%!%!%!!%%%%%%?!?!%?!!?%%!?%!!%?%!!%!%%%?%!%!%%!%%!%?%!!?%%!?!!%%!!!%?!?!%!%!%%?%%?%?%?%!!%%?%!%%!%!%%!!!!%%??%!!!!??%%%!%%%!%?%?!%?!!%!!!!!!!%??%!%%%?%%%!?%%%?%!%?!%!!%!!!%!%%!%!%?%%%!%?%%!?!!?!%!%?%%!?%?%%%%%!!!%!%!?%%%!?%?%?!!!?!%%%!%%%%%!%?%!?!?!%%!%%%%%%%!?%%!%?!?%?%!%%%?!?!?%%?!!%!%%%!!%%!%?%%!?%%?%!%!%!!!%%!%!%%!%!%!!!!!%!!%%?!!%?%!%!!!%%%!%%%!%%!%?%?%%%%%%!%%%%?!%%?%%%!!%%!%%%!%%!!!!%!%%!%%%?%%!%%!%%%%%%!%%!!%!?!!!%%%%%%%!!%!%!!%%%??%?!%!%%%%!%?%!!?%%%?%!!%!?%%%!?!%%!!!%%!%!!%!%%!?!%!?!%%!!%!!%%%%!%!!?%%!!?%?%%!?%??!!%%%%%?%%%!%%%!!!?%%%?%!%%!%!!%%%%?!%!!%?%!!!!!!?%!%%%?!%%!%%%%?%!%%%%%%!?%%?%%%!?%?%!%!%%%!%?%%??%!%%!!!%%?!%%%!%%!?%%!!?%%!!!%%%%?!!!!!!%!!!??%!%%%!!%%?!!?!!%%!?!!%?%!%!!!????%!%%!!%!!?%%!%%!%%%!%!%!!!%!%%%?%?!%!?%!!%%!%%??%%%???!!!%%!?!!!%!%?%?!!%%!?%%%%?!!!%%%%!!!%!%!!%%?!%!%%??!!!%?%%%%!%%!?%!?%!%%%%!?%!!%!%??%!%?!%?%%%%%%%%%?%%!%%%!%%%!%%?!?!%?!%!%%%!!%!?!%!!?%!%%%!??!?%?%!!%%?!%%%%!%%?!!%%%%%%?!%%??%!%%%%%!%%!%%%!%%%!%%%%%?%!!%!%%%%!%!??%!%!!!%%?!%!!!%%%%%%!!%%!%!%!%%!%%%!!%!%?%%%%%!%%%!%?%?!%!%%%?%?%!!!%?!!??!!!%%!%%%?!%%!%%%!%%%%???!%??%?!?!!!%%!%!?!%?%!%%!!%%?%%%!%!!%%%%??%%%%!!%!%%%!!!%%%%!%%%%%%%%%?%%%%?%?%%%?!!%%!%!%%!%?%!%%!!%?!%%?%!?!?%%%%%%%!%!%%%!%%%!!%!%!!??%?%%%%%%%%!?%!%%!%%?%%?%%%!%%%%!?!!?%%?%%%%?!%!%%%!?%%%?%%!?!%%%%!%%!%!%!%%!%?%%%%!?!!%??!!%!!!!%%!%%!!!!%!?%%!%%%!%!%!%%%?!??%%!!!%%%!%!%!%%!!%%!%!!%%?%!%%?%%%!!!%!%%%?%%%%%%%%%!%%%!%%!%!%%?%%%!?!!%%%?%???!!!??%%!%%%?!!!!?%%%!%!%!!%!%%!%%%???%%??%!?%%%%!%%%!%!%!!!!!!%%%??!!!?!?%!%%!%%!%?%!?!!%?!%%%%!!?!!!!?!%!%!%?%%%%%!!%%!!%!%%!!!%%!%%!%!%!%!!%%%!%??!%%?!!?%%%%?!%%!%!?%%??!??!%%%%%!%?!%%!!??%!!!%%?!?%!%!??%%!%?%!%%%!%!?!!!?!!??%%!%%?!%!?!!%!!??%!?!!!!?%?%!?%%%%%!!%%!%%!?!%?%!?%?%%!%?%%!%%%?%!!!!!%%!!%?!?%!!?!!?%%!!%!%!!%%%%!%!%?%!%%%??%!%!%!%%%%?!%!!?!!%!?%%?%!%?%!!!%%?!%%%!%?%%%!?!!?!%%%?%%%%%!!%%%%%!!%%%?%!?%!!%!%%!?!%!%%!%!?%!!!!%!%?!?%%%%%!!!%!?%!?%!%!%%?!!!%!!!%%??%!%?!%!??%%%!!%!??%%%%%%!?%%%!%%%%%?%%%%%!?%%!%?!!%%%!!!??%%%%%?%%%!%?%!!%%%%!%%?%%!%?%%!!%!%!!!%%%%%%%%!!!%%!!%!%?%?%!!?%%%!%!!%%%!%%???%!%%!?!%%?!!?%?%?%?%%%!%%%%%!%%!!!?!!!%%%!?%%!%%?!!!!%!?%%%!%!!?!!%!!!%?!!%%!!!!?!%%%%!!!??%%%?%%?%%%%%%%%%%%%%%!??%%%%!?%!!!?!%?%!%?%%%!?%%%%%!?%%%!%!%!!???%!!!%!?%!%%%!%%%!%?%!!%!?%%!!!!%?!?!!?!%!!%!%!???%??!%%!?!%!?!%%!???%??%!%%?!%!!!%?!%!?%!?!%?%%!%!%?%%??%%!!!?!%%!!?%%!%!!%%%!?!%?%%%%%!%%%!!%%%%??%%%%!%%!%%%!%%%!?%%?!%%!%!%%!%%!%?!%!!%!%%%%%%%!?%%%!%!!?!%!%%%!?!!?!!%?%?!?!%%%%%%?!!!??%%!%!%%%!%!!%%%%%%%!%%!!??%?!?%%?!!?!%%!%!!??%!!%?!??%%!%!!!?%!%%!!!?!%%!?!%??%!%%%!%%%!?%%%!%%?!?%!!%!!!%???%%?%%%!%%%!%%!%%%%%???%%!!%!%%?!%!!%%!?!%!!%?!%!!!?%%????%%%???%%%??%!?%!!!?%%!%%?%%%%!%%?%%!!%!?%??%%%%?%%!%!%%!%%!%%%!%?%!%%%!!%!%%?%?%%%!%!?%?%%%??!?!!!%%%!%%%%?%???%%%?!!!%%%%%!%!!?%%%%%?!%!%!!%%%?!????%?%!?!%!!%!%%%!?%?!!?%!!!!%?%!!!%!%%%%!%?%!%%!!!%%??!!!%!%!%%?!!%%%%?%%%%%??%!%!%!!!!%!!%?%%%%%!%!!?%!!?!!!%%%%!%%?!!%%?%%%%?!%%%%?!%!!%!%%!%%%!%!%%!?!!%!!?!%%%!!!%?%!%%%%!%!%%%!%%%!!%!%%!%??!?!%%!?!%%%!?!??!!!!!!??%!!%??!%%??!!%%!%%!!%!!%?!?%%?!%?%%%?!%!?%!!%%%?%%%%%!?!%!%%?!!%%%!!!%!!%%??%!!%?!!!%%%%%%?!!%?!?!%!%%?%!!%%%?!%%%?!!%%!!?%%!???%!%!%!%%!!!%!%%!%%!%?!%!%?%!!%%%%%!!%!%%!!!?!!%%%??!%%!%%?%!?!!!%!%!!!!?!!%%?!%!!!!%%??!!!?!!%%?%%%!%%%!!!%?%?!%%%?!!%%!!%?%!%!!%%%%!!%%%%!%%?!%?%!%!%%%?!?%%?!%%!%%%%!!%%%%?%!%?!!%!!!%%?%%!%%%!?%?%%%?!!%%!!%??!!!%%%%?%%?!??%!?%%?!%%!%%!%!!%?%?%%%%%?!!!%%%!!?%?!%!%%%%%?%%!%%?!%?!%??!!!!?%!%%%!%%%%%%%!%!%%%%!%!??%%%%!!%%!?%!%!%?%?%%%!!!?%%?%%!%!%%%%?%%!!!%%%!!!%!?%!%??%??!!!?%!!%%%%%?%%%!%%%?%%%%%%%?%%%!%!!%!!!%%%!%%?!%?%%%%%??%!!!%!?%%%%?!!%%!!%??!%!%%!%!!%?%%!!%!!!%!%!?%?%!%%!?!!%%%!!!?!!!%%!%!%%?!%?%%%%%!?%?!%%!!%?%%!??!%?!?%!!%%!!%%!%!!!%?!!%?%?%!%?!!%%?!%%%%%!%%%?!%%?!!!?!?!!!!%%!!!!%%%%%?!%!!%?!!%?%?%%!!!!?%%!!%!%%!%%!%%%?%?!??%%%%%%%%%%%%%!?!%%%?!%%!%%%%!?%?!%%%!?!?!%%%%?!?!!%%%%!%!?!??!!%%%%!%!%%!%%%!%!?%%%%!%!%%??!%%%%%%!%!%?!!?%?!%%%!%??!!%%%%?%%%?%?!%?%%?!!?%%!!?%?%!??%%!!!%!!?%%%%%?%?!!%?!!?%?%?!%%%%%?!%%?%!%%%?!!?!%%%!!!%?%%?!!!?!!%%?!%!%%!!!%!%!%%%%%!!?!%%%!%%??%%%!%%?%!!%!!?!%?%%?%%%%%!!%%!?!?%!%?%%%?!%!%%%?%!%?!%!?!!!%%%!?%%!%!!!%%%%%%!%%%%%%%!?%!%%%?%%%!!%%%!?!%%?%%%?%%?%%!!%%?%!%?%!!%!%!?!%%!%?%!%%!%?%%%%!?!!!%!%%%%!!!?%%?%%!%%??!?!%%!%?%%!!!?%!%%!%%!?%?!!?!%!?%!%!!%!%!?!%%%!!!!%%%?!%%%%%%!%%?!%%?%%%%%!%!!!!!!%%%%!!!!!????!!%!%!%%%%%%?%!%%%%%%%!%%%%%!?%%%!!%!%!%%%!%?%%%%!!!%?%%!!%%%%!?!!%?!%??%%%?!!!!!?!!!!%?%%!?!%%%!!?!?%%%%!!!!?%!!!%!%%%!!!%?!!!!%%%%%!%?!??!?!%!%%?%%!%%%%%%??%%%!!%%%??!?%%%%?%%%%%%!?!?%!?%?%!!!????!?%%%%!%%!!??%%%%!%!%!%%!%%%%?!!%%%!%%!%?%!%!%%!?%%%%!%%%?!%!%%?!%?%%??%!%!%!%!??!%%%%%!%%!!%?%!%??!%%%%!!%!%%%!%%!!!%?%%%!%!%%%!%?!%!?%?%!%%%%%?!!!%!%%%%!!?%?%%!!!%%%%!%%!%%?%%%%%?%%%%??!%%%?!%?!!?!!%%!%%!!%%!!%%??%!!%%%%%!!%!!??!!!!%%%%?%%!?%%%!%%???%%!!%!!%?%?%%%%?%%!%??!%!!%?%%%?%!!!?!!%%%%%!%%%!!%%%%%??!%%!%!!%!!%!!!%?%!!!???%%!%%!!%%!%%%!!!%!%%%%??%%%%%%?%%?%!!!!%%%!%%%!!%%!!!%%%!%%?%%!!?%!%%%!%%%!%%!?%!%!!!%%!%!!!%%%??!!!!!?%%!%?%%!!%?%?!!%?%%!!%?%%%%?!%!!%%!!?%%!%%%!%%%!%?%%!!%%%!!!???%!?%%!!%?!%!%%%%%%?%??%!%%%%!%%!%!%%?%!?%%%%!!!!%%?%%%!!!!!!!%!??%%!%!!%%?%!%!%!%!?!!!!!%%!!!?%%%!?%%!???%!?%!%!%!!%%!!!!!%%%%!?%!%%%?!!!%%%?!!%!!%%!!!!%??%%%!%!%!??%!%%!!!!%!%?%?!?%?%%%!!%!?%?%%%??!%%!!%!?%%%%?%%%!!%%%!%!%?%?%%%%%!%%%?%?%%?!!%%?%!%?%!!%!?%%%!%?!%%!%!???!!?!!%%!!%%%?!%%!%?!!%%?!!!%!!!%!%?!?%!%%!!!%?%?!!!??%?%?%!%!%??!%!%%%?!%%!%%%%?%!%!!%%?%%%%?!%%!%%%!%%%%!!%%?%!!%%%!!!??!%!%?!%%?%%???!!%%!%!%??%!%!%%?%%!!%!!?%?!!?!!!%%%%%%??%?%??%?!%?!?%!%???%%!%%%!%%?%%!?%%?!%%%%%!%%!?%?%!%!%%!!%??%?!%!%!%!%!%%%!?!%!%!%%%!!%%%%%%%%%???!!%%%%%%%%!!%%!?%!%%%%%%%%%?%%%%?%!%!%%?!%!??%%%%%!!%%!?!!%?%!%%%%%!!!%%?!??%?!%%!%%%!%?%%%???%%!!!%%??%%%%!!?!!%%?%?!?%%?%?%!%!%!!!%!!!%%?%!?!!%%%?!?%%%%%%?%%!%%!!!%%!%!!%!%?%%?%%!?!%!!?!!?%%!%%?%!?%!!!%%!!%%%?%%%?!!%?%!%%%%!%%%??!?%!%%!!!?%!?%%!!!?%?%%%!%%!%%%%!??!??%!!%!%%%!%%%%!%!!%%!!??%%%%!%!%%!%!!!%?%?!%%%?%?!%%?%!%!%%%%%!%??%%!%!!%?%%!%!!%%!?%!%?%?!!!%%%!!!?%???!!?!!%%?%!%%?%%!!!%!%%!?%?!!!!%%!!!!!!%!!%!%%!%?%!%%%!%!%?%!%?%?!!%!%%!?!!%!%?%?%%!?%??%?!%%!?!%%!%!%!%%?%%%!!%%%%!!!!!!!!!%?%%???!%!%%%!?%!%%!!!%!%!!%%%!!??%!!%%!%%%%!?!%%%!%?!%!?%!?%%?!?!%%?%?%!%%%!!?%!%?%%!?%!!%%!%%!%?%%%!%!%%?%?%!%%??!?%!%!%?%%!%?%%%!!!%%!??!%?%%%!!%?!%!%%!%!%%%??%?!?!%!!!?%!!%??%%!%%?!%!!?!%%!%%%?%%%!%!%!?%!???%%%%!!%!%?!!%!%%!%!%?%?%?!%!%%%!!?%!%!!%%!%!%?%%?%!!!!?%!!%?%%!%%!%%%%%?!?%%?%!?%!!!!!!!%!%!%!!%%??%!!%%%%%%!%%!??!?%!%%!!%%!!%%%!!%!!%%!?%!%!%!!!%%!!!%%!?!%%!?%%%%?%?!%?%!%%!!%%!!%!?!!%!??!%?%%!?%%!%!!%%!!!%%?%!!%%%%%!!%%!%%%%?!%!!%?%%%!!%!%!%%!%%%%%!!%%!?!%?!%?%%!!%!??!!%?!!%%??%%??%?!!%!%!%%%%?!%!!%?%%%!!%!%%?%%%!%%?%!%!!%!%!!?!?%%!%!%%%!!?!%%?!?%!%%??%%!?!!%%%%!%!%!%%%?%%%%%!%%%!%%!!!%%!!%?%%!%%!?%!!%%!%?%!!%%!%%%?%%!!!!!%%?%%%!?%?!%%!%%!!%?!!%?!%%%!!%!%!%!%!!%!??!%%%%%%%!?%??!%%!?!%!%!?!!%?%!%?%%%%!?%%%!%%%?%!%%!????!%%!%%!!%!!%%%!?!?%%%%%%?%%?!%?!!!%!!%!%!%!?%?!!%%%???%%%%!!%!!?!?%!%%!%%!!%%??!?%%!!!?!%%%%!%!%%%%!%%%%!!%!?%%%!!%?%?%%?%!??!!%!%!!%%%%%%!!%?!%%!%%??%?!%%%%!!%%?!!%!!!!%!?%!%%%%!!%%!%!!!%??!?%%%?%%%%%?%%%%!%?!%%!%?%%?%?%??%%!%!%!?%!!!!%?%!%%%%%%???%%%%?%?%%!?%!%%%???%%!%!%%%%%%?%%%%%?!??%%%%%?%%!%!?%?%%%%%%!%!!%%%%%!!!%!%%???!%!%!%%%?!%!%%%!%!?%%!!!!?!%!!%%%%%%?!%%%%!%%%!%!?%%!!!%?%%!!!%!%%%%%%%%?%%?!?!!!!!!!%!%!?%%?%?%?%!?%%!?%??!%%?%?%%%!!!!%%?%?%!%%%!%!%%??!!!%!?!%%%%!%!%!!!!!!%!?!!!!%?%%?!%%%%%!%%?!%!%%%?!%%%%%!%!%!?!!?%??!!!%!%?!?!%%!%%%%?%%%!%%?!!!%%!!%%!%%!?!!%%??%!%%!?%!!%%%?!!?%!%%%!!%!%!%!%%!%!%%%%%!!?!%?!%?%%!%!!?!?!????%?%%!?!!%!%%!%%!%%?%!!%?%%%%%%%!!%%%%!!%%!%%!%!!!!!%%%%%?!!%%%!?!???!!?%%?%?%%%%%??%%?!!?!?%%%%%!%!%!!%%!!%%%%!%%%!?!%!?!!!?!?!?!!?%%%!!!%%%!%%!!!!?!%%%%?%?%!?%%?%%!?%!%!??%!%%?%!!??!%!%%%%!!%!!%%!%!?!%%%%!%%!!!%%%!%!!%!%%%%%%%!!%!%?%!%%!!%%?!!??%%!%%!%!%!!%%!!!%!%!!%!%!!%%?!%!%%%%%!?%!?!%%%%?%!?!!?%??%%%?%%%%%??%!??%%!%!%!?%%%%!!%?!???!%%%!!%%?!%%%!!%??%%!%%!%!?%?%?%?!?%!?%%%!?!%%%?!!!??!%!%!%!!%??!%?%%!%%%!?%!%%?!!%!!%%!??%?!?%!%%!%??%!%%%!!!!!%%%%!!%%%!%%!%?%%!%!%%!%%!%!%%%%!?!!!%%%!%%!%?%%!%?!%%%!%!%!!%!?%?!???%!!%%!%%%!%?%%!%!%%%%%%%!%?!%!%?!!!?%!%%!!%!%%!?%??%?%!%%!?!%%!%?!%%%!!%%%!%%!!?%!%%%%%?%%%%%%%%%%%!?!??!!??!%%!!!%%!!!%!?!!?%%%%%%%!%!%%!!?%!??!?!??!?%%%%%!??%%%!!!%!!%!%!!%%!!!!!%!%%!!?%?%%%??!%!!!%%!?%%%??%??%%%%?!%?%%!!%!%%?%%!?%!%%!%%!!?!!%%?%%!%!?%!!?!!!?!%!!%%??%?%!!!?%?!!%?!!%!?%!%?!!!%%!%%!%?!%!%%?!!?%%%?!%%???%!%%%%!?%!%%%%!?%!!%%%%%??!%?%%%!%!??%%%?%%%%%!?!%!%!%!!%!!%!%!%?!!%!!?%!%%?%%%%?!!%%%%!!?%?%?!!%%!%?!?!%%%%%?!%!%?%!%%%?!%!!??!!%%%%%%!%!%%!!%%!!!%!%!%!%%%%%?%?!!!%!!!!%%?!%%%!!!!!!%%%%%!?!%!%!?%%!%%%!!%%!!!%!%%?%!%%!%%%!%%%!%%!!%%!?%!%%%%?%!?!%!%!%?!!?!%%%%!!!%!%?%%!%%!%?!%%%!%!!%%!!?%!%%%?%?%%%%%!%%%%%%!%?%?%?!%%%%%!%%%!%!?%%?!?!!%?%?!%!%??%%%%%!!%!!!!!?!%?!!%!%!!%?%!%?%?!%!%!!%?%!%!?%%?!%%!%%!%%!!%??%!!!%!%!!?!%!!?!?%!%!!?%%!!?%%!%%%%!?!!%!!?!%!%%!%%!!%%!%!!!?!%%??%!%??!%%!%%!!!%%%%!!?!%!%%%%?%%%%%%%%%%%!%?%%!?!!%!!%%!%%??%%%%%?!!%%%%%?!%%!%%%?%!!!!%%%%!%%%%?%%!%%!%?%?!?!%%!?!%%?%%%%%%!!%!!!?!%%%%%%%!?%!%!???%%%!!!!!%!%%!!%%%!%?%!!?%%%%?%%%%?%%%?%%!!!%%%%%!?!?!!%%!%?%%%!!%%%%?%!%!!%!!%%%!!!?!?%?%?%?%!?!%%%%%%%?%!!!%%%%!%!!%???%?%%%%%!%%?!!%%%%%%%%!%!%!%%%!!!%%%%%!!??!!?%!???%%%!%%%?%??%%%!%%%!%?!?%?%%%%%?!?%%!%%%!!??!?%%?%%??!%!!%!!!%?!%!%!%!!?%?!!%%%!??%!?!!%!!!?!?%!!%%%??!!!%%??%%?%%%%!%%%!!%!%%%!!!!!!!%%%?!!%%!%!%!!%!!%%!!%!%!%%!!?%%?!??%%%%%%%!%%!!%%!%!!%?!!%?%?!%%%%%%?!?!%!%!??!%!?!%%?!%%!!%%?!%%!%??%!%%%%!%%%%%%!!?%%%%!%!!??%%%?!%!%%!?%%%%!!?!!%?%%?%!%??%!?!!%%%%%%?%%!%%?!%%?%%%%%%%%%%?%!%%%?!%%%%!%%!%!%%%!%!%%?%%%%%%!!%%%%%%%%!%!?%%%%%!%!%%?!%!%!?%%%??%%?%!??!%!?%%!!%?%%%!%%!%%??!!!!?!%%?%%%!%%%!%%!%%%!!??!?!%%%!%%?%%%%%%?%?%%!!%?%%??%?!!?%?%!!?%%%!%%!?%!%!!!%?%%%%%%!%!!?%!%?%?!%%%!!%%?%%%%!!?%!%?%%!%%%%!%!?%%%%!%%%!?%!%!!!%%%?%!%?%%%%!%!%!!%%%!%!%!%%?!??%!!!?!%!?%%%%!!%!%%!?%!%???!?!!!%%%!?%%?%?%%%!%%!%%!%%!%!!%%%??%!%%%?%%%!%%%!!%%%??%%%%!%%!%!?!%?!%!%%!%!%!%!!%%%%%%?!%%?%%%?!?!%!!%!%!%%%%!!?%!!%%%?%!!%?????!???%%?%!!!%%%!!!%?!!%%!%!??%%!!!%%!!!%%!%%%%%%?%%%%!%!!%%%%?%!?%%?!?%%%??%%%!!%!%!!?!!%!%!%%%%!!%%%?!!%!!!%%%%%!?%%%!%%!%%%?%!%%%%%%%%!?%%!%!!!!%%%%%?!%!%%?%%%%%!!%%%%%!%!?!%%!%!%!!%?!%%?%!%%%!!!%?!!!%?%%%!%!%%%%%%!?%%!?%%%%!%%%!!%!%??!!%!%%!!!%!%%!?%!%%%!%!%%!?!!%!%%%!?!%!?%!?!%!!%!!%%%!?%%%%%%!?%!%?%%%%!%?%!?%!%!?!?!%??!%%%??!!?%%%?!%!%??%%%?!!!!%%%?!!%!%!%%%%!!?%!%%%!%?%??%%!%%%?!!?%!%?!??%%%%%%!%?%%?%%!%?!%%%!!%%%!!?!%?%?%?%!%!%?%%%!%%?%!%!!%%%?%!%%%!%%!%!!!!?!??%!!!??!?%%??!%!%!!!%%!!%!!%%?!%?%%%%%%!?!%!!?%?!%!!%!!%?!!%!%%??%%!!%!!!%%?!?!!?%!%%%!%!%!%?!%?!?%!%%!?%%?%%%!%!%?!!??!!!?!%%%%!%%?!!%!%!!%%!!?%%!%%!%?!!!??!%!!%!%!%!%!%%!%%%!??!%!%?!!???%!%?%!?%%!%%%%%%!%%%!%?%%!%!!!??!%!?!?!%?!!!%%%!%!??%%%%%!!!!%??%!!!!?%?%%!%!%%%!%%%%%%%%%%?%?%!!%%%!%!!%%!!%%%??%%!?!!%%%!%!!?%!!?!!%!%%%?!%?%!%%%%%!!%%%%!??!?%!%!?!!%%?!%!%!!%%!!!%%!!!%!%%!?%%%?!????!%%?!?!?!!%!%!%%%%?%?!%!!?%!%%%??%%!?%?!%?%%?!?!%%?!%!%%?%!%!!%%%%!%?!%%%%%%%!%!%!%!!%%%%%!?%%%%%?!!%?%?%%%%!%??!%%!%%%!?%%?!!%!%%!%?!??%%%%!!?%%%%?%?!%%!!!???%?!%%?!%!%?%%%%?%!%!%%!%?%!?%!!%!!%%?%!%%%??%!!?%%!%?!%!%!!%%%%%%%%%!%%!!!%!?%?%!!?%!%%!!%%%!!%%!%%!%%!%%!!?!?%?%%!!?%%%!?%%%%%!%%!%!!!%!%?!!%!%!?!!%%%!!!%!%%?!!%!!%!!!%%%%!%%!%!%%!!%?%!%!!!%!!%%%%%%?%?!?!?%%%%!%!!!%%?%!!%%!!%%%%!%%%!%?!!%%%!%??!!!!%%?!%!%%!%%%?!%%%!%?%%!!??!%!%!!!%%!%%%!!%!%%?!!%??%!%%%!%!!?!%!%!%????%!!%%!?%%!!!?%%%%%%%!?!%?%%!!%??%?%%!%!!!!%?!!%%!%!?!!%%%!%%%%%%%!%?!?!%?%!%?!?!!%?!?%%%%%%%!!!%%%!?%%!%%%%%%!!!!??%%!%%!%%!!%%%!!%?!!!%%%%?!%!?%?!%!%!?%!%%%!%%!!?!!!%!!%%%?%%?%%!?!!!??%!?!%%!!%!%?%!?%?!%%%%?!!%%!%%%!%%?!%!??%??!!%%?%%%?!%!!%?%?%%?%!!%%??!%?%%%?%%!%??%?%!?!%?%!!!%%!%%!?!!!%%!%%!!%%!!%%%!?!%!?!?%%?%%!!%%!!%%%?!%!%!!!?%!%%%%!!?%%!%%%%!%%!!%%!?%?%!!%%!%!?%%?%%%%%%!?!%?%!?%%%?!%%%%%%%!!%%?%%%!!%?%%%!!%!!%!!?%!?!!%!!?%%!?!?%?!%?!?%%%?%!%!%???!%%%%%%!?%%!%%%%!!!?%?%%%%?%%!??%%%%!!??!!!?!?%!!%%!%!!!!!%!!%?!!!?%!%!!%%%!!!!%%?!!?%?!?%%!!%%%%!!!??!%%!!%?!%?%!!!%!%!!!%%?!!??%%%%%!%!%%%%%%?%!%!%!?%%%%%%%!%!%%%!%%%%%%%%!%%%%!!%%?!!%%%%%!!%%%%%%!!%!%!%%?%?%?%!??!!??%%?!??!!?%!%%%!%?!??%??!%%!%%%!%!%!%!!?%?!%!!%!!%!%!%%!?!%?%%%?%!%%%!%!%%!!!%!??%%%??%??!%?!!!!%??%%%%?%!?%%?%!?!!?!%!!%!%%!!%%!!%!%%!%??!%!!?%%%%%?!!?%!!!!!%%%%?%!!!?!%!%?%!%?%%%!%!%%!?!?!!!!%!%!?%%%!%!%!%!!!?%!?!%?!%!!%%%%!%!%!%%!%%?!%?!!?%!%?%%%!?%%%!!%%%!!?%!%!%!???%?%???!%!%%!!%%%!%%?%!%%!%!%?%%!??%%!%%!%!%?%%%!!%%!%%%%%!!!!%%???%%!%%%!!%!%%%!%%!%?%%%%%!%!?!!?%%%?!%%?!%%?%?%%!!?!%%%%!???%%!!%%?!%!%%%%%%%!%?%%!%%!?%%%?%%?%%%%!%%!!?!%!%!!%???%!?%!%%%!%%?%%%!%?!%%?!%%%%%%!%!?!%%%!!%%%!?%?%%%%%!?%!%!%!%%%%!%?%??!?!%%%%%?!%!?!!!?%%!!?!!!%?!?!?%%%!!!%%%!%!!?!?%%%!?!%%!%%!!%%!!!!%?%%!%!!!!%%%!?!!%?!!!!%!!%?%?%!?%%%!!%%%%!!!!!?%?%%%?!%!%%%%%%?!%%?%%%!%!!??%?!!%?!%!!%!%%???!%!!%?!%!?%?!%!!!%%%!!??!%!%!!!%%!%?%%%!%!!%!%!?%!%%?%!!%!%%%%!%!!%!!!!?!!?!?%??%!%%?%?%%!?%!!%%%!%%%%!!!?%%!%!%%!%!!%?%?%?%!%!?%%%%!%?%%%%?!%%!%%%?!%%%!%!%?!%%%%%!!%%!?%!!????!!!??%%?!?!%?!%!%%!%%!!%!?!!??%?%!?%!%%!!!%%!?%??%%%%%%%%%?!%%!!!!%!%!!%%%!?%%?!%%??!!??!%%??!%%%%%!%%%%%!!???%?!!!%?!???!%%!%%%!%%%!%%??%?%!!?%!!!!?!?%%%!?%%!%%!!??!!%%!!%%!%%!%%!?%%%%!%%%!%?!?%%%!%%%?!%%!!%?!?%%%%!!!!!%!%%%%?%%%!%%!%?%!?!%!?%!%%?%!!!!!!%%!%%%%?%%?!?%?%!%!!!%!%%%%!%?!%!%%!!%%!%%!%%%!%%?%!%%!!?%%%!!?%!%%%%!??!??%%%%%?!%?%!!%%%%?!!!!!%?%%!!?%%!%%%!%%%%?%%%%%?%!%%%?%%%?%%!!%%!!???%%%?!%?!%!?%%%%!%!%!!!%!%?%%%!%!%%!?%%?%?%!!%%%!!%%!%%!?!!!!!%%!%!%!%%%%%%%!!%!%!%!%??%!%!!%!!%%!%!!!?%%???%!%%?%%%?%%!!!%!%!!%?%%!!!%!%%%!?%?!?%%%!%?!?%%%?!!%%%%!!%!!!!!??%!%!%!%%!!%%!%!!%%?!%%!!%%%%!%%%%!%?%!%%!%!%%!!%%??!??%!!%?!%%%!%%%!%%??%?%%%?%?%%!%!?%%%%%%%?%!!?!%%!%%%%%!%??%%%%!%%!%%!%!!%%%%%?%%%%!%!%?!!%%!!?%?%?!?%?%%??%!!!%%%%!%%!%%%%!?!%%!!!!%%%?!!!%!%%!!!%%%%%%%!?!!!%!%%!%%?%!?!%!?!%%!!%%%??%%%!!!%%%%?!!!%%%!%%!?%!%?!!%%!%?%%%%%%?%?%%!!%%!!??!!%!!%!?%%!!!%?!%%!%%!%%%%?!!!%%!%%!%!!%!%!??!%!!%%?!!%%%!%%?!%?%?!!%%%!!?%?%%!%%%%%!%%!!%%%%?%!%?%%!%%%!!%!!?!%%%!!!%?!%%%?%%!%!%%!!%?%%!!?!%!%!%%?%%!%%%!??!%!!%!!!%!%??%?%!%%%%?!!!%?!!!%%%%%%%%%%%%%%%%%!%%!%!%!%!?!?%%%%%!%%%%%?%!!%%%?!%?%??%%!%!?!%%?%!!!?%%!!!%!!%%!%%%%%?%??!%%!?%??%!?%!%%%%?!!%%!%%!!!?!%%!%!%!%!%?!!%!%?%!?!%?!%%!%%!!??%?!?%%%%!%!????!%!!!%?!!%%%%!%??%!%%?%%%?!?%??%!!%%%?%!%!?%%%!!%%?%!%!?!?!%?!%?%%!%%?%?%!%!%%!%%%!%%%%%%%%%!!%%!!%!%%%?!!!!%%!!!%%!?!%!%!%!%%!!?%%%%?%!!%!??%%%%%?%%%%%?!%!!%%%?!?%%%%!%!%%?%?!%?%%!?%?!%%%%!?%%?%%!!?!%%!?!%!%%%!!%!%%!%%%!%%%%%%%%!!%!%%%!!%%%?!%!%?!%?%%!!%%?%%%%??%%!%!%!%%%!!!!!!%?!?%%%%%?%%!!%?!?!%?%%%%%!!%%%%%%!!!??!!%%!%!%%%%%!!!%%??%%%?!%!%?%%!%!?!?!%%%%!!!!?%!!?!!?!!?!!?%!%!!%?%%%?%!%%!%!!%!!%%%?!%!!?%!%!!??!%%%%%%%%!?%%!%?%!%%!!!!%!!!%%!%%%?!!%!%!!!%%%%?!%%%!%?!%%??%?%?%%!!%%!!%?%??!!!%%%%?!?%%???%??!%%!%?!%%%%%%%%%!%%%%?!%!!?!%?%!!%%!%%%!!?%?%%%!?!???!!%!%%!?!!!%!%?!?%%?%?%?!?%%!%!!%%??%%%%%!%?!%?!!?%%!!!!!%!!%%?!%%?!!%!%!!!?!%!%!%%%???%%%%!%!!%!%%%%%!?%%%%%%%%%%%!%%!%%!?%?%!?!!%%%%!!%!!%?%%%%%!!%%?%%?!%%!%!?%%?????!%?!%!!?!!%%!!%?%!!%!??%!!?%!%%!!??%%%!!!%?%?!!%?!!!%%%%!!!%%!%!%%!!%%%%?!%!%%%%%%%!?%??!!%!%%%?%!%!!%!?%!?%??%!%!!%?%%%?!!!?%%!!%!!%%%%?%%??%%!%%%%??%%!%%?%%%!!%%%%%%%%?!?!%?!%!%!!%%?!!%%!!!!%!!!!?%??%%??%??%??%!%%%%!%!!%%%%%!%%%%%?%!!!%%!%!!%?%%!%!!!%!?!!%%%!??%?%%%%%%%!%??!!%%!%!!%!%??!%%%!!!?!%%?!!!!%!!%?%!?!!%!%!!?%?%!!?%%%?!?%!!%%?%?%%!!%%%!%%!!%%?%%!!%!?%%!%!%%%%%%!!!!!!%%%%!?!!%%!!%%%%%!%?!!%%!%%!!%?%!%%!?!%%??!%!!?%!%!!!?%?!?%!!%!%?%?%%?%!!!?!!%?!%%%!?!%!!?%!!%!%%!%!?!?%!?%%%%%?%?%%%%?!%?%!%!%?%%?%??!%!%?%%!%%?!%%!!%?!!!!%%%!%%%%%%!!?!?%!%!%%?!%%%!!%%%!%!!%%%%!%?%!%!!%%%%!%%!%%!?%%%%?!%%!?%%!%??!?!!%!!%%%%%!%%?%!!%!%!?!%%%!%?!%%%!%?!!!%%!%?%%%%%%?%!?%%!?!!%%!%?!!%!!!%!%%!?%%%%!%%!?%%%!!%!%!%%%%%%?%!%%!?%!!!!!!%!%!%%!%?%%!%!%%%?%%%%%%%%!%!%!!!!?%%!%%%%%!!%?!%!%!??%?%%%%%%%!!?!!!!%%!!%%!%%!!?%?!%?%?%!!%!%!!!!%%!!??%!%%?%??%%%!%?!?%%!!%%%%%%!%%%%!%%%!!!?%?!?!!%%!?%%!??!%%%%%!?%%!%%%!!%!?%%%?%%?%%%!%!?!%!!!%%!?%?%%?!%%!!%%%??!!%%%%%%!%%!!%!%%!!?%%%%%?%!!!%%%!!!!!%%!!%??%%!%!!!%?%%?%!!!%%!%!!??%?!%!%%%%%%%%!!%%%%%!%%!?!%%%!?%!?!%!!?!%%%!%!!!%%%%%!%%%%%%?%!!?%!%??%%%%!%!%?!%!%?%?%%!%!!??!%?%%!%%%%%%%%%%!?!?!%%!%?%%%%%%?%?!!?!%!%!!%!!!?%%!%%!%?%?!%%?!!%%%!%!!%!%%!%%!?%!%!%%!!?!%%!%??%!!%%!%%!!%!%%%%!?%%!%?!??!??!%!%%%%%?!%!!!!!!%?!!%??%%%%!?!%?%?%%%!%!!!%%%%%%%!!%?%?!?%%!!!%?!%?%%%!%%!%?!!%%%%?%%%!%!?%??%%!!!!!%%?%%??%!!%!%!!%!%%%?!!%!!%%?%%%!%?%?!%!!%!%%?%%%%%%!%!%!%%!%%%%%?%!%!%!?%?%%?%!%!?%!%!!!!%!?%!?%??!!%%!%%!??!!?%%%%%!!%?%?%%?%%????%!%?%?%!%!?%%%%!%%!%!?%!!!%!%!?%!!!?%%%%!%%!?%%?%%%!!!%%%!%%!!!%?%%%!!%%%%!%%!%???%%%%%%!%?%%!%%%!?%%%!??!?%?!%!%%%?!!%!??!!%!!?%%%!!!!%%%%%!%%!!%%?!!?%%!%%!?%%%!%%!!%!%!%??!%?!!?%%%!%!%?%!%%%%%?%%%%%%??%%%%%%%?!?%!%!!%!!!%!!!!%%?!!!%%!!!!?!%%!?%?%%?%%!!!%?%%%%%??!?%%%!%%!!%%%%!%!!%%%%?!%%!%!!%!%!!?%??%!%!%?%?%!!%!!%?!?%%%!%!!%!%%%%%!!!!?%!%%!%!%!!!%%%!!%%%%!!%%%%!%%%%%!!!%%%!!%!??!!%%!%?%%%?!!?%%!%!!!%%?%!%!%%%!%!%!???%%%?!!!!!!%?%%!%?!!!?%!%%%%!!?!%%!%!%%%%%!!!!%!??%!%!%!!%!??%!!%!%!%!%%!%%?!!?%!%%?%!%%%%%?!!!?!%!?!!?%!!%!%!%!!!?!%%%?%!?%%%%%%%!!!%!%!%?%%%?%!?%!!%%%?%!%!!!%%?%!!%!?%!!%%%%%?%%?%%!%%!!%?%%%%?%%%!%?%?%!%!?%!%!?%!?!%%!%%%%?!!?!%%%%?!!%%%%!!!?%?%%!%%%!%%%%!%%%%?%?%%%!!!!?%!%!%%!%?%!!%!!%!!!%%%%%%%!%%%%%!%!!%%%%!!%??%%!??%!%?%%%%%!%%!%%!!?%!%%%%!%%%!%%?%!!%!%!%%!%!!?%%!%%!%!?%!%%???%!%!!!!%!%!%?!!%?%!?%%!%!%!%!?%!%%%%%!!!!?%?%!!%!!?%!%!%%?%%!?%%%!!!%!!%!%%!!!?!!%%%!!?%%%%%%%%!%!!%%%%%!!!%!!?!!?%%!%%?%!!?%?%%!!!%?%?%!!!%?%%%??!%%%?!%!!%!!%!?!?%%%??%!!%?%%%?%%??%!%!%%%?!!%%!??%%%!%?%%%%!!!?%%??%%%!!!%!?%!!%!?!%!%%?%%!!%?!%?%!!!%%%?!!!!!%???%!?%%%!?%!!!!!%%!%!?!%%!%%?!!%%!%!%!??!!!!!!!!??!!???%%!%!%!%%!%%!?!%?%?%%%!?%%!%%!%%%%!%!%?!%%?!%%%?!%!%!?!%!?!%%?%!%!!!!%%?!%!!!!%!%!!%%%%%?!!?%%%!!%%%?!%!?!!%?%!%!!!!%?%%%%%?!?!!%%%!!%!!%%?%%!!!!%?%%%!?!!!%?%?%!%%!!%!%%%%!%%%%!%%?!!%%%?%!!%%%!%%?%!!%?%%%%!%!%%!!%!%%%!!!!!!???%!%%%!%!%!!!%%%?%%%??!%%%?!%!%!%%!%%%!!%%!%!%?!%?%%?!%!%?!!!!%!!%%!%?%%%%?%%%%!%%%%%%?%!!!?%??!%%%!!%%?!!%?%!?%%%!!!!!?%%%%%%%???!%?!%!%?!!%%%?%!%!!?%!%%%!?%!%%%??%??%%%?%%%!?%%%%!!%%!%%?%!%%!%!%???%!!%%%?%?%!%%??!!%%%%%!%?%!???%%!%%%%?%!%%%?%?!?%!%%%%?%!%?!%!?%?%%%%%!%!%!%!!!?%!%!%%!?!!%%%%!%%%!!%!?%?!!!%%!?%!%!!!!%??%?%%!%%%!?%%%%%%%?%??%?!%%%%%%%%%%!!?!%?%!%%%!!%!!%%%!?%%!%?!!?%?%!%!%%%%!?%%%????%?%!%!%??%%!%??%%%!!%%!%%%!%!!%!!??!%%%%%!!!!!!!%?%%!%!%!%!?%!%%%!%?%%%%?!!%%!%%!%!?%?!%%%?%!??%%%%!%?%%!%!%%%!%!%%!%%!!!?%!?!%%%!!%%%!%!%!%?!%%?%%!!%%%!?%%%%!??%?!!??!!%!%?!%%?%%%?!%%%%%!!%!%!!%!%!%%!!%%!%!%??%%?%!%?!?!%%%?!!%!%%%!%!!%%%%!?%?%%!?%?%%!?!%%%%%?%!?%%%%!!!??!%!%%!%%!?%%??!!%?!%?!?!!!?!?%%?!%%!?!%!?%%%?!!?!!!%%?!?%!!????%%%%%!%%!%%%%%%!%!%!%%%%%%%!%%!!!%%!%!%%!!!%?%%!%%%!?%%?%?%%%!?%%%?%!%%%%!!!%%%!%!%%!%?!?%!%!%!!%%%?%?%!!!%!!%%!!!%%%!?%!%!%!%%%%%!??%!%%%%!!??!!!!???!!!!?!?!%?%!!?!!%%%%%?%%!?!%??!!%?%!!!%%%?!%%!%%!!!!%%%%!?????!%?%!%?%%!!%!!!!%!!?%!!%%%%%!?!!?!!!?!!!?%!%!??%!!%%%??%%!!!%!%!?%%%%%%%?!%%%%!%%?%???%%%%!%%!?%!%?%!%%!?%!%!?%!%!!!%%%!%%%%%!!%%!%!!%%?%%%?%!!!%!!!%!%?%!?%%!%!%%%?%??%!!!!!%?%!!?!%!?%!%!%!!!%?%%?!!!%%!%!%!!!!!!???%!%%%%!!%?!%!%?%?!?!%!%!?!!!%%!%%!???!%%%%?%%!%%?%%%%!?%%%!%%%%%%%?%!!!%%!!%%!%!?%!%%!??!%??%!%!!!?%!%%%%%?!?%%!!?!!%!!%%!%%?%!%!%%!!!?%%!?!%%%%%%!!!%%%?!!?!%!%%!%?%!%%%?!!!%!!%%%!!%%%%%!%%%!%%%%%%%!!!!!%%?%?%!!?!%%!?!?!%??%!%!!!!%!?%%%!?!?%!%?!%!!%?!!?%??%%%!%!!!!!?!%!%!%??%%%!%%??!%?!%?%%%!!%!?%%?????%%%%!!!%?%%%%!%!!??!%%%?%%!%!??%%%%!!%%?%?%??%%!!%!%??%%%%!%%!!!?%%!?%!%!!%%?!%%!%!%!!%!%!%%!!%!%%!%!!!%??%!%!!%!%%!!%%%?!%%%!?%?!!!!%!%%%%!!!?%%!%!?%%%!%%%%??!%?%%%%%?%%?%!?%%!?!!%%?%!%%%!?%!!!!%!!?!?%%!%!!!!!?%%%%%!%!%!%%%%%%?!%!%!%%!%%!!%%!!!!!!?!!!%?!%%%?!%!%!%!%!?!%!!?%%?%?%%%!!!!!!%!!!%%!%!%%%!!%%%?%!%%!%!%!!%%!%?%!!?%?!%%!%!%!%%%!%!?%%%%?!!%%%?%?!%?%?!!!?!??%!%%!!?!!%!!!!?%!%!!%?!!%%?%?!??!%%!!?%%%!%!%?!!!%%?%%?%%%%!%%!!!%%%%%!!!?%%%%?%?!!!%%!%%%!%?%%??%!!%?%%%!%%%%!%%%!%%%%!%!%!!%%??!!?!?!?%!%!%?%!%?%%%?%%?!!!%%%%%%?!?%!!!%!%%?%!%?%!!%?%!%%%%!%!%%!!?!%!%!%?!?%%!!%!%%%%%?%%!%%%%%?!%%!!!!!!?%!%??!%?%!%%%?%%?%%%!%?%!!!%!%%!?%%%?!?%%%?!%??%!%!?!!%!%%!%??!!%%?!!!!!!!%%%%?!!%!!%%%!!%!!!?%%!%%%?!!?%%%%%!!!?%%!??%!!%%!%%!!!?!!%%%%%%%?%!!!!?!%%!!%%%?%!%!%!%?!%%%%%!%?%%%%%!?!!!?%%!?!!?!!!?%%%?!!!%!%%%%!%%!%!%%!%?!%!!!!%%%%%!?%!!!!%%%!!!%?%?!?%!%!%%%!?!%%!?!%!%?!%%%?%%%%?%!%!!%!!!%!!!!%%!!%%!%?%%?!%%%%%!?!%%!?%!!%%%?%?!%%%?%?!%!%!%%!?%%%!%?%%%%%!??%!%%%%??%!%%?%?%?!%!?!!?!%?%%%!!%%%%%!!%!%%%%??!%%%%!%!!%!!?%!%?!!!%!!!%%%%!!?%!%!%%!?%%!!!%!!!!!%?%!%!%%%%!%!??!!!!!??!?%!%%%!!!%%!?%!!?%%!!%!%%!!%%!?%%!!%!%%%!%?%%%%!!!%%!!!!?%%%%%%%%?%!?%?%%%%%%%!%?%%?%?%%!?!!!%%?!!%%!%%!?!!!%!!??%?%!%%!%!%!?%!%%%?!%!%%%???!%?!%%%%%!%!%%%%?%!%!!%%%?%%!%!%%%!%%?!%%%!?%?!%?%!%%%%%%%%!%!!!!!%%?!!?!!%?!?%?%%%%!%%%%%!%!%%!%%%%!%!%!%?%%%%%%%!%%%!!!?%!%?%%!%%??%%%%%!?%%?%!!??%%%!!%!??!??!!!%?%%!%%%%!!!%!!?!?%%?%!!%!%!%!?%%!!%%%??!%!?!%%%!%!!!!%!%%!!%%%%??%%!%!%%?%%!%?!%%!%??%%!!?%%%!%%%!?%!%!%?%%!%%!%!%%!!%%%%%!%!%?!!%%?!?%%%%?!?!%!%?%!%?!%%%!?!!?!%!??%%!%%%%%%%?%!!%!!!??%%!!%%%%?%%%!!!%%!!!!%!?!!%%%%%%%%%!!%!!%!%!?%%!?!%?!!%%%%%!%???%!%%%%%%??!!%%%!%!!!!?%?%%!!?%!%?!%%?%%%%!??%%%!!!%%!%?!!!%?%%!?!%???%%%%?%%%%!!!%!!%%!?%??%!!!%%???%?%!%?%%!%?!?%%%%?!!%!%%!%%?%!!%!%?%%!%!!!%!%!%%%%!%?!%?%!%%!%??%?!%%%%?%%%?%%?%%%%!%%!!!%%!?%!?%%!?!!%%!%%!%%?!%%%%!!%%%?%??%%%!!??%%%?!%%!%!!%!?%%?%%%!?!?%%!%?!%!?!!!!%!%!%%%%!%%!%%%%?!!%%!%?%!%%?!%!%!%!!?%%!%%!!!!%%!!???%%?%%%%%?!%!%!!%?!%?!%%!%%%%%!?%%!!???%!!?%?!%!%!%!%%%?%!!%?!!%!%%??!??%!%%!%%!!?%!%?!!?!!%%!!%%%!%%%%??%?%!?%!!%%?%%%!%!?!%!!%?%%%!%%%?%?!%!!%?!?%%!!%%?!??%!%%%%%%%%?!!?%!%???%%!%!%!%%!%!%!%%!!%%?%%%!???%%%%%!!%%!!?!!?%!!!!!!!%!??%%%%?%%?!%%%%?!%%???%!?%%%%%!!%%!!!%?%%%?%!%%%!%!%!%%!%%?%%!!%!%%%!!%%%!%?!%%%?%%%%!!!!!?%!!%?%!%!%%!?%%%%%%!%%!!%%!!%!!%!%?!%!%!!?!%?%!%!%%?%?%%!%%%?!%%!%%?!!%!%%%!%%%%?%%?%!%%?%%!?%?%!%%!%!!?!%%!%?!!!?%%?%%!!%%!%%%%?%%%!?%!%!%?%%!%!!!%%!%!%%!?%%%%!!%!%%!?%%!!!?%??!%!%?%%%%!?!!?!%%%!%%?!?!!%%!!?%%%!!%%%%!%?%!%%!?%%%%%%%?!?%?%!?!%!%%%%!?%!%%%?%!?%%?%%%!!!%!%??!%?!%%%%!%!?%!%%%%%!!!!?%?%!%!!!%%%%%%!%%%?!!!%??!%!%!%!!%!%?!?%?%%%%!!%%!%!%%?!%?%%!%?!%%%!%!??%!%!%!%?!%%?%!%!!%%!%%%!!%??%!%??%!?!%%%%%!%!!%%!!!?%!!!!%!!!%!!?%!%%%!!?!%%!?!!%?%!?%?!%!!%%?%%%%%!?!!%!!%!%%!?%!?%%??!?%%!%!!!%!?!%%%%%!?!%?!!%!!!!??!!!!%!??!%%!%!%%!?!%%%%?%!!!%!%%%!%%%%%??%?!%?!%%%%%!%!%!!!%?%%%%%??%%?%%!%!%!!!%%!!%?!%?%!%%?%%?%%%%!%?%!!%?%%%?!%%?%%!%%!!!%!%%?!%%%%!?%??!!%?!%!%!?%%%%%%!%%?!%%%!!!!%%%%?%?!%%!?!??%%!!?!!?!%%%!%%!!!!!%!?%%%!%!%%!%!?!%%%%%%?%%%!%%?%??!%%%!!!!?!%%!!%%%%?%?%%%!!!!%!%%?!!!%?%!%%!%!%%%?!%%%?%%!%%%%?%%!%!?%%!%%%%!!%?!?!%?%%%%?!?!%!!%??%!%%!!%%%%%%%!%%%?%?%%!%%!!!%!%%%?!?%%%?!%%?!%%?!%%%%?%?!!%%!%%!%%%%!!?%!%%?!%%%%!!%!!??%!%!!%!!?!%!??%%%%%?!!%%%%%!%?%%%!!%%!!!%!?%!%??!%!!%%%!%%%%%%%!%!%%!!!%!!?!!!!!?%!?%%!%%?%!%!?%%%%!?!%%?%!%%%?!%?!!%%!%%??!%%?%%?!!%!%!%!%%%?!!%!!%?%%%!%%%??%!?!!%%!%???!!!!!%%%!%%%%%?%%%%?!%!%?!!%%%%??%%!?!?%%%%%?!!?%%!%!!%%!%!%%%%!%%!??!!%!!?%!%%%!!%%%%%%!!%%%???!%!??%!?%!!?%%%%!!!%?!%!%!%%?%!!?!!!%%!%!!%%%!%?%%%%%!??!?%!%%%!%%%%?%?%!?%!!%!!?%?%%%!?%%!!%!%!??%%%?!%!???%%?%?%?!%%!%?!%%%?%%!%%!!%%!?%!??!%!!!?!!%%!!!?!!%%!%%%%!?%%?!%??%%%?!%!%!%%!!!!%!?%?!?%%%%!%?%%!!%%%%%%%!%%?%?!!??!%%%%%%%!!?!%%%!!%?%!!!?!%%%%?%%%?!?%!%!%%%%%%!%%%%%%!?%%?!%!%%?!%?%?%%??%?%%%%?!%!%!%!!%!%!%%!%?!%%%%%!!%?!%!%%!%!%!%?%!!%%!%%!?%!%%%!!%%%!%!%!?%?%%!%!%!!!!%%!!%%%!?%%%!!!%?!%%%!!!%%%%%?%%%!%!!!??%%!%%%!??!!?%!%%!%?!!?%!!%%!%?!%%%%!%?!?%?!%!!%!%??%!%%%%%!%?!%!%!%%%!%!%%!%!%!!??!%%???!!!!?!?%%?!!!!?!%!%%!%?%?%%!!!%??!%!%?!%%%%!!!!!?%!%%%!!%%??%!!%%%?%%!%!!%??%%!?%%?%!!??%%%%%??!!?%!!!!!%%?!!!?%!%?!%%%!%!%!%%!?!%%%!%%%%%%!!!%!%%%%?%%%?!%?!%?!?!!%!%!!%!?%?%?%%!??%%!%?!?!%%!??!%%?!%%!%%!!%!%%?!??%%%%%!%!!!!%%%%%!%!%%!%%%%!?%%!!?%!%!%!!!%%%!!!!!%%%!%?%%?!%%%%%!%!%!!%%?%?%%%%!!%?%%%%%!%!%%%%!%!%!?%%%%%%!!%%%%%!!??!?%%%!%%!!%%%%?!?!!%%!!%!?!%%%?%%!?%?%?%%!??!!!!%%!%%!?%?!!!!%%!?%%%%!!%!?%%!%??!?%%%?%?%%%!!%?!%%!%%?!??%%?!!!%!%?%!%%%%!!!%%!?!!!%?%!%!!%!%!??%!!??!!%!%!!?%!%?%!%!??%%?%?!?%%!?%%%%!%!?%%!!!%!?%%?!%%%!%%%%%%%!%!%?!!%%%%%?%%%?%!!%%!%%!!%????%!?%?!!%!!%!%!!?!!?%??%%!%!!??%%%?!%!!%!!!%!%%!!%!%!!!%?%!%!%?%?!%%?!!!!%?%!%!%!!%%%%%%%!!!!?%%%!%%!%!?!%!?!?!%!?%%%%%%%!%%%%%???!!%%!%%%%!%%%%!!%%!!!!!%!?%%%%%%!!!!!!%%?%!%!!%%!!???!!%%!!?%%%%%!?%%%??%%??%?!%!%%%!%%%?%!%%??%%%?%!%%!!!%!!%%!!%%%%!%%!%?!!%%!??%%%%%%%%%%%%%!?%!%!!%%%!%%!!%%%!!%!!%%?%%?!!?%!%!?%!?%!%%?%%!%!?%%!%%%!%?%!!?%%!!%?%%?%%?%%!%%%%?!%%%%%?%%?%%%?%%%!%%!%!!!!%!!???%%%%%%%%?%!!?!%%%?%!%%!%%%?!!%!?!%!??%%!%%!%!!!?%%%!?%?!%!!%?%?!!?%%!!%%%%%%!%%%!!%?%!%%!%%!%?%%!!%!%%!!?%!%%!%!%?%%%!!?%%%%!!?!%%!?%%!%?!??!%??!%???!!%?!!%?%%%?%%!!!!!!%%!%%%%%%%!!%!!%%%%%?%%%!!!%%?!?%%?%!%%%!%%!%%%!!!%!%!%%!??!?%!?%!!!%%!%?!!%?!?%%?%%%%!!!!%!?%?%%!%%%%%%%%%%%%%?%%?!!%%%%???%?%%%%%%%%!?%!!%%%%!%%%?!?%%?%%%??%%%!%!!%!%%%%%!%?%!%%!!!%!!%!!?!?%%!%!!!!%%%%!!!?%%!%!%%%%%!%?!%!%%%%!!%?!%%%!%!!%!%%%!!!!%%?!!!!!!!%%!?!!%!%!%%!%%?%%%%%%%%!!?!!!!%%!?!%!%!%!%%%%??%!%?%!!%%?%?%%?!!!%%?%%%%!!%%!?!%!%%!!%!!%!%?!!%??%%%?%?%%!%%%%%%%%?%%%?%%%%!%???%!!%%%!%%%?!!%!%!%!%!%!%%%%!?%%?!!?%!%%!%?%!%!?!%%!!%%%%!!%%?!%%%%%%%!!%!%!!%!??!?%!%%%!%%??!%%!%%%%%%%%!?%!%%!!!%%?%%!%%%?%!%%!?%!%!%!?!?%!!%!%%%?%%%%!%!%%%%!!!%%!!%!?!%?!!%!%%%!%!!!%!!%%%!!!%%%%?!!!?%%?!?%?%!%%?%%%%!?%!!!?%%!%?%%%%!%%?%?%?%%%!!!%!%%!%%!%!%?%!?!%%%%!?%??!!!!!!?%?%%%%??!!%!%%%%??%!!%?%%%!!?!!%?%%%%%%!%!%?!%!%?%%!?%%%%%%%%%%!%%!!!!%%%!%!!%!?%!?!%!%!%%%!%?%%%%!!%?%%%%!%%!?%%%%!!!%%!?!%%%%%!??%?!!%?%!?!!!!!%%!%%%%%!%!%?%?%!%%!!%!!?!%%%!%%!?%?!%!%%%!%%%%%!?%%%%%%!!%?!%?%?%%%%%??!?%%%!!%!!!%%!%%%!?%!%%%%!?!%%?!%%%%%!?!%!%%?%%?!%!?!!!!?%!%%%%%%%!!%???!%%!?%???%%%%!%%%%%!%%!%%%%?%!!!?%!!%%%%!!%%%%%%!!!!%??%%!!%%%%%!!!?%?!?%%%!?!%%!??%%%%!%?%%%%%%!!?!%!%%!%!??%%%?%?%%!!%!?!!%%%%%!%%!%%%!%!%%%%%%!!%?%!!?!!?%%%%!!?!%?%!?%%%?!!%%%%%!%!%%!%%!%??%!??%?%%%%%%?%%%!?%%%%!?!%%%!%%!!!!!!%?!!%?%%%?%%%?%!?!%!!%!%?!?%?%!%?!%!%%?!%%%%?!%?%%!%%!?!%%%%!!?%??!%%?!!%?%%%!%?!!%%!%!%%!%?!%%%%??!!!%%!%!%?%%!%%!!%%!?!%!?%!?%?!%%%%?%%!%?!%!%%%?%?%%%!!!?!?!!%%%!?%%%!!%?%%%!%%?%??%%%!!%!!%!!%!?!!?%%%?!!%?!%%!%%?%?!%%%!!?%%!!%!!%!%!!!%%%%%%%%%!??%%%!%!?%%!!%%!%!%%?!%!%?!!%%%!%%?%!!!%?%!!%%%%?%?!%%!!%!%%?!%%%?!!%%!%%?!!!%%??!!?!%%%%?!????!%%%%%%??%!%!!%%!%!%??!?!!%!%???%!?%??%?%??%%%%?!%%?!?!%!%?!%%%!%%%%?%%!%%%%?%?%%%%%%%!?%%%%%!%?%%!%?!?%%!%?%!!%!%?%%%%%%!?%!!%%%?!%%!!?%!%!!!!%%!%?%!!!%?%%!?%%!!!!%!%?%%!%%!%%!?!%%?%!!!!%?%!???%%%!%!!%!%?%??%!%?%%!%%?%!%%%%%!!%!!%%!%?!%%!%%?%%%%%!%!!!!?%%%%%%!%!%?%!%%%!%%%?%%!%%?%%%!%%!%%!?%%!%?%%%!!!!%%%!%%!?%%%%%%%%?%%%%%%%%!?%%!%!!!%%%?%%!%%%%!%!%%??%!%%?%%%!%%%!%%%!?%%!%%!%%?%%%!!%!!?!%%!%%?!%?!!%%?%!!!!!%%%!%!%?!%?!%?%!??%%!??%%!%%!%%!%?!%%!!%!?%!%!!%%!?%%%%%%%%!%?!%!!%!%!!!?%%%!%%!?!!%%%????%%%%???!?%?!?!!!!%%%%%!?%?%!%%?%%%%!%%%%%!%!?%%%%%%%%%%!?%!%??%!%!%%??%%!!%%%%%%%!%!!!%!%!%%%%%%!!?!?!%%%!%%?%%%%?%%!!!?%?%%%%!?%!?%?!!?%!?%?%%%%?%%!!?%?!%!%%%!?!!%!!%!!!!!?!!?%!?%?%?%!%!%%%?%%%%?%%!!!!!!%!!%%%?%%%%%%!%!!!??!%!%!%!?!!%!%%?!%%?%%%%?!%!?%%!%!!!!%%%%?!!?!?!!%%%%%%%?!%%%%%%!!%!%!%!%??!??!%!%!%%%!%!%%%!!%%%!?!?%!!%!!!?!??!%!?%%!%!%!%!?!!!?%!?!!!%%!%!%??%!%%!!%?!!%%!%%?!!!!!??!%?!%!!?!!!%!%%%?%!%!!!!%!%!!%%%!%%%%%!%%?%%%%%!%%%%%!%%!!%%%?%%%?%%!%!%%%%%%?%?!%%%!!%?%%?%!%?%?%!%!%%?%%%!!%?%%!%%!%!%%%%%%!!%%!%???!%%!!%%%%!%%%%!%?!%%?%%!%??!%%%%?!%%!%%%?!!%%%!!!!%!%%%%%!%%%%%?!!!%!%!%!!%!%???!%%%!%?%%%?%%?%%?!%%?%?%!%?%%%!?%!%%%?!!%!%%%%?%%!!%!?!!?%%?%%?%!!%??!!?%%!?!%%%!!!?%%???!!%%%%?%%%!%%!?%!!%?%!%%?%%%%?%%%!%%!?%!%%%!%!%!%%%!?%%??%%?%%%?!!%!!!%%%!!?!%%!!%%%!%%%!!!%%%%%%?%!!%%!%!%!!?%!%%!%%%?%!%%%?%%!%!!!!%?!??!%!?%??!!%!?%!!%%!%!%?!!?!%?!%%%?!!%%!%?!%%%!!!%?!!!!!%!%%%!!!%!%%!!!!!??!!%!%%!%%%%%%%?%%%!%%?%??!!?!%!%!%%!%??%?!?%!!!%!???%%?%!?!%%%!!%!!!%%!?!?%%%%%!%%!!%!%%%??%??%!!!%%?%!!%!?!!?%%!%!%!!?%!%!%?!?%%?!!%%!!%!!%%!%%%%!%%!!!?%!%?%%?%!!!%%!%!%!?%%!!!!%!!%%!%?!%???%?%%%%%!!?%%!!??%!%%%%%%%%!?!%!%!!!?!!!!%?%%%?%!%%!!?%?%%%%!%%!%%?%%%!!%%%%%!??!!%?!%!!!?!?!%!%!!%!%%%?%%!%%?!%!?%%%!%%%?!!?!%%%!!%!%!%%%!??%!!!%%%%?!%%%!?%!%!%?%!?!???!%?%%?!!!%!%%!!!!!%!%%?%%!%%%!%%%%!%!%%%%%!!!??%!!%!%!!!!%%!%%%%!?%%!!%%%!!!%!%!?%!!?%!%%!!%?!%%!!?!%!%?%%!!?%!%!%%%!%?!!?%%%!%%%!!%!?%!%?!%?%%%?!!!%!%%%?%%?%!%!!%%?%%!??!!%%%%!?%%%%%??%!%?!?%%?!?%%!!%%?%!!!?!%!%%?!%!%?!!%!!?!?%!%%!!%%%!%!?!!%!%!!!?!%%?%%%!!?!!!%%!?%%%%%%%%!!%?!!%!!?%%!%%!%?%%?!%%%!!%?!%%!%%!%%?%!!!%%%%%?%??%!%%?%!?%%%%%%%%%%%%%!%%!??%%!%%!??%%%!?%?!!!%%%%!%%!!%!%!%!%!!!!!!%!%%!!%!?%!!?!!%!%!%%%?!?%%%%%%?%?%%!%%!%!!?%%?!%!%!%%%%%%%!%?!%!?!%%!%!!%?%%%%!!!%%?%!%??%?!?%%!%!%%?%%!%!%!!?%%!%!!%%!!!%?%??%%%!!?%!??%!%%!%?!%!?!!!%%%?!%!!!%!!%?!?%!!%%?!!%!%%!%!%?!%?%?!%?!%!%%%!?!!%%!!%!%!%%%!%%%%?%%%!!!%?%!%!%%%!%%!!%!%%%%!??%!!%%%?%?%!%%!%%???%?%%%!%%%%!?!%?%!%?%%!?!?%??!!%%%%%?%%%!!!!%%%?%?%?%!!%%%%?!%!!!%!?%?%%?%%%%?!%%!!%?%?!!%%!%!!%%?!!%%%%%%!%!!%%%%!!%%%%???%%%%!!??%?%?%%%!%!%%%%%%%%!?%??%??%?!%%%?%??!?%!%%!%%%?!!?%?!%%?%%%!%!%?!!%%%%?%!!%!%%!??!%%!!!%!%!!%%!?!!?!%!!!%%?%!!%%%!!?%?%%!!!%!%%%?!%%!!%%%%%%!!?%!%%%%?%!%!%%%%%??!?!?%%%?!%%%!?%!!%%%%!%!%%%!????%!%!!!%%!%!?%%?%?!%!?%!%%%%!!!%!%!%%%!%%%%%!?%%%?%!?%%?%%!%%?%!?!!!%%%!%%!!!%%!!%!?%?!%?!!%!%!%!??%%%?%!!%%%%!!?%%!%?!%%!%%!!%!%%!?!!%!!!!?%?!!%??!?%!%!%%%%!!!%!%%%%%%!!?!%%%!??%%!!%?%?%%%%%%??!!!%%!%%%%!%?%!?%%%?!%!%%!%%%%??!!%%%%?%?%!%??%%!!%!?%!%!%!?%?%!?!!?%!?%?%%!%?!?%%!!!%!%!?%%???%?%!%%!???!%%!!!%!?%!%!!??%!%%!?!!!!!%!!!??%%%%%%%?!?!%%?%!%%!%%%%??!%!%%%!%%%!?%!!%?%%?%!??%%?%%!%%?!?!%?!%%!%%!!%!???%?%!!!%!!!?%%%%%%!%!%!%!%%%!%%%!!!%%!%%!?%?%?%!%?%%!%%%%!?%%%%%%%?!%!%%!?%?!%%%%%%!?%!%!?%%!%%%%!%!?%!%%!%%!!%!%!%%!%!%!!!%%?!!!%%%%%!?%?%%!!!%?%!%?%%%?%!!!%%%!%%!%??%%%?%%%!%%%!%%%%!!?%??%%%%!!%!%!%??!%%%%!%!%%%?%%!%%%!%?!!%???%??%%%?!%%!%!!%%%%!!?!!!%%?%!!?%!%!?%!!%??%?!%?%!%?%?!%?!%%%?%%%%%%!%%%%!%%%!%%%%%!?!%!%!!!?!!%%%??%%!!?%!?!%!??!%?!!%!%%%%%??%%!!!%?%%?!%?!!%!%%%!%%?!!!?!??%%%%%%?%!!%!!%!%!%!?%!%??%%%%%%%%!%!!%%%%?%%?!%?!!!!%%%!%!!!?%?%!!%%!%!!%%%%!%%!!%%%%%%!?%%!%??%%!?%%%%?%!%!%!%%!!?%!%?!!%??%%%!?%?%%?!!%?!%!%%!?%!%%!%?%!%%%%!?%?!!%%%!!%!!%?!!!!%?!%!!!!?%%!%%%!?!?%%%%%%%%!%?!?!?!%%!!%%%%%!%?%%%?!%%?!%??!?!%%!???%!%%%!!!!!??!%%%!%%%%!%%?%!%%%!?!%!!%%%%%%!%!!!?%!%%!%%?%%?%%%%!%%%%%%!%!%?%!?!!%%%!%!%%!%!!%!!%%??!%%%%?%%%%%!%!!!%%%!%%??%%%%?%!%!%?%%!!!%?%!%!??%%?%%%%%!?!!?%%!!?!!%!%%%%%!%!!%%!%%%?%%%%%%!%%!%!%??%!!%!!%???!%%%!?!?!%%%%%?!!%%%!%%?%!%?%%%!!??%?!%!%%!%!!!%!%?!?!%%%%?%!?%!%%%?%!!%%%%?%!!%!?%?%%%%%%?%%%!?%?%!%!!%%%!??%!!!%?!!%%%%!%%?%%%%!%%!%!%%%%?????!%!%!?!%%!%!%%%!%%%?%%!%!%%%%%?%%!%!%?%%!!!?!%!!%!%%%!!!!%%%%%!!%%%!%!%%%!%%%!?%%%%?!%%%!%!%%!%%%???!%?%!?!%%%?%!!%!!!%!!%!%!!!!%%!%?!!!%?%%??!%!!!%!%%?!%?!?%%%%?%%!%!%!!%%!!!%!!?%?%!!?!%%!!%!!%?!!%%!%%%!%%!%?!%!!!%!%%!%!!!%!%%!%!%?!?!%%%%?%?%!%!?%%%???%%%!?%%%%?%??%?!%!!!%!!%%???!!??%!%!%%!!%%?%%!%%!?!%%%?!!!?%%%!%?%?%?%%%%%%%???%?!!!!!!!%!%%!%%%?%%!%%%%%%?%%%!%%%%%!%!!%?!%!!%%%%?%%!%?%%%%%!%?!!!?%!%%!!!%%%%?!%?!!%%%%%%%%%!%!%!%?!!!?!!%%?%%%?!%%%%%%!%%?!!!!%%%?!!?%!%%!!%?!%%?%?%??!!%?%!!?!!%%!%%!!%%!!!!?!%!?%%%!!%?%%??!??!%%%!%%%%?%!%?!%%%!%!?%%%%%%???!!%!!!?!%%!?%%%!%!?!%%%???%%%%%%?!!%%%!%%%!%!!?!%!%?!%!!?!%%%!?%%!!%%%%%%!!!%!?%%%!%%!%%!?%!?!?!!?%!%!?%?!%%%%!%%?%%%%!%!?%%!%%%%!?%%!%!?%%%%%!%%?!%%!?!%!%%%%!?%%%%!!%?%!%%?!?%%!?!?!%?%%%%%!!%%??%%%%!!!!!%!!%!?%?%!!%?%?!!%%!%%!%%%!%%?%!?%?!!!%!%%?!!%?%!%?!?%%%??!?!%%%%!%%?%!%!?%%%%!%!%%%?%!%??%%?%%!%%%!?!%??!!?!%!??%%???%%%!!%!%?%%!%%!%!!!%%%?%%%?%!!%%!%%!%!%!!%!!!%!!%%%!!?!%!?%?%%?!%%%!%%!!!%%!%%!%%!%!!!!%%!?%%?!!!%??%?%!!!%%!!%?%%%?%!%%%%?!%%!%?%%%%?%?%!!%%%%%!?!%%!!%%?%%!!!!!%%%%%!!%!%!%%%?%%%!%?%?%?%%%!%?%%!%!%%?!?!!!%%!%!!!!%?!!?!%!?%%!!!?%?%%?!!%%!?!!!!!!!%%%%%%!!%%!%!!!%?%?%??%%?!!!?!%!%!%%!%%!?!?%!!%!%?!%%%%!!???!%!!%??%!!%!!!!!%!%%%?%%???!%%?!?!%%%%%?%%%%%?%!%?%%!%?%!%?!%%!!?!%%%!%?!?!!!?!?!%%!%!!%!%%!%%!!?%!?%!%%%%%!%%%%%%?!%%%%%%!%!?!%%!?!!!!%!%%!!??%%%%!!?%?!?%!%?!%%?%%!%?%%%%%!%?%!%??%%%!?%%?%%%!?%??!?!%%!%!?%%!!%!!%%?%%!%%?!%%%%??!???%!!!!!!!%%%%%!%??%!%?%%%%!%%%%%%%%%!?%%%???%?%!%!!?!%?%!!%%!%!?!%!%!?!!!!%!%%%?%??%%%!%!!?%%%%!!%?%!!!%%%?!%%!?!%!%%%!%%!!!%!%%!!!%!!%%!%!!%%%%%%%!!!?!%?!%!%%!!%!%%%???!?%%%%%%%!%%!%%%%%%!??!?%%%?%!!!??!%%!%%!%%%??!!%!!%?%!%!%?!???%%?%!%!%!?%!!!%?%%%%?!!!!!!%%%!?!%!%%!!%%!!%!%!?!!?%!%%?!%%!!%?%?!?!%%!?%?!!%!!%%%%!!!%!!!%?!?%!%!%%!%?!%!!?%%%!%%??%!%%???%!%%??!%%%%!?%%%!%!?!?%%%%??%%!!%%!%%?%?!%!!%%%!%?!%!%%%%!!%??!!!%%?%?!%%%??!%!%%!%%?%%%%!%%!!?%!%%%%?!?!%!%%%!%%!?!%!%%???%%!!%!!!!%!%?%!?%%??%?!%%%%?%%??%!%?!!%%!?%!%%%!%?%?!?%!%!%!%%!%%!%%%%%%%%%!%%%!%!!?!?%!?!%%%%%!!?!%%!%%!%!%?%!%!%!%!!%%%%%!?%%!%%?!!%%!!%!%%%%?%!%%%%%%%!!!%!%%%%!?%%!!?%???%%!%%%%%%!%?%%!%!!!%%%%!!%?%%!%%!%%%%%?!!!!!!!%%!?!?%%%%?!%!?!???%!!%??!!?!?%??%%!%%%?%!!!???%%%%?%%?!%%%?!%!%??!?%!!?%!%!!%!?!?%%%?%?%%%%?%!!%!%%!!??%?%!%%!!%%?%!%!!?%%!?%%%%!?!%!???%%!%!!?!%%%%!!%!%%%?%%%%!%?%!!%%%%!!!?!?%?%!%!!!%%!!%?%%?%%!!?%?%!%?!?%%!%%!?%?%?!%%%?!!%%%!!%!!%!!%%?!!%%!?!%%%?!%?!!%??!%!!!%%%??%%?!%??%???!?!%!!!??!!%%%%!?%!%%!%%!%%%?%%?%%!!%%%?%!!?%!??%%%%%%!%%%%%%!!?!?%!%!%!%?!%%!!%%!%%%%%%%%!!%%!%!?!%%!%?!??%%!!!?%?!%?%%%!!%?%%%%!?%%?%%%%%!!!%%%!?!!?!!!!!!%%??!%?!!?%%?!?%?!!%%%?!!!%%%%?%!%%%!!%!%?!!!!%!!?%%%!%!%%!?!!%?%%%%%%!%!%%!%%!??%!%%!!!??%?!!!%%%!%%!%%%!%%!%%!%?%!?%?!%%%!%?%!!!%%!?%!%!!??!?!!%%!%?!!%!!!!!%!%!!%!?%!%%%!??%?!%%!!%%?%!%!?%%%!%!!%%!!%%%?!%?%!%!!!!%!%?%!%!%!%!!%%!!%?%!%!!!!%!!%%?!!!%!!%!%%!!%%?%!%%%!!%%!%!%%%!%%%%!!!%%%%%%%!?%!%%?!%?%%%%%%%%%%%!%%%!%%%!??%%?%%?!%%%%%!%!!%!??%%%%%?!%%!!?%%%!%%!!?%%%?!!%%%%%!?!?%%%!%!?%!!%%!!%!!!%%!%%!!%?%%%?!%!?!!%!!?%%?%!!%!%%!%!%!%!%%%!%%?%%%!%!!!?!%!%?%?!!!%%??%!%?%?%%??%?!!%%?%!%!!!!?%%%%????%%%?%!!!?!!!%?%%?!%%%???%%%%!%%%?%%!??!%%%!%!%%%%%%?%!!?%!%%!!%%%%!%%%!%%?%%%!!%%%%%?!%%%%?%!!%%?%%!!%%!%%!!%!%%%%!%?!??%?%%%!!%%!%%%%!%%!???%%%?%!!!%%%?%%!%%!!%%!%%?!%!!!%%%%%!!?%%%%%%!%!%%%!%!%%%%?%%!!%!%%!%?%!!!!!?!%%?%!!%%%?!?!%!?%%%!!%%%!%%!??!?!!%%?%%!!!%%%?%!!%?!%%%?!%!%!%!%%%!!%?%%%%!%%?!%%!%%!?%!%%!?%%!?!?!%%%%!!?%%!?!%!?%!%!%!%!%?%%!??!%%?%!%%!!%?!?%%!%%%%!%??!%?!%!?!!!!!!?%!%!!%!!%?%?%%%!%%%%%?!!%%%%!%%%?!%%%?!%%%%%%%%%?%?%%%%?%%%?%?!?%?!%!?%?!%%%%%%!%%%?%!!!!!%!%!!%?!!?%?%?%%!%%%!?%??%%!%%!!??%%!%!?!%%%!%?%!!%!%%%%%!!?%!!%%!?%%%?%%!%%%%?!?%??%!???!!?%?%!%!%?%%!%%%%%%%!%!!%!!?%!%%!!%!%%%?%!?%%%%!%?!%%%?!%%!!?!!?%%%?%%%%?%!%!!?!%!%%?%?%?%??%%!!!!%%!!%!?!!%%?!!%!%%!?!!%?!%%!%??%%%%%?%%%?%%%!?!?!%!%%?%!!!!%!!?%%%?%!!!%%%%%%%?!%!%%%!!%?!!!!%!?%?%!?%!%%!%!!!%!%?!!%%%!!%??%%?%%%%%%%%!%!!?%%%%!??%%??%%%?%!?%%!%%??!%%!%??!%%%!!%!!%%!%!!!%%!!!%%%%%!%!!%%!!!%%%!%!%?%?%%%%!%?%!!!%!%%%??!%%?%!!%%%%%%!%%!!!!???!!!%?%!%!%%!%%%%%!?!%%%???!?%%%%%!%%!!%%!!%!?!?!!!%!%%%%!!?%%%?!%%%!%?%%%%%?%%!%%%!!%!!?%!%%%!!%!!??%!!%?!!%!??%%!%%?%!%!???%?%%%!???%%%??%%??%!%%%%%%!!%%%%!!%%!?%!?%??!%%%%?%%%%!?%?%!??%%?%%%??%%%%%%!!%%%?%%!!%%?!%!?!%%%%!%?!!!%?%?%%%%?%%?%?!%!?!!!%!%%%!%!!!!!??%?!%!%!!?%!!%!%!%%?%!?!!%%%!%%?%!!!%!%%!!%%!!%!?%!?!!%%%%%?!%??%%!!%%!!%%%%%!%%%?!!!!!!!!%%%%!%%?%?%%%!%%%%%%%%?!!%%!%%!%!%!!!%%%%%?%%!?%!%%!%%%%%%?!%!?!%%%%??%!%%%!?!?!%%%!?%%%!%!!?%%!%%!%%!%?%%!%!%!%?%%%%?%!!%%%!%?!%!%%!%%%%%%?%!%!!%?!%%%!%!%!%%%%!!%%?!%!!!!%!!%%!?!!!%??%!!%!?%??!!%%?%??%%!%%!!%%!%!%%?!%%%%%?%!%%%%!%?%!%%%!%!!?!%%%!?%%%%%??!?!!!?!?!!%!!!%!!?%?%!%!%!%%!!?!!%!!%%%%%?%?!%!%%!%%!?!!!?%%??%!%%%%%?!!?!%?!!%?%?!!!?!%?!!%%%!%%%%%!%%!?%%!%?%!%%?%!?%%%!%%!%%!%??!%?%%%%!%?!!!!?%%%%!%%?%%?!%%??!%%!?!!!!%!%%%%%%!?%!!%%?%?!%%?%!%%?%!??!%!%%%?!!?%%%?!!%!?%%%!?%?%!%!%!??%?%%!?%!!%%%?%%%!%!?!!?%%%%%%%%%???%%%!?%%%!?%%%%%%%%%!%%%!%%!%!!?!%%??%?!?!!!?!%!%%!%%!??%!%%%?%!!%%%%!%!?%%%%!%??%!%!%!?!?!?!%%!??!?%%%!%%%!%!?%%%!%%%!!??%!?%%!?%%%%%??%%%%!!!%!%%!!%%%%%%?%?%!?!!%%!%%!!!!%%?!%%%%%%!!?%%%%%!%!%%%%!??!%!%%%%?!%?%!?!??!!!!?%%%?%?!%!??%%%%%%!%!%?%!%%%?%%%??%?!%!!!??!?!%!%?%!!%%!%!%%%?%!%%%%%%%!%%!%?%%?%!%!?%%!!!%!%%%!?%%%?%%%?!%!%!%!%%?%!!%%%?!!%%??%?%??%?%!!!%%?!%%!%%%%%%%%%!?!%!%%!%!!%%!%%!%%??!!?%?%?!?!%%%!%%!?!?%%%??%%%?%?%%!?!?%!%%%%!?%%!%?%%!?%!!!!?%?!!%?!!%?%!?%%%%%!%!%!%!???%%!%?!%%?!!%%%!?!%!%%%%%?!%!??%?%!??%%?!?%!%!!!%?!%%%%%%!%!!%!!%!%??%%%%?%!?%%!?%%%?!%!%?%??%!%%!?%%!?!!!%!!?%!%%%%!%?%%?!!%!!%%!%%%!!%%%!%%!%%%!%!!!%%%?%%!!!%!%%!%%%?!%%!?%!%?%%%%%!%%%%?%%!%%!%%%!?%?%!%%%%!!%!?%!%?%!%?!!!!%?%%%!?!?!%!!!!%%%%%%!!%!%%%!%%%%%%%!%%!%%%%%!!?%%?!!?!!%%!%!%%%%?!%?%%%!!%%!%?%?%%!%%!!%?%!?%%%%!!%%%%%%%!!?%%!!%!%!%!!!?%%!%%%%%%%%!%?%!!%!%%%%??%!%!%??%%!%%?%?!!?!%%%!%?!%%!%?!%!%%!?%!%!%%?!!?!!??%%%%!!!%%!!?!%%%%%?%!!!?%%%%%%%%!%%?%!!!?%%!?!%%%%?!%?%?%%%?%?!??%%%%?!%!%%%%?%%!%!!!?!!%!!%%%%%%%%%%!%%!!%!%???!!!!%%%!%??%%%?!%!%%?%%%?!%%!!%%%%!%%!?!%?%!!!%!%%??!!%!!%%%!?!?%%?!%!?!!!!%?!%%%%%!!%?%!%%?%%%!!%%!%%%%?!!%%%!%!!%%!%%%%%?%!%%!?%!!%%%!!!?%?%%%!%!%%%%%??!!%??!%%?!%%%!%!!%%%!%?!!!!!!!%%???!?%!%%%%%%%?%%%!%%%!!%%%??%%!!%!%!%%!%%%?!%%!!!?!!!%!?%%?%%%%!!%%%!%?!%%!!%%%!!%%!%!%%?%%!%%%!??!!!%??!!!%%%%%!!?%!!%?!!?%?%%!%%%%!!%!??%?%?%!%%!%!!%%!%!?!!!%?%!?%!!!%%%%%%%%!!%%%!?!!%%%!?%%?%?!?%%%%!!%!!%?%!%%%%%%!?%%!%!?!%!%?!%%!??%!%%?!!?%%!!%%!?!!!%%?%%!!%!!?%%%!!%%%?%!%!!%?%?!?!%%!!!%%%%!%%%!!!!!%!%!%!?!?%!%%%!!?%%%?!%!%%!%%%%%%?!!!??%!!%!%!!%%!!%%!!%%!!!%%?%!?!!?%%!%%!%%%%%!!%!!!%!%!%!%%%?!!!!??%%%!%!%%%!?%%%!%?!%%%%!!?%%%%!!?%!%!%?!%%%%!%%?!?!!%!!???%??!%%!%!%?%%!!!%???%%!%%!!%!%%?%?%%%?!%!!!!%?!%%?!%%!!!%%!%?!?%%!??%%!?!%%!%?%%?!%!!%%!?!?!!%!%%%%%%%!!?!!%%!?%!%%%?%%!!%%!%!%!%??%%%?!!!%!%?%!%%%?!%!%!?%%%?!%!%!%%%%!%?%%?%%%%!!!%%%%!%!%!!%!!%%%!%%%?!%?%%!!?%?!%%?!%%?!%%%!%%?%!%!%!%!!!!%%!%%!%?%%%?!%?%!%!%%!%!%%%%%!%%%!%%!%?!%?!?%%%%%%%!%%%!%!%!!%?!?%?!??%!!%???!?!%%%%%%!!%%?%?!!!%%??!%!!%!%!!!?%?%%!%%!%!!%%%%%%!%!%%%%%%%%??!%%?%!!%%%!??%!%!%!%%!%!%%%%%%%%%%!!!%%%?%%%!%%?!?%!!!!?!%%%%%!??!%!%%%%%!!!%?!!!%!%%!%!!?%?%%!%%?%!%%%!%%!%%!%%!%?!?!!!%??%!%!?%%%!%!!?!%%%?%??%??%?!%%!%!!%%%%!%?!%%%%%?%%%!%%!?!!?%!??%%!%!??!%%!%!!%%%!!?!!??!%%%!!%%!!!!%?%%%!?%!!%?%%?%!!%%!??%?!!%%!!%!?%%?!!%%%!%%%?!?!!!%%!!!%!!%!%%%%!%!!!!!%%%!??!?%%??%!%%?!?%%%???!!!!%?%%%%%%%!%%!!!??!%?%%%%%%??!%%%%!%!?!!!%!!?!!%%!?%%!%%%!%!%!%!%%%!%%!%!!!%?!!%?!%!?%!!?!%%!%%%%!!!%%?!%!%!!??!!%!%!!!%%!%!%%%!%%%%!%!!?%?%%%?%!%?%?%%%%%!!%!!%%%%%!%%%%%!?%%%%%%?%%%!%%%!%%%!???!!!%%%!?%!%%%%?%%!%!%?%%?!!!!%!!!!?%!%%?%?!!?!!%??%!%!%%!!%!%!%!%%%%%%%%%%!!%?%%?%%!!%%!!%?!%%%%!?%%!%%?%!%!?!?%%%%!?!!!!?%!!!%%%%%!!?%%?%%%%!%%!%!?%??!%!%!?!!!%!!?%%%%!%%%!!%%%%%%%%%%%%%%%!!!%!%%?%%!%%%!%!%%%%!%!!%%%%!%%%!???%?%%%!!!?%%!%%%?!???!%!%!!!?!?%!%!!%!!!?%?!?%%!%%%??%%%!!!%%?%%%!%?%!%!!!!%!%?%%!!%%%?%%?!!!%!!%!%%!%%%%%!?!%%%%!?!?!!%%!%%%!%%!!!!%!%%!%%??!%!%??!!%!?!%????%%%!%%!?%!%%%%%%!%%%%%%%!?%!%??%%%?%%%%%?%!?%%!%%!%!%!%%%%%%!%%?%%?%%%!%!!?%%%%%!!%!?%!%?!?!!%%!!%%!?!%%%%%%!?%!?%!!!%%%%%%%%%?%%!!%!!%%!%!!!%!%!?!!%!!%%%!?%%%!%?!!%!!%%!%!!%!%!!%%%!??!?%%%??!!!?%%?!%!!?!??!!!??!?!%%!?%%%%%%!!!??!!%%??!??%??%%!%!%%!%!%%!???%!!!%!?%%%%%?!%?%!%%%%!%%%%?%%%!%%%?!?%%!!!%!%??%!%!%!!%!%%%!??%%%?%!!?!!?!%%%!%%!!???%%!%!%!???%%%%%?%!??%%!%!%!%%!%!!%%!???%!!?%!%%%!%?%?%!!!%!%%%%!?!!%?%!%%%%%%?%!?%%!!!%!%%!%?%%?!%?%%?!%?%!%%%!?%!%%?%%%%%%!!!%!?!%!!!%%?%%!!!!!%%%?%?%!!%%!?%?%!!%!%!%?!%!%!!!!!%!?%?!?!?!!%?%?%!%!%!?%!!%!!!?!!!%%%%?!!!%%?%!%%%%!?%??%!%%!%%!!%%!%%%?!?!?!%%%%?!!?%%?%%?!?%!!%%%?%!?!%%%!%?!?%%%!%%!!%?!?!%!!%!!%!!?%!%%!%%%!?%%!!!%%%%??%%!!!??%%%%%!%?%!%?!!!??%?!%%%%%%%?%!%%%%!%?!?!%!%%%%?%%?!!!!%!%!!!!%!%!!%!!!!%?%%%%%%!%???!%%%!!!%%%%%?%!%!%!!%%%!!%%!%%!??%%%!?%?!%%%!%!%%%%!?%%!%!%%%%!%%!%!%?%!%!?%%%%?!%!%%%?%%!%%!%!%%!%!?%%?%!%!%%!!%%?!?!%!%%%?!!%!?!%%%%%!%??%%%!!%?!?%!!%%%!!%%%?!?%%%%!%%!?%%%!%!?!!%?%!?!%%!?%%!!?%%%%!%?%%!%%%%?%!!%%!%!%?%!%!?!%%%??%!%%?!!?%!!!%?%%%!?!?!?!!%!!!%?!!%!%%%!!%%%%!!%!?%%%!?!!!!%!%%%%!%!!%%%!?!?%%!%?!%%?!%%%?%%!!!%?!!%?%%%%%?%%%!%!!!%%%?%???!!%%?!%!?%%?%!?!?%%%%%?!?%!%%!%%!%%%!!%%%%!?%%?%?!?%%!!?%%?%?%%?!!?%%%%!%%??%!!%?!%!%!%?%?%!!%%?!%!%!%!%%!!%!!%??!?!%!%%!!%!!%%!%!%!?%!%?%%?%!%!%!%%%%%!!%%%??%%%%?%%?%%%%?%%??%%?%!??%%%!%%%%??!%!??%%%%?!?!!%!!!?!%%?%?!?%?%%!!%%!!%%%!???!%!!!%%!%!%%%%%!%!???%%%!!?%?!?!!%%?%%%%%!!%!%%%!?%!!!%%!%%%!!%?!%%%!!%%!%%%?%!!!%?%%%%%!!%%%?%!!!%%!%!?%%!%!!%%!??%?%!%%!!%?!%!%%!%%%%%?!%!!%%%?!%%%%!%%!%%%!%!%%%%!!%?%?!%%%%!!%!?%%!%%%!!!%%%!%!!!???%?%%!!%%%!%?!%%%%%%%?%?!%%?!%%??!!%!!%!!%%!%!?!!%%%%?!%!%%%%%%!%!?%%%?!!!%!!%%!%%!!%%%%%!%!?%%%!!%%%%!%%!%%%!%%%%%%%!%%?%!%!?%%?%%??%%%!!%!!?!!!%!?!%!%?!%%%%!%%%!%%%!%%%?!?%!%?%%?!!?%!%?%%?%%%%%!%!?%%%%??%!?%%!%??%!%%!!%!%!%%%!%?%%?%!%?%!!!%!!%%%!%%?!%?%%!%%%!%!!?%!%!!%!%%!%%%!?%%%?!??%%!?!%?!%%!%%%?%%?%%%%%!%%%!!?%%?%%!!%%%%?!?%%%%%!!!%%%?%!?%!??%%!%??!%!%!!%!!!?%????%%!%!?%%%%%%?!%%%%%!?!%%?%!%!%%%!%%%%%!%!%??%%%?!%%%%!?!%%%!%!%?%%%%%!%%?%%%%!!%%%%%!%!?%!%!?????%%!%?%%%%??%!?%%!%%%!?%%%%!?!!%?%%%!!%%%%%!!%%%?!%%?%!%!?!%%!!%%!!!%%%?%%?%?%%!!!%!%%!%%%%%%%%%%%%!!%%%%%%%%?%%%%!%?!!%?%!%!!%%%%!??%%?%!!?!??%?!%?!%%!%%%!%!?%%%%%!%%!?!!!%%%%%!%%%%!!%!!!?%??!%%!?%%?%%%%%??%!!%!%!%%%%?%!?!%!!!%!%!!!?%!%!%!%%?%?%%%?%%!!%?!!?%%%!!%?!%%??!!%%?%!!%%!%!%!%%%??!!%!%%!!?!%?%!!!!!%%?!!?%%?%!!%%!!%!%%??%%!?!!???!%!!!?%!?!!%!%%!!%%%!?!%%!%%!%%?%!%?!?%%!%%%%%?%!?!%%%%!%!!?%!!%!???!%!!!%%!%!%!%!??%%?!%!%!%%!%!%%%!%%%!%!%??%?%!!%!!?!?%%?%%?%%!%%!%%!%%%%%%?%%%!?!%!%%!%!!%%%%?!%%!!!??!!??%%%?!%%%%!%%%?%!!%!%%!%%%%!%%?!%%%%%%%%%!??!%?%?%!?!%%%?!!%%!%%!??%%!?!?!!%%!%%!!!??%%!%%?%%!%!!%!%!??%!!%!%%!!%%%%%%%%!%%%%%%!%!!%!!!%%%%!%?%!%%!%?!!%!?!%?!!%%??!%%%%%!%?%%!%?%%!%%!!!!!!%!?!%?%%%?%!%!%??!%!?%%%%??%%!%!!%!?!%!%!%!??%%!!%%%%?%?!!!!!%%%?%%%%%!%%!!!!%!?%%%%%?%%!!%%%?!%%%%?%!%%%!%!!%%!!??!!%%?%%%%!%!%%??!!!!%!?!!?!!?!!%%!!?%%%%!%?!!!?%%%%?!%!%%%%%%!%%!%?!%?!%?%%!%%!%!%!!!?!%%!%!%%??%!%???%%%!!??%!!!!??!!!%!!!%!%%%%%%%%%?%%!%??!!%%%%!??!!!?%%%%!!%?!!%%!!%%?%!?%%?%%%%%!%!?%%?!%!!?%!%?!?!%!!!%!%%%!%%?!%%?!%%%!%!%!%!%!!!!?%%%?!%%!??%!!%%%%%%%?%?%%%!%%%%?!%%!!%%%?%!!?!?%!!!%!%%?!%!%?%%%!%?%%!!!%%%%%!%%!!?!%%%%?%%%%%!??!%?%?!%!%???!?!!%%%%%%%%%%!!%%!!?%!!%!!%%%%%%%%%%?%%%%%?!%!?%!!%?%?%%!?!!%!!%%!!%%%%?!%%??!!!?%!!%?%%%%!!?%%!!%%!!%??%%??!!!?!%?!%%!!?!??%!?!%!!??%%!!!%!?%%!!%!!?%%!%%%%?%!%%%%!!!?%%%!%%!!%?%?%??%!?!%!!?%%%%%%?%%%!!%%!%%%!!!?!!??%!?%!%??!%%%!%??%??%!!%%!?%!!!?%!!%%%%%!%%!%%%%!%!!%%%%!%%%%!?!!???!!%%!%%!%?%%?%%%%!!!%?%!%%%!!??%!%!!%%!!%!%!!!%?!??!%!!!??!%%?%!!%%%?!?!%!%!?%%!?!?%?!%!!%%%%!%%%!!!?%%%!%%%!%!%%!!%?!%%%!!!!!%!!%%%%!!?%%%%!%!?%%?%%!%?%!?!!!%!!%!!%%%?%%!!!???!!!?!!!%%%?!!?%%%!?%!!?%!%%%?%%%???%%!!!%!%%!!%%!%%!!?%%%!%%!!%%%%!%?%?!?%%%!%%%??%%!%!??%%%!!!%?!?!%%?!%%%!%%%%%%!%%!?%%%%%!!%%??!%%%%!!%%%!?%%!!%%%!!!%%!%?!%!%?%!%?!%%!%%!!%?!%%!!!%%!%%%%!%!%!?%%%%??%?%!!!!%?%%!!?%?%%!%!??!!%%%!%!%%%%!%?!?!!!!??%%%!%%!%!%!?%?!%%!?%%%!??!%%!%%?%%!!!!!%%?%%!?!%%!%%!!%!??!%???%%!%%?!%!?%!?!%!?%!%!%!?%!??%%%%?!!!%?%!!!!!%!!!!%!?%%!%!!%!%%!%%!!%%%!%%%%%?!%!%!!%%%%%??%%%%!%%!??!%?!!%%%%!!%!!%%%!!??!!%%!!%!!!%???%%!?%!%!%!!%?%%!%!!?%??!%%!%!%%%!%%!!?%!!!?%??!%!%!!%%%!%!?!%!!%!%??!%%!%%%?%!?!%%%%%%%%%!!%!%?%%!!%%?%%!%%??%??%!%!!?%!!%%%%%%%!!%%%??%%%!%!!%%!%%??%%?%%%%%%!%%%%!!!??%!%%!%%%!??%%!%%%%!?%?%??%??%!%%!%%!%!%%?%%%!%?%%%%?%!?!%%%%%%!!%%%!%%%%%%%!%!?!%%%!%!%%%%%%%?%!!!%%%%?%!!!!!%%!%!?!!?%%%!!!%%!%%%%!%!%%%?!%!!%%?!%%!!!!%%!%?!%?!%%!!%!%!!?%%%!%%%%!%%%!%%!?%%!%!?%!!%%%!!%!!?%%!%%!%!%%%%%%%??!%%%?%!??!%%?!%!%%?!!%!%?%??%?!%!!!%%?%%!%%!!%?%%!%%??%%%!!!?!!!!!%%?!%%%%%!!%%%!!%?!%%!%%%%%!!!%%??%?!!!!%!%%%%?%!%!!%?%%?%%!%%%%!!%%%!!%!%%%%!%!!%!%!??!%!?%!!?!%%!?%%%!!?!%??!%!?!%!%!!!%%!%%%!%!%!%!%!!?%%%%?%%!%%??%%!%!%!%%%%%?%%%!!?%!%%%%!%%!!!%?!%%!!?!!%%!!!!%!%%%!%%%%??%%%!???!%!%%%?!?%!!%!%%!%?%??%!%!%!!%!?%%%%!%%?%%!%!!%?!?!%?!!??!%!!%?%?%%?!%%?!%!??!!%!?!%!!!!!!!!%%%%%%!?%%?%%%!??%%!!%%%!!%!%%!!%?!!!!?%!%?%%!!%?%?!!!%?!%!%?%!%!!!!%?%!%%%?%!%!!!%%!!%?!%%%%!!!!?!!%!!%%!%?!%%!!?%???!%%%%!?!?!!%!%!!%!!!%!%!%%%%%%?!%%!%%?!%!!!!%!%?%%??%?!!%?%%!%%%!%?%!!%!!%!%!!%%!!!!?%!!%!%%%%??%%%?%%!%?%!!%!!%%%!%!!!?%!%%?%!%%%%!%?%!%%%?%%??%%!!?%%!?%%%?!%%%%!!%?%%%%?%!??%%?%%!!%%%%!%%?!!!!%%?%%!%%!!%%?!%!%%!!%!%%%?%!%%!%%!?!%!!!?!%!!!?%!!?!%?%!%?!%%?%?!%%%%!!%%!??!!%%?%%%%!%%%!!%!%%%%!%%%%%%!!!?%%!!%%%!!%?!?!?!%?%%!%!!%?%!?%%!%%!%%%?%!%%!%%%?%%!?%%%%%%!%%!%?%%?%?!!%!%!%%%%%!%!!%!!%%%%?!%%%%??!%?%%?!!%%%%!!!!%%?%????!%%%%?%!%%??!%!%!%%%!?%%%?%%%!???!?!?%!!!%%!??%!?%%?%%%!%!%%%!!%?%%%!?%!%%!!!!%!!!!!%%?%%!%!%%!!!%%!%%!%%??!!!!!%!%!%?%%!!%%%!%?%!!!?%%%?!%%!!%!!%!%%!?%%%!%%%%!!?!!%?!%!?!%%%!%!%%%!%%?!%%%%%%!%%?%!!%?%!!!!%%??%?!?%!?%%%?%!?!%!%%!%??!%!?!!!%%!%%?!%!!%?%%!%!%?%!%%!%%?!%%%%!?%%?!!!%%!%!?%%!%?%%%%!!!%!!!!%?!%!??!%%!!%!%?!?!%%%%??!!%!%??%%?!!?!%!!!%!%!!%%%%??!?%!%%%?%!%%%%%!!!?%?!!%?!%!!!!!!%??!%%?%%%!!!%!??!%%!%!?%%%%!!!??%%%!!!%%%?!!?!!%?%!?%%?%??%!!%%%!??%%%%%!%???!!?!?!%%%%%%??!!!!%%?!!%%%!%!!!!!%!!%!!!%%%%%%%%!!%%%!%?%%!??!%%%%%!%!%%%!%%?!??%%%%%%%?%!%%!!%!!%%!???%%!%%!%!!%!?%%%%?%!?!%%?!%%%%%%!!%!!!?%!?!?%!%%!%?%!%%%!!%%%!!!%!?%?!!?!%!%%%?!!!??!%%%!%!%%%%?!!?%!%%%%%%!%!!!?%%%?!!%%%%%%!??!%!!%%?%%?!%!!%%?%%%!%!%?%!%%%?%!%?!%!%!%%!%%%%%?!!!?%%%%!%?%%?!!!!!%!%?%%?%%?%%%??!%%!!!!%?!%!??%?%!!%%%%%%???%?%?%!%%%?%%%?%!??%%%!%%!%!%!!%%%%!%%?%%!%???!!%%!%!%%?%%%%%%%!!%%%%!!!?!%%%??%%!??%!%%%!%!%??%?%%!?%!?!%!%%%%%%!!!%!!!!%!%%%!%!!?!!?%!!!%!!%!?!?%%%!%%%%?%??%%!%%%%?!!!%!%!?%%!%%?!%%%%%%!%!!%!!??%%%%%%?%%!%!?%%%%%!!%%!?!%!%!!!?!!!!!%!!!%%%!%%!%%!!%!%%%!%!!!??%!%%????!!%!%!?%!!%%!%%!%?%!??%%!%%?%%%!%?%%%%%!!?%?!%%!%%%!%!%%%!%!!%!!%%!?!?%%%!%!!?!!!%?%?!?!%!%!%!!!%%%%!%!?%?!%!?!?%!%!%%!%%%%!%%%%!%!?!?%!%%%!?%%%!%%?%?%?%?%%%%%!%%!%%!%%!%!%!!%!%!?%??%?%!!%?!?!%!%%%%?!??%%%?!!%%!!??%!!%%!!!!%?!%%!!%!?%!%!%%%!%!%?%%%%%?%!%?%!?!!!%!%!!?!%??!%!?!?%!%!%%%!%%!%%%!%!%%%%!!!%!%!%%!?!!!%?%!%%?!%!?!%%!%%?%%!%!%%!!!?%?%?%%%?!%!!%!?!?!%!!?%%%%!%%%!%%%%?%%%%?!?%?!!?!%!%!!?!?%?%?%!%%!!!%%%%%%!?!!%!%%!!%%%!!!%?!!%??!?%%!%%?!!%%??%!?!%?%?%!?!!!%%%%%!??%!!%?%!%%!%%%!%%%!!%%%%!%%%%%!?!%?!%!!%?%%!%?%%!!%%%%?!%!!??%%%%%%!%%!!!%%!!??!!%!!%!%!%??%%?%!?%?%?!%!%?%!!%%!%!%%!%!%!%!!!?!?!?!!%%!?%?!?%?%!%%!%%?%%!?!%%!!%??!!!%%%!!?%!%!%%!%??%!!%%%?%!%%%%%?%%%!!%%?%!!?%??%?%%%!%%%!?%%!%??%%!%%%!!%!!!%%?%!!!!!%?!!!%%!?!%%?%!%!%%%!!!?%!%!%!%?%?!?%%%?%%%%%%%?!%!!%%!!!!!!%%%!?!?%?!?!?%%?%?!%%%!!?%!%?%%%%!%%?%?%%!%%!%!%%%%%!%%!%!%!!%%%%%?%%?!%?!%??%???%?%!%?%!%%%%!?%?%!%%!!!%%?!%??%?%?%!!%!!!!%%%%?%%%?%?%?!!!%%!%%%%!?!?%?%%!!!%%!%%%?!?%%%!!%!%!%%%%?!!%%%%%%?!!%!%%%!!%%?%%%%!!!?!%%%?!%%!%!!!%%%%???%%?%%%%%%?%%!%?!!!%?%!%%%%!%%%%??!%%%?%%??!%%?%!?%!!%%%??!%%%%%!!%%%?%?!%%!%?%!%%?%%%?!?!?%?%%%%%?%!!!?!!%!?%%%!!!?%?!!?%?!%??%%%!!!%!?%%!%!%!!!!?%!!!!%?%%?%!%!%!!!!!%!?%?!?%?%!%%!%%%%!%!%!!%%!%!!!%?%%?!%%!!%%%!%!%%?!?%?%%%%%%%!%!%%%%%%%?%%%?!?!%!!%%%??%!!%?!!!!%?!%%!%!%%!%!%%%?%%!?%?!?%%!%!?%%!%%%!%!%!!%!%%%%%%%%!?!%%%%%%%!?%%!%!!!%%?!!%!!?!?%!?%%%%??%%%?%%!??!%!!%???%%?%%%%%%%??%%!!%!%!%%%%%!%%%%%?!!!!?!%!?%!%%%??%!!!%!%??%%?!!%%%%%%?%?!?!%!%%%%%%%!!%%%%%%!!!!%%%%%!!!!%%!!%!%%%?%%!?!?%!!%!%!!!%?!!%!?%??%!%!%!%%?%?%%%?%%?!!?%%?!!??!%%%?%?%???%?%!%!?%%!%!??!!%?%%%%!%?%!?%!?%%!!%%%%!%%%%!%%!%!!!!%?%?%%%%%%%%?%!%!%!!%%!!!!%?%%%!!?%%!?!!?%!%?!!!!!%??%!%%!%%?!%%!!??!!%?!!!!?!%%%%?%?%%!!%?!!%%%!%%%%%!%%%?%!!?%!%%!%%%!%%%!%%!%%!%!!%%%!!!!!%?%!%%%%?!%!%%!?%??!?%?!?!?!?!!!?%%?%!%%%%%%!!???%!!%%%!%?!!!?%!?%!%?%%?%%?%%?%?!%%%!!%%%!?!!!!%?%%??!?%?%!!!%!?!?%?%%%!%%%!!%%%??%!%%%%!!!%!%%%!!%%!?!!%!!?%?%%%%%?!%?%%!!!%%!!!!%%?!!%%%!%%%%%!!%%!!%?%?!%??!!!%!?!?%!%%!%?%%%!%%%%%!%%!?%%!%!??%!%!!!%%!!%!?!!%!!?%%!%!%!%%%%%!%%%!!!%%?!%?%!!%%!?!!!%!%%!%%%%%%??%!!!%%%!%%%!!%%%!%!%%%!%%!%%!!!!?!!!!?!%%!!%!!%%%!%%!%%?%!?!!?%?!!?%%?%?!%%?%?%!%?%%%?!%?%?%%%!%%%?%!%!%!%%!?%!%%!!!?!!%!%!!%%!%!?!?%%%!%!!%!%!?%!%%%!%%%%!!?!%!%!%!%%%%!!?!%%!!!??%%%!?!%%%%%!!?%%!%%!%!!%!!%%!!?%%!??!!%?%??!?%%??%??%?!?!!!%%?!!!!?!?%%!!%%!?%?!!??!%!?%!?%%?%%?%%!%%%%!!%%%%!?!!%?!!!%%%!?%%!%?!%?%!!!??%!%?!?!%%%%!%!%!%%%?%%?%%!!?%!!%%??!!%%?%%!%%?!%%%!%%!%??%%%!!?!%%!%!%!%!???!!!??%!?%!%%%!%%%?!%!%%!?%%?!%%%%%!??!%!%!!!%!%!?%!!%%?????%%!!!?!!!%!!!!?%!%!!!!?!%?%!!?!%%!!%!%!!%!%?%%!?%%!%%!%%%!?!%!%??%!%%%!!!!%?!?%?!!%!!!%%!%?%!%%?!!??%!?!!%%?%?!%!!%!%%%%!!%!%%%!%%!!!!%%!?%%%!%%?!?%!%!!??%%%%?%%%%%%%!%!?!!%!%%?%!%!?%!%%%%%!!%%!%%!!%!!?%!!%!!%%%%%%!!!%%%?%?%!!%%!%!%?!%!%%!%%%?!!%%%%%!%%!%%%%!??%!??%!!%!%!%%%!!??%%!%!%%%%!!!!%?%!!%?%%!?%?!!!%%!%!%!%!?%%?%!%!?%%%%!%?%%%!%!%%%?!%!!%%%%%!%%%%?!!?!?%%%%%!!???%!%%?%%?%%!%!%?%!!!%??%%%%??%!!!!%!!%!%?%!%%%%!%%!?%!%!%!!!!%%??%%%%!%%%?%!!!%!%%%%!%!?!?!%%%%!!%%?%%%!%!!%%%?!%!%!%%?!?%?%!%!!!!%?%!!!?%%!?%!!%!?!%!%!%!%!%%%!?!%%?!%%%%!!%%!?%!%!??!!%!!!?%%!%%%%%%%%%!%!%%%!%%%!!%?!!!%%!!!!%!!!%!!%%!%!%%!!%!%%!%%%!%%%!%!!%%?%%!%%%%!?!!%!%!!%??%%%?!%%?%!%!%%?!%%!%%%??!?!%??%!?!!!%%%%!%!???%!!%%?!%!%!%%%%!%?%!%%?!!%!%%%%%%%!%!%%!!%!%?????%!?%!????%!!%%%%?%%!%%%%!%!%%%!?%%?!!!!%%!%%!%!%!!%%!%!!!%%%!%%?!!?!%!%!%!%!%!%?%%%%%!?%%!%%!%?!%%%%!%!?%%!%?%%?!!?!%%%%%%%!%?!!%!%!?%!?%%%%!%%%%!!%?%%%!!!!!!%%%%%?!%%?!!!!!%!%!%!%?%%!%!?%!%!%%!?%%!%?%%!!!!%!%!%!%%!%!!%?!?%!?%!!%%!!%!?!!%?%%%%!!!!%!%%!%!%%%%?!?!?!%??!!!%!!%%!%!%!!%%!?%!%%%%?%!%%%!!!?%?!!?%%?%!%%%!%!!!%!%?!%%!!%%%?!%!%%%%%!?!?%?%!%!!!%?!??!%%%!!!!!!%?!%!%%%!?%%!%!?%!?%%%!%%%%!%%!%%!%?!?!%%%%%%!?!%!!%!%%!!?%%%%%%%%!!%%!%%%%?!%%%!%%%?%!%%%?%?!?%%?%?%%%!%?!%?!%%%%!%??%%!%%!!!%!!!%?%!%%%%?!!?!!%?%%!!%%!!!%!%%%%!!!%%%%%?!!!?!!!%!%%!!%%%%!%%!%%!!!%!!%%??%%%%%?%?%%!%!?%%%!%!?!!?%%%%%%%%??!%%%??%%?%!%?%!%%%?%!%?!!!%?!?%!?%%%!!%?%!%%%!%%%?%%!%%!!%%%%%!%%?%!%?!%!!%%?%!!???!%?!%!!!!!%%!%%%%%!?%%!%!%??%%?%!%!%!%?%!%!%!?%%%!!?!%?!!%!!%!%%%%%%%!?%%%!%??%!?%%??!!%%%%?!?%%??!!%%%!?%!?%???%?%!%%?!?!%%%??%%??!??!%%?%!?%!?%!!!%%?%?%%!?%%%%%%%!!%%!%%%!%%!?!?!!!!?!!%%?%!?%%%%!!!!!!?%!%!?!?!!!!%%!!!?%!!?!!?%%!%%%!!!!!!%%?!%?!!!%!%!?%%!%%?%%?%!%!%!%!?%?%!!%%!!!%%%!!%!?%?%?%!!%!!%%%!!%%%%!%%%%%%!??!%!!?!%?!%!!%!%!%%%!!%!%%%%?%!!!%%?%!%%!?%!%?!%%%%%%%??%%!%!?%%%?%%%!!!%?%??!%%%%!!%%%%?%!!%!%!%!!%!!?!%%!?!!%%!!!?!!!%?%!!%%%%%??%!%%%%???!%%!!%%!?%%%%%!%%!%%!?%!!%?%!%!!!!%%%!!?%!?%%%%%%%%!!%!%%%?%%?%%%?%%??%?!%%!!!!!%?%%!?!%%!!%!%!%%?%%%!%%%!!!%%%?!%!!%%%%%?%!%!!%??%%?%%!!%!!!!%%%!%!%!?%%%%%?%%%%%!%?!%?%!%?%!%?!%%!%%!%??%!%%%%%!%%!%!%%!%!%!%?%%%!%??%!?!%!!%%!%!!?!?%%%%%%??%!!!!!%%%!%?!?%!!%%!%!!!%%!?%%!%!%%%%!!!!%?%%!%?%??%%%%?%%%%!%%%!%!%!%!%?%%%?%%%%!!!%!%%%%%%?%%!!%%!%%?!!%%%%%?%!!?%%%!%!%?%%%%?%?!%%%%!%%%?!?%%!%!%?!?%?%%%%%!!!%%%%?%%%!%???%!%!%!!??%!!%%!%%%?!!?!%%%!%%%%!%!%!?%%%!%!?!!%!!%%%?%%%%%?%%%!?!%??!%%%?!%%%!!!!%%?%?!%%%!!?!!?%?!%!%!%!%!%%%%?%?!?!%%%!!!?!!%!%!%!??%!%!!%%?!??%%%%%%%%?%%%%!?%%%!?%%!%??%!%?%!%%!?!%%!!%!%%%!!!%%!!%?%%!?%?!?%%!!?%%?!?%?%%%?%?%%!??!!?%!%?%!?!!?%?%?!?!%!%?!!%%!!?%%%!!%%%%!!%%!%%%%??%!%%???!!%%%%%??%%%!%!!%?!%%!%??%!%%!%%%!%?%%%%%%%%?%%%!%%!!?%!!!?!?%!%%?!?!??!!!%%%%!!!?%%%!!%%%%%%!%%%%!!%!%?%%!%?%%!%!!??%%!%%%??!!!!%%%!!!%%%?%?!%%%%%!%%%!!?!%%!%%%%?%!??%?%%%%%%?%!?!!%!!!!%?%!?%%%!%!%!?!%%%?%!!%!!%??!%!!%!!%?%!?!%?%?!!?%??%??%???%%%%%!?%%%%%%!%%!%!!?!%%%%!%%%%?!!!%!%!!!%%!!%??%%!%%!!%!??%!!!!!%?%%?%%%%%!%%%?!%??!%!!!%!?%?%?!?%%?%!!!!?%!!?!!%?%??%%!!%%!%?!!%%?%!%?!%!?%%%?!!!%!!%!?%!?%%%%!!?%%??%!!%!!%!?%%!%%%!%!!%%%?!!%%!!%%!!!?%%!!!%!%%?!!!!!!??%!%!!?%%%?%%!%%!!!!!?%%!%!%%?!%%%!!!!?%!!%?%??!!%?!!!%%%%!%?%!%%?%!%!%!!%!%%!?%%?!!%%%%%!!!%!!!%%%?!??%%!!!%!%%??%!%%%!%!%!!%!!%%%%!%%%!?%%%!!!%%?%%?!%%!%%%%?!?%?%!?%%!%%%%%%%%!%%%%%!!%!%%%!%!%!%!!!%!!?%!%!!%???%%%%??%%%!%%!?!!!%%!%%%?%%!!?!!%!!%!%!?!%%?%???!!%!%%%%%!%%??%!%%%!%!%!!??%!%%!%%%%!!???!!%%%%!%%%%!%%!%!%%!??!%%!!%!?%%!%%?%!?!%%!!!?%%!?%%!!!%!%%%%%%?%%!!%!%%?%!!?%%!%!!%!%!?%!%%!!?%!%%!!%%%!%!?!?%!!??%%%?%?!!?!%%?!%!?!!?!%%%%?%%!%%!!%!!%!%?%?%%?%%!!!!%!!%%!!?!!!!?!!%%%%%%%%%!%?%%!!%%!%!%%?%!?!!?%%!!%%%%!%?!??!%?%%%!%!%%%!%?%%%%!?!%?!!%!%%%!?%%%%!!!!?!%%%?%!%%!%%!%%%??!%%%%%%!?!%!%?%%%?%%!!%%!%%%!??!!?!!%!?%%?!%%%%!%%??%%!?!%%!???%%%%%%%%!!%??%!?!%!?%%!?%%%!!%%%!!%!%!%!!%%!%?!!!!%%?%?%??!%%?!!!%!?%%%??%?!!%%%%!!%?!%%!!?%!%%%!%?%%%!%%%%!!%!%??%!%%!%%!%?!%%%%%%%%?%%%!!?%??!!!%%%!%!%?!%!%%!?%%!!%!%%!%!!%%!!%!%%%%%??!?%%%%?%%%%!!!?!!%%%!%%!%%%!!?!!%%%%%%?%??!%%%%%!??%!%%!%?%%!!!!?????%!%%%!?!!!%?%%!%%%%%?!%!%?%%%%%%%!!?%?%?%!?!%!!?%!!!%%%%%?%%?!%%%!%!%%?%%?%!%?%!%!%!%!!!??%??%!!!%%%%?%!%!%%!%%%!%%%%%!%?!%!%%!?!!%%?!!%?%%!%?!!%!%%!%%%%%%%?!!!%%%?%?%!?%!!?!?!%!!%?!%!%!!?%%?%%!!!!%%%!%?%%%%%%%%%%?!!%%!%%%%%!!?%!!%%%%!%%%%!?%?%?!%!!%%%!?%!%?%%?%%!%?!%!%!?%??%%!%%!?!%%!%!!!%%!%%!??%!?!%?%%%%%!%%!%!%?%%%!%%?%?%%%!!!?!%%%%%%?%%?%%%!!!%???%!!!%%%%%%%%%%%%!%%%!%!%%%%%!%%%!%!!%%%?%%!%%%%?%!!%%%?!%!?!!!!?!%!%%!!%%%%%!?%%%!%%!!%%!%%%!!%%!!%!!%%!%%%!%%?%%!?%%?%%%%%!%!%!%%%?!??%!%%%?!%?!%!%!!?%!%%%!!%!!%%%!??!%!!%%%%%!!?!%?%%%??%!%%?!!!?%%%%!%%!?%?%!%!!%%%%?!%%%!?!?%!!%%!!!%%!!!%%%?!%!%?%%?!%!%%%!%!!?!%!%?%%??%%%!%%!!!!%!!%%%!!!%%%!!%%%!?%!%!%!??!?!%??!?!??%%?%%!!!!%?!?%!%%!!%%%%?!!!!!!%!?%!?%?%%?!!?%%%?%%%%%%%!!%%%%?%%!%?%%!!%%!%!%?%%%%!%%%%%%%%%%%%%!!%%%!???!%%%%%%!%%!%%!%%%!!%?%%?%!%%?%!!?!?%%%!?%?!%!%!%?%%%%%!?!%?!%?%%!!%!%!!%%%%%!%%!%%!?%?%%%?!%!!%?!%%%%!%!!?%?!%%%%%%!!!%%!%?%?%%%!!%?%?!!%!%%%%%!?%%%%%??!%%!%%%?%!%!?!!%??!?!%%!!!%%%%%!?!%?%?!%?%%!%%?!%%%%%%!%!%!?!%?%%!?%?%%?%?%%%%!!!!%!!?!%%%%!!!!%%%!?%!%!!?%%?%!!!%%!!%%%%!!?%???%%%%%?!??%!%!?!!!!?!!%!%%!%%%%%%!!%%!%!%%%%%!%???%%!?%!!!%!%?%%???!?!%!!!!!!!%%%%%?!%%!!!%!?!%%%%!!%!!%%!%%!?%%!%%!%!!!%!%%%!!?%?%%%%%???%?%!!!!%%!!%%%%!%%!%%%!?%!?%!%%??%!!?!!!%!%%?!!!%%%%?%%!!%%%%!?%!!%%!!!!%%!!%!!%?!%??!!?!??!!?%%!?%?%%%!%%!%!!%!%?%??!!%??%!!%%%%?!%%!!%%!%!!%?%%!%%%?!%%?%!%%!??%?!?!!%!%!%%!%%??!!??!?%%!!%!!!!!%!?%!%%%%!%%%%%%?%%%%!%!!%!%!%%%%%?%!!?%!!!!!%!?!!%!%%%!!%%?%%!!%!%%?%!?!!%%%%!%%%%%%!%%%??!%!!%!%%????%%%!!?%!%%%?%!%??%%%!!?%??%?%!?%!!!?%!%%!%%???!!?!!!%!%%?!??%%!%!%%!%%%!?!!?%!%!!%!?!!!%%!!?!!%!%%?%%%%%%%!?%%%%!!!?!!%%!!!!%!%%%%%!%!%%%%!!%!%%!%%%%!!?%%%%!%!%%%%!%%%%?%%?%!%%!?%%?%%!?%%!%!!%%!!!?%%!?%?%%%!?%?!%%%%%!!%%?%!%!!%%%?!%!%%?!%%%!!%%%%%%??%?%!%!!!?%%?%!!!?%%!?%%%%%%?%%%!%%%!?%%%!%?!%?%?%%%%!!%%%%!!!%!!!!!!%%%?%%%%%%!%?%??%?%%%!%?%%%!%!!%%!%%%?!!%!%?!%%%%??%%%?%%%%%!%%%%%?%?!!!%?%%%??%%%!!!%??%!?%%!?%!!%!!%%%%%!%?%!?%!%%%%%!!%!%%%%!%?%%%!!%%!!%%!%%%!%!%%!%!%%??%%!%??%!%!!%!%%?!!!!%?%%!%%%!%?!%%!%%!%!%?%%!%!!!?%!%?%!%%%!?%%%%?!?%%?!%%!!!%%!%!%%%!!!?!%%%%%!!%!%%!!!!?%?%%%!!%%!!%%!!%!%%%!?%?%!!%?!%!?!!%!%?%?%!%!!?!!!!!?!%!%?!!?%!%!!%%%%?%%%!%%%!%!%%?%!%%%?%%!%?%%!%%?!?!??!%%%?%%??%!?%%!%!%!%%!!%!!%%!!!!%%?%%%!%%%%!!%%%%%%!?!!%?%?!!%%??%!%?!?!!?%!%!!%!?!?!!%!!%!!?!!!%!!?%%%%%!!%!%%!%%%!!%!%%%!%%%!!%!%!%!%%%%??%!?!%%!!%%?%!%!%%?%%?!!%%%!?%?%%%%%!%?%%!!%!%%%!?%%%!%%%!%!%%%%!?%%!%!!!!%%!%%!%%?!!?!%?%!!!%%?%!%!%!%?%%%?%!%!!!?!!%??%%%!%%!%%%%!%?%!!%%%?!%%!%!%%%%%??!%?!!?!!!?%%!!%%%!?%!%%?%%?!%?!!?%!%!!!????%%?%?!??%%%!%%!%!%!?%!!%%!%!!!!%???!%!%!%%?!?%?%%%%%%%?%%!%%%!!?%%!%%%%?!!%%%?%%%%?%!%?%%%!!?%!%%!%!!!%!!!%?%!%!%%%%%?!%%%!!!!%?!!%!%?%!!?!%%!!??!!?!???!!%!%%%???!%?!%%%%%?%%%%?%%%?!%!%??%??!%%!%!!%%%!?%??!%%%!%!%?!%%%%%%??%%?%!?!%!%!%%?%%%%!!%!%%!?%?%!%??!?%?!!%!%!!!%?!%%%%%!!!%%!%!?%%%%!%%%%%%!!!!?%!!?!%?!%%!!!?%%%!%%!%?!%%%%%%%%%!%%!?%??!%!!%!!!%???%%!!%!%%%?!%!??%%%%%?!%!?%!!?%%!%!%!?!%??%!%%%%%%%?!?%%%%%%%!?%%%!!%%%?!!?%%%!%%?!!!%%%%%!!%?%%!%!%!%%!??!!!%!%%%!%!%%?%%%??%%%%?%%%%!%%!?!!!?%!!?!!%%%?%?%!%?%!%%%!!%%%%%?%?%?%!!%!!%!!%%%!!%%?!%%%%!%?%%!%%!%%?%!!?!%%!?!?!?!%%%!%%%!%%%%!!?%%%!%%?!%%!??%!%!!%?%%!!?%%!%%%!!%?%%!%%%%!%%!!!?%%%%?%!!?!!!!!?%%!%??!!!!?!!%??%!%%%?!%%%!%?%%?%%?!%%%?!%%%%!!%?!!%%!!%%?!%!%?!?%%%%!?%?%%%??!?!?%%%!%%??%!%!!%%%%??!%!%!%!!?%%%!?%!%%%%!%%%%!!!?%%!%!%!!?%%%%??%%%!%%!%%%%?%%?!!%%?!!?%?%%%?%%%!%!?%!!?%%%?%!?!%%?%%%%%%!!%!!?%%%??%%!!!%%!%!!!?%!%%!?%?%%%%!!!!!%%?%???%%?!%%?!%!?%!!!%%%%%%%%%!%%!%%!!%???%%%%%%!%%%%?%!%?%%!!!!%!%?%!%%%%?!!!%!!%%?!%!%?%%%?%!%!!%%!!!!%%%%!??%%%!!?!!%?!!%%%??%?%?!%?!!!%%!?%!%!%?!%%%%%%%%?!%!%???!!%!%?%?%!%??%!!%%%!%%!%%!!!?!?!%%%!%%!%!?%%!!!%!?!%%??!!%%!%%?!%!%%%!???%%%%%!%?!%%%%%%!%!!?!%%!%%%?!!%??!?%??!!%!%%?!??!%!!%!%?%%!!%!%%!%!%?%%!%!%!!%!!?!!!%!!%!%%!?!!%%%%!%%!!%!%!!?!%%!%%!%!%!%?%%%%?%!?%!!!%!?%%%%!%!!%?!!%?%??%!!?!??%!?!%%%?%%%%%!!!%!%?%%%%%%%?%?!%?!%%%!!?!%?%!%%%%%%!?%!%%!??%?!%!%%%!%!%%%%%%!?%%%!%%%%!%!%%%%!!%?!%%!?!?%%%!%%!%%?%%%%?%!%%%?%%%%!!?!%!!!%?%!!!!%?%!?%%%!!!%%!!?%!!%%!%%%?%%%!%!!%!!!?%!?%%!%?%%%%!%??!%%%%%%%%%%%%?%!?!%!%%?!!?%%!!%%%%%%%!%%%%!%%!%%!%!!%%!%%%?%%%%%%%!??!%%!?!!!!%!%!?%!!%%!%!?!?!!%%%%!!!!%%!?%!%!??!!%!%%!%%!!%%%!%%!%%!%%?%%!%!%!%%!!!%!?%%%%%%?%!%??%%%?!!%!%%%%%!%%!?!%%?%!?%???!?%?%!!?!??%%!%?%!!!%???%?!%!%?%!!!?%?!%%!!!!%%%%!!!%!!%?%%??%%!!%%%%%%%?!%!!!%%%%%%%%??%!%%%%!%%%%?%%!??%%!%?%%%%%!%!%??%%!!!%!?!!!?!%%!%??%%%%!!%%!%?!%!!%%!%?%%?%!%%!%%!!%?%%!%%%!%!!!!!?%!%%%?!%!%??!!%?%%%!!%?%!%?!?!?!?%?%%!!%!??%%%%%%??!%!!!%%%%%!?!!!%?%%!??!%%!%%!!?%!%%%?!!%%?!%%!?%!!%%!%!%?!%?!?%%%%%!!!%!!!%%%%?%?!%%%?%?%?!!!!!!%%%%%%!!!%%?!%!%%%%!%?%%!%!!%%%%%%?!?%%%?%%%%!!!%%%%!!%?%!%%%!?%!%!!?%%!%%%!%?!?%!%%?%!%%?!!%%%?%!!!!!!%!%?!%%!%?%%%%!%%%?!!!?!!%!%!!!%?%!!%!!%?%!!%!%!!%!%%?%%%%%%!?%!%%!%%!%%%%?%!%%?!?!!!!!%%!!%!%%%%!%%%%%%!!%%%%%%!%%!%?%!??%!%?!%!!!%!%%%?%?%%!%%!%%!!%!!%!!%?!!%!%%%!%?%%!%??!%%!%%%%?!%!%!!%!!!!?!%!!%%!%!!!%%!%?%!%!%!!?%%!?%%%%!%%%?%?%?%%%%%!!!%!!%%?%%%%!!!!?%%!%%%%!%?!!?!!?%%?%%!?!!!!%%%!%%%?!!%!?%%!%%?%?%%?!!!%%!%!%%%!%?%%%!!?%!%%%%!!%%%?%%%%!%!%?%!!!%%!%%!?!!%!%!%%%!%!%!!%%%%%%%%%!!??%%%%!?%%%?%%%!%!!?!?%%!%!%!%?!?%??%!??%!!%%%!!??%%%?%?%%!!%%%%!!%%%?%%%%?!%!%!%%!!%%%?%%%?!!%!%?!!%!%!%%%%%!%!%?%%%%%!%%%%?!%%?%!%??%%%!!%!%%%%!%%!%!!%%?!%%%%?!!?%?%!?%%%!?%!%%%!%%%!!%!!%!%%??!%%%%?!%!!!!!?!%??%!%!%!%!%%%!!?!!%?!%%!!!!%%%!!%?!%%!%%!%?%!?%%%%%?%?%!%?%!%!!%!%?%!%?!?!%%%%%?!%??!%%?!?%%???%%%%%%%?%!%!%!?%%%%?!!?%!%%%?!%%!?????!!!!%!!!?%!%%!%!%!!!!!?!%%%!%!%!%!!!!%??!!!!!!!%?!%!%%?!%!%?%%!%!%%???%!%%!?%%?!!%%%?%!!?!!!!?!%%%%!%%%?!?%%%!!%%?!%!!?!!%?%!%?%?%%%%!!%%%%!?!!%?!?!%%!?%?%!%?!%%!!!?%!%?!!?%!%%!%%!%?!%??%?%?!!%%!!?!!?%%!%%%!??!%%%!%!%??%%%!%%%?!%?%!!%%!%?%!!%%%?!%!!%!%%%%?%%!!!!!??%!!%!%%!!!%!!%%!!?%%!%!%!?!%%!!%%%??%!%%!!!!!%%%%!%!%%%!!%%%%%%%%%%!!%!%%!!%!?%%?%%!!%%!%!?!%!%??!!%???!%%??%?%!%%!%%%!%!?%?%!!?%?!!%?!?!%%!!%%%%%?%!?%!?!?!??%%%%%!%!!!!%!!%%?!!!%!!%!%%!%%%?%%%!%!%%%!%?!!?%?%!%?%%%?%%!!%%%?!?!!!%%%!?!??%%%!?%%!%%%%%!!%!!?!%%?%!%%!%%!%%%%!!!%%!%!!??%!!!%??!!!%%%%!!%%!%?%!?%%%!!!!?!?%!%!!!%!%%%!!!!%?%%%?%?%!!%!!%?!!%%%!%%?%%%%?%!%%%%%?%%!%?%?!%%%!!%?!!%!!??!!!!%%!!%%%%?!!?%!?!?!!%%%%?!%%!!%!!!!!%%%%?%!%!!!%%!!%?%%!%!%%%%?%!!!?!!?%!!?!%%%%%%!!%%%!!!%!%%!?%!%%!?%!!%!??!%%%%!?%?!%%%!%!%%%%!%%!%%?%!%!?%?%%!%%!!%%%?%!%!!%?%%%!%%!?%%?%%%%?!%?%%%%%%?%%!!%!%%?!%?%!!%!!!%!!?!%%%%?!%%%??%?!!?!%%%!%%%%%?%?%!!%?%?!%!%!!%!%%%!?%%%!%%!%!%%%!!!?!%!%%!!!%%%%%%??%!!!?!%%%!%%%%%!!%%!%%%%!?!!%%%%%%?%!%%%?%!%%%!%%%%%%%!!!!!!!%%!%!?!%%%%%?%%%%!?%!%??%%%%!%%%%%?!!%!!!%%%%!!!!%?%!!%?!%%?%%%!%%%!?!%%!%!!%%%%?%?%!!!%%!%?%!%?!!!%!%?!%!%!%%!!%%%!!%%?!??!%!%%%%!%?%!%!!%!!!%%!!!%%!!%?!!?%%%%%%!%%%%%!%?%%%!%!%%?%!%?!%%!%%%%?%!%%!%!%!%?!?%??!!%!!!?%!%?!%%%%%%!?%!%!%%%%!!??!?!!%%%%%%!%?!%%%%!%!??%!?!%!!!!%%%!?%%%!?!%%%!%!%!??%%!!?!??!%??%?%%!%%%!%%%%!!%!!%%%!%%%?!!%%?!%!%!%%%!%%%%%!%!%%!%!%%?%%!!%?!!?!!%?%!??%%?%%!?!!%!!%%%!!%!??%!!!%!!%!!?!%%%%?%%!!%%!??%!%!?%!!?%%!%%?!!!?!!%?%%?%??%%%?%!!?%%%!?%%%?!!%%?%%?!%!%!%%!!?%!%%?%!!!!%!%?%%%%%%?!!!!!!!!%%!!!%%?!%!%%%%!?%%%%!?%%%!!!!!%!%%?!!%!?!%%!!?%%!!!??%%%!?%%!%%?!!?!!%%%!%!%!!?!!%!%%?!???%?%%%%%%??!%!%!?!%%%!?%!!%?%%%%%%!!%!%!!%!%%!%?%%?!?!!%%%!?!%?%!!!?%%!%?!%%!?!!%!!%%%!%%?!!%!!%!%?%!%%%%!??%!!?!!?%!%%%%!%%?%!!%%%%?!%%!!%%%!%%??!!%%%!%%%%!%%%%!!%%%%!!?!!%!!!%%%?%%!!%?!!!!?%%??!%!%!%!%%!%!%%%??%!?!?%%??%?%%%!%?%!%%?%?%%%%!!!?!%!%%%%%!%???%!!?%%?!%?%!%%!%%?!!!!%?%%!%!!!%!!%%%?%!!%%!%!!%%%!%%?%!?%?%!!?!!!!%%%%!%%????%%!?%%%?%%?%%%?%?!?%%!%%?%%?%?%%%%%!!??!%!%?!?%?%%%%!!!?%%!%%%%%%%%%%!!!?%%!%%?!%!%??%%!%%!!%%!?!!!!!!%%%?!?!%?!%%!%%!?!!!%!%%%%?!!%%!%%%!!%?!%!%?%%!%!%%!%?%?%%!!%%%!%%?!?%!!%%!%!!!!!!!?!?%!%%!%%!!%!%!!!?!?!?!?%%%!!%!?!!%%%!!%%!%%%%!?!!%%!?%%!!%?!%?%!%!!!!%%%?!!%?%!%%!%!%?%%%!?%%!%%!%%!%%?%%%%?%!%%!!?!%??!%%%%%?%!%%%%%!%??!!?!!?%!!%?%?%%!?%%!?%%%%!!?%%%%!%!%!%%!%!%!!!!%!?%%%%%%?%!!??%%!%%%!%!%!%!%!!%%%!!%?!%!%%!%%!?%%!%!!%%!!!!%%?%%!!%%%!%%%!%%%%%%%!%?%!%!%%?%%%?%!%?%%%?!!%!%%!%!!%%%!!?%!?%!%%!!!!!?%!%%%!?!!%!%!!!%!!%?!%!?%%!!!%!%%!?%!%!!%!!%!%%!%%%%%?!!%!!%%%?%%%?%?!%%!%?%%!%?%%%%?%%?!%%!!%!!%!?%%?%!%??!%!!!%%?!%%%%%%%%!?!%%%!!!%%!!%!%%!!!%?!!%%%!%%?!%?%!!%%%!!?%!??%!%?%%!%%%!!!%?%!!!%%!%!!!!%!%%%?!!?%%%!!!!!%%!?%%%%%!!%!%!!%!!?%!!%?!%?%%%!%%%!%?%?!%!!!%!!%??!%%?%!?!!!%%%!%!%%%????!?%?!!?%%?!?!%%%%!%!!!!%%%!%!%!!%!?!%%%%%%!!%!%%!%%%!!%??%%%%?%!%?%%%?%!!?!%%!!%?%?%?!!!?!?%!??%?%!%!%?%!%%!%!!%!!!%%%%%!%!?%!%%%!%!%%%%?!%?!%%%%%%!%!%?%!!!%%?%%%%?%?%%??!%?%?!!!!?%%!!!?%%%?%!%%%%?%!%!!%???%%%%!%!!%%??!%%%%?!?%%?!%!%%%!!!%!?%!?%!!%!!!%%%%!!%?%%!?!!%%!%%?!!%?%%?%%!%%%!%%!%!%?%%!%%!%?!!?%!!%!?%!!%?!%!%!%?%!?!!!%?!!%!!%!%%?%!%!%%!%!%!!!!!%!%?%!!%%%%?%!%%%!%%!!%!%%%?!!%??!!%!!?%%?!!%?%%?%!%%!%%%%%%%%%!!!?%??%!!%!!!%!%!%%!%!!!%%%%!%?!%!%!%!%!!%!!!%!?%!!%%%?%?!%%!!!?%!!!%!!?%%%%!%%%%?%%!!%%!!%%!%?%?!!!%!?!%%!!!?!!!%%?%!!%%?!%%!!!??!%%!%!???%%%%%%%!%%!?%%!%%%%!?!%%?!%%%%%!%%!%%%!%%%?%!?!%??%%!?!%%!!%!%?!!!%%?!%!%!!??%%!??%!%%?%%!!!%!!?!%%%%%%!!?%%%%!!!%%!%!%!%?%%!!??!%%!%!%%!!?!!%%%!%?!!%%%%%%%!%?%!%%?%%%%%%%%%%%!%%!!?%%!!!?!%!?!!!%!!!!??!%%%?!!%!!%%!!??%!!%!%?!???!%!%!!%?!%%!?%!!?!?%%%%%%%!%%!%%!%%!!?%%??!?!!!%%%??!!!???%?!?!%%%?%!%!%?%!%%!??!!!%!%%%?%!%%!%%!%%%?%!%!!%!%%%!!!%!%%%%%!%%?%!%%!%%?%%%?!?%!!?!!%%%?%%!%?%!%%!?!!!%%%?%%%?%%%%!%!%%%%?!?!%!%!%!%%%%%!!!!%%?%%!!%!!?%%%%!!?%%!%!%%?%%%%!!?!%%%%%!!%?%?%%%!!!!?!?%%?!?!%%%!!??%%!%!%%%!!??!?%!!?!?%%!?%?!%!??%?!!!!!??%!!%?%%%!!%%%!%%%%!??%%%%%!%%%!%%%%!%%!%%?!!!%?%!?%?%%!%%!%%!!%!?!??%%%!!%%!%%??!!!%%%?%%%!%!??!!%%%%!!%?!%%!%!%?%%%!%%%!!%?!!!%!%!!!%!%!%!%!!%%!?!%!%!!?%%?%%?%!%?%%%%%%???%?!!!%!%?%%!%?%!%!%!?%!?%?%%%!?!%%?%%%%%!!!!!%!%%%%??!%%!!!?!%?%!!%!!?!!%%%%%??!!??%%%%?%!??%!%!%%%%%!%?%?%!?!%%!%!!%?!%%%?%!!%!%!%%!!?%%%%!??%!%%!?!%%!%%!!???%?%?%!%!%!%%%%!?!?!%!!%%?%?!%%!%??%!?%?!?!?%%?%%!%%%?%%!!?%%!!%%!!!!%!%%%%%?%%!%%!%%!!!%?%%!%!%%%%!%%%%%%!??%?%%%!%%%%!%%?%?!%!?%?%!%!!!%?!?%!!%!%%%??!!%!%%!!%!%%%!%!!%%%%%%%%!?%%%%%!?!?!%!!!!%%?%!%!?%%??%%!!!!!?%%%%?!%%?%%!%!%%!%%%!%%%%!?%%!?!%%%%!%!!!%%%!!%?!%%!%%%!!%!?!%%??%%!!!?!%%%%%?!%%%!%%!%!%?%!%%%!%%%!?%%!?!?!?%!%!???%%%%!%!%??%!!?%%%!?!!!!!%!!!%%%%?!?%%%%%%!!!%?%!??!?%!%%%!?%?!?%%!?%???%!?!%!!?!!%%%?!!!%%??!%%%!%?%%!?!%!%%%%!!?%%%%%!!%?%%%!%!%%%%%!%%%!%%!!%%!?!!!%%%%?!!!%%!%%%!%%%%?!!?%%!%%%!!%?%%?%%!%%%!%!%!%%%%??%!!%%!%%%!%!%%%!%???!%%!?!%%!!?!!!%???%?%%%!?!%%?!!!%%%%%%%!%%!%%%!%%!!?%!%%%%%%%%!%%%%%%!?%!!!?%???%!%!%%%%?%!!!!!%!?!%!!%%!!%!%?!%?%!%%?%%%!!%!%%!?%!!%%%?%!???%??%%!%?%!!?%%?%!!!?%??%%%%%!%%!%%%%!%%%%%%!!!!!!%%%!%%%%!%?%%%!%!%%%%!!!%%!?%?!?!%?%!%?%!%?%!!?%%!!%!%?%%??%%?%%%?!%%?%!%!%?%!!?%!%!%??!%%%?%%!!!%?!%%%!!%%!!!!%!%!%%%%%!!!!!!%%%!%%?!?!%%%%%!%!?%!%%%?!%?%%!?%!%!%%%!%%?%?!!%???!!%%%!%!%%!%%%!?%%%%?%%!%!%?%?!!!%%%%?%%!!%?%%?%!!!!!%!!%?%?!!%?!%%!?!!!??!?%?!!!?!!%%%!%?!?%!%%%!%!%?%%%?!%??!!!?!!?%%!%?%%!!!%!?%??%!%%!%!!%?%%%%!%!!%%%%%%%%%!!%??%%%?%!%!%%?!%!!%%!%%??!%?%%!%!%!%%%%?%%%!?%?!%%%?!%?%%%%%!%!!??%%%%%!%!??!%?%%%?%?%%!?!?!%!%%%!!?!%?!%%%!?%%?%!!%%!%!%?%%%%%%%!!%!?!%!!!%?!%%%!?!?%!%!%???%!%%%%!!%??!!!?%!!%!%?!!!%?%!%%%!%!%%%?%%%%?%%?!!%%?%%%%%!?!!!!!!!%%!!%!%%%%%%%%%?!%%%%!%%%%??%!!?%!!%!%%!%?%?%%!!!?!!?%?%?%!?!!%!%%??%%%!%??!%!%!!?%?%%!!?!%?%%!%%%?!!!%%??!%%!%?%?!?!??%!?%%%%!!%%%?!??!?!!%!!%%%%%%%%%%!%%%%%%!%?%%?%?%?!!%%?%!!?%%%?%%%!%?!%!%%%??!!%%?!%?%!!!!%%!%%%!!!?!%?!!!%??%%?%?!!!%!%%%%!!%%!%%%%!%!%%!?%?%?!!%!%%%!!!!!!!!!!?%!%%%%%%!????%!%!%%%%!%%%?%%!%%%!?%!??!%!%%?!!!!%%!!!%%%!!?%!%%?!!%%!%!?!%%?!??%?!!!%%%%%%!??!%?%%%%!%%!!!!!!%%%%!!?%??%%%!%?%%%%%!%%%%?!%!?%%???%!%!%!%?!!?!%?%!?!!%!%?%%?!!!?%%?!%%%!!?%!?%???!?!%?%!?!?%!!%%?%%!?!%!!%?%%?%!%!!??%%%%%?%%%!%%%??%?%%?%%!%%%%!%%!%%%?!%!!%!%?!%%!%!?%!?%%%!!?%!%%%%%!!%?!%!!?!!!%!%?%%%%!%!?!!%%!!%%%%!%%%!%%%%%?%%!%%%%%%?%?!!%!!!!!!%%%!!!??%%!!!%??!??!%?!%%!!%%!!?!%%%%%%%!%?!%%?!%?!!!%!%!!!?!%%%!%%%%!%%%!%%%!!!%!!%%%%%%%%!%%!!%!!%%!%%?!%!%!!%%?%%%%!?!!!%%?!%%?%!!!%!%%%!%!!?!!%!%!?%%%%?!!%%%%!?%%%%%!!!!%%?%%%!!!!%?!%?%%%%?%??!?!?%%!%%!!%%%%!%?%%!%%????%%!%%%%?!%%!%%!?!!%!%%!!!!?%!%!%!?!!?%!%!%%%%!?!%!%!%%?!%!%??%%%!%%?%!?!%!!!?!%%%!%!%%!%!%%%??%?%%%!%%!!!%!?%%%!!?%!%?%%%%!%%!%?!%!!%!!%%??%!!!%!!!!?%%%%!!!!%%?%%%%?%%%!!?!!%?%%??%!%?!%%!%?%?!%%%?%%?%!!%%%%!%?%!!%!?!%!!%%!!%!%%%!!!??%!!%!%%!??!%%%!%%%%??%!%??!%!!%!%?!%%??%%%%!%?%!!%%%%!?%!%?!!%%%%%!!%%!?!%%%%%%%%%?%%%!%!!?%!%%%?%??%%!%!??!%!%%%!%%???!!!%%%%!%%%%?%!!!%?!%!!%%!%?!!%%%%!!%%!%%%!!??%%?%?%%%!%!!%!!!!!%%%%!%%!!%?!!%!!%%%?!!%%!!?%%%%!!%!!%%!!?!%%?!!?!%%??!!%!!!%%!%%%?!%%%%?%!%%%%!%%%?%%%%%?!??%%%?%!%!%%!!!%%!%%%%!?!!%%%!%%%!%!%%%%!%%!?!%%?%!%!!%%!!!%!?%!%%?!!%%?%%?%%!%!%!%????%?%!!%??!%!!%!?!?!!%!!%%%!!!%!%%?!%!!!?!%%!?%%%%!!%%!%!%%%!!%!!!%!!%%%%!!%!%!%%?!%%!?!%!?%!%%%%!!!%%%??!!!%!!!?!!%!%%%!?%%?%%?%%%?!%!!??%%!%%%%%%%%??%?%%%?!!%%%%%%?%!%?!?!%!%!??!%!%%%%%!!%!!%!%%!%%%%!%%%%%?%!!!!!%!??!!%?%!!%??%%%!??%?!!!%!%%%!!%%%%%%!%%%%!%%?!!?%%?%!!%!?%%!%%?%%!%?!??%%?%!%%%%%%!%%!%?%%%???!%%?!%?!!%!%?%%!%%%!!%!?!%%!%?%!%%??%!%%%!%!%!?%%!%%%!!!?%!!%?!%!%?%!?%%%%%%%%%%%?!%%!!%%%%%%%!!!!??!%%%!!%%%%!!%%?%%%?%!!%!%?!!%!?%%!%%!%?!%%%?%!%%!%!?%??%!!!?!%%%%%%!?!%!?%?!%!%%%!?%!!%!??!!%%%%!??%%%!%?%%!?%%%%!%%!!!%!!?%!?!%?%!%%!%!!?!!%!%%%???%?%%!%!!!!%%%%!%%%?!!?!%%?!!!%%%?!!%%%??%%%%%!!!?!%?%!%!%!!%??%!%%%?%%?!!!%!%%!!%%%%%!%!%!%%?!%!!!!!!!!!%!%!%%???%!!?%?%!!%!?%%!%??%!%%!?%%%%%%%%%%%%!%%!??%%%?!%%!!%%%%??!%??%%%%%%?!!!%!%!???!?!%%!!?%?%!?%!%%!!!?%%%!%!?!%%?%!?%!!%?!%!%!%%%?%%!%!%!?%?!%?%??%%!%?%?%!%%%%%%?!%?!%??!!%?!!%%%!!%%!?%!!!%!%%!%??%%???%%%!%!!!%%%!%?%%%%!?!%%!!!%!%!??%%!%%!%!%!%!?%!?!!!%!%!%%%!%%%%??!%%%%%?!!%%?%%!!!??%!!??!%%%?!!%??!%%%?!%%!%?%%%???%%%%!%%%!%!!!!%??!%!?!!%%%?!%%%%%!?!%?%!!?%?!!!!?!%%%%!%%?%%!%%?%%!!?%!%?!%!?%??%!%%!!!!%?!!%??!%!%!?!!!!?!%%!%%%?%!!!%%%!%%!!??%!!??%!!!%!!?!?%?!%%!%%%???!!!%!%!?%?%%%%%!!%!%%%%%?!!!%!!!?%!!%%%%%%!!%!%%?!%%?%?%%%%!%?!%!%!?%%!%%?%%!%?!%%%%?%!%!%%%%%%!!%!!%!%%!%%!?!%%%%!%%%%%%!%%%!?%%%%!!%%%!%%!%%%%!!%%?%??!%!%!!?%!%%%!%%%%%%%!%!%%%!!?!?!!?%!?!!!!%%%%?%%?!?!?!!!!!%!!!?%%!!!%%%??%?!!%%%?%%!!%%%!?!%!%!?%%%%%%!!%%%%!%%!!?!!?!!!!%%%%!!%!%!?%?%%%%?!?!!%!!!?!!%%!%%%!%!%%!%%!!?%%!??!%?!!%??%!%?!%%%?!!!%!?%%!%%!!%%!!!%!!!%%?!!!%%??!%%%!%%?!!%%%?!%?%!!!%%!%!!!%%!!%!%!%%%%!!!??%%%?!%?%!%%%!%!!?%%%%!%%!%%!!?%%!%%?%%%%?%???!!%!%%!%%!%%%%?!%%?%?%?%%!???%?%%?%%%!%%%%?!%%%!%?!!!%!!!?%?%%!!%%?%!%???!?!!!!!?%%%!%%!%!%%!%??!%%!?%!%!%?!%!%%%!!!!?!%%!%!%!%?%%!?%!?%?%%%!!%%%%%!!!%?!?%?%%!%%!%%%%%%%!?%!%%!%%!%%!%!?%!%%?%?%%!?!?%?!?!%!!%%%!!!%%!%?!?%%%?%!%%!%%%?!%%!%%%!!!!!!!!%?%?!%!%!!!!!%%%%?%%!%%?!!?!!%!!%%%%!%%%!%!%%!%%%%%?%%!?!%%!%!%%?%%?!%%%!?%!%%?!%!?!%!%!!!!!?!%!%%%?%?%%!%%%%!!!!%!%?%%%!%!!!!?%!!!?%%?%?%!%!???!!%!%%%%!!?%%?%%%%%!!%%%%%%%?!%?!!!?%%?%!%%!%%%!%%%%!%%?%%!%!!%%!%%%!%%!!%?%?%%!%??%!?%%!?!!?%%%!%!%%%?%%?%!!%%%%%?%%%!%!%!!?%!!!%%%??%%%?%%%%!%!!%%!!%%%%%%%%!%%!?%?!%!%!%%%%%?%%?%%%%!!!%?%!!?!%!?!%%!%!%%!%%!%!!%!%%?%%%%?!?!!%%?!!!!!!!%!%%!%?%%%%!%%%!?!%%%%%?%%%%!!%%%%%??%?!!%%%??%!?%!%%???%!!!%!?%!!!?!%%!%?%??%%!!%!%%!!!%%%!!?%%%%%!!%%%%%!%%?%%%%!%!%!?%!!%%?!!%%!%%%!%!!%%%%%%!%!?%!%%!!!%!!!%!!%%%%%!!!??!%?%%?!%?%!!%?!!%!!%!%%%%!??!!?!%?%!%%!!%!!%%%!!%?!%?%!!%!!?%!%%%%?%%%%%%?%!!%%?%!!%!??%%%%!?%!!!?!%??%??%%!%%!!%%?%?%%%?%!?%?%?%%%???!%!%%%!%?%!!%%%%%!%%?%%%%??%%!!%%%%%%!!!!!??%!?%?%%!%?%%!?%%%%%?!%%%%%%%%%!!!?%?!?%!%%!%!%??%%%%%%!%??%!%!!!?!??!%?!%!??%%%??!%?!!%!%%%!?%%%!%!!!%%%??%%%%?%%!!%%!???!%%%?%!?!%?%%%!%%!!!!!%!!!!%?%!%!%!%%%%%?%?%!!%!%%%%!%!?!%%!?%%!%!%?%!%%%%!!!%%?%%!%%%%!%!?%%%!%!%%%%%!?!?!%!?%%?!?!%?%%!%%%%%%%?%?%!!!!?!%!!%!%?%%%!%%%?!%!?%!!%%!!%%?%!%!!%%%??%%%!%%%%%!!%!%%!%!!!!%?%!%!%%%!%%!%!%%%!%!%?%?%!?%!!!%!%!?!!!!!%%!%%!?%?%%%?!!%%!%%!%%%%?!%!!%%%!%!!?%%%?%!%?%%%?%?%!%!%%?%?%!%??%!!%%%%!!%???%%%%!!%%!?%!%!%!%?%?%%%%%!%!?!!?%%!!%%!!?!%!?!%%%%!!%!!!!!%%%%%?%%!!!!!%%%!%%?%!?%%!%%%%!%?%!!!%?%%%%?%%%!!!%%!%?%%%!?%%!!%%%!%%%%?%?!%%!!%%%!%!%?%!%%?%!%??%!!%%%?!%%%%%!!%!%?%!%?%%%%!!!?%%?!%%!%?!%!?!%!!?!%?%%%!%!%?!!?!!?%%?!%%!%?!!%%%!%!!?%!%%?!?%%!%%%%?!!%!%%!!?%%?%!%!?!%%%?%?!%%!??%%%?!%%%%%!%?!!!!??%!!%%?%!!%%??%%!!?!%%%%%%!%%!!%??!%??!%%!!?!%!??!%!!?%!!!!%???!%%%??!%%!%!%%?%?%?!?%!!%%%?!%%?!%%%%%%?!%!?!??%!?%%?%!!%?%%%!!%?%%%?!%?!%%?!%%!!%?!!!?!%%!?%!!!%%?!!%%!%%!%!%%%!!!%%%%!%%?%%%!%!%!%%?!%!%?!??!?%%?!%??!%!%%%%!%%%%?%?%?!!%!%%!!?!!%%?%!?!%!%%%?%%?%!?%?%?%%?%!%!!?%!!%%%%!%%%%?%?%!%%%!!%!!!%%!%!%?%?!%!%%?%!!%?%%!!?!%%!!!!!?%%%%%!?!!%%%%!%?!!?%%!!!%%??%%!%%%?%!??%%%?!%%!%!!%%%!%%%?!%??!%%?%%?!!!%!%%!!%!!%!%?!!!??%!%%%%!%!!!%%%!%!!?%!?!%%!%%?%!%!%?!?!%%%%%%!%%!!%!%!%?%!%%%!!!%%!%%%%!%%?%!!!%%?!?%?%%%!%%%%%?!??%%%!!?%!!%!?%!!??!!%!%!!%%!%!%!%%?%%%%%%!%%!%!!%?%%!%?%!?!%??!%!%?%??%%%??!%!%%?%%%!!%%!?%!?%%%!%?%!%%%%%!%!!!%!%!!?%!??%?%%?!?%%%!%!?%!%%%%%!%%%?%%%!%%?%%!!!!%%?%!!!!!?%%%%!%!!%%%%!!%%%%!%%?%!%??%%%%%%%%?%%%%?%?!%?%%!?!%?%!%%%!!%??!!!%!%%%!!!%%%?!%%!!%!%!!?!!!!!%%%%!?%??%!?%%%%!%???!?!%%?%?!!%!%%%%%%!!?%%!!%%%!%%?%!%%%??%!??%%%!!%!%%!!%!!%!!?%?%%%!%%!?%%%%%%!!%%?%%%%%??!!??%%?%!!%!!%%%%%?!!%%%%!!%%%!!!%%!?%%!%%%!%%!%%%%%%!%%!!%%%!%%!!%!!??!!??%%?%%%?%%!!%%!%%?%%???!%??%!!???%%%%%%!?%!%!%%%%%!%%!!%?%?%%!?!!!?%%%%!!%!!%%!!%%%!!%%!?%%!%!!%?!%?%%!!%!%%%%%?!?%%%?%%!%!%!%%%%%%%%%%!!%%!!%?%!%?!!!%%??%%%%?%!!!?%?!%%%!!%%?!%!!%!!!?%!?%%!%!!!?!!!%!?%%!!%!!?!!?%!?!??%%%%%?!!?!!?%?!?%%%!!?!!%%?%!?!!%?%!%%%%?%!!%%%??%!%!%%??!%!%!%?!!?!%!?%%%%%%?%?!!?%!!!?!!!%!%?!%?%%!!%!%%?%!!%!%!%!?%!%!?%%?%%%%%%%%!%!%!!?!%!%?%%?!?%%%!!!?%%%!%%!%%?!!%%%?%%%%%?%!!%!!%?%%%%?%!?!%%!!%?!!%?%%!!!?%%%%%%?%?%!!?%%%!!!%%%?%%!?%?!!!!?!?!%!?!?%%!%?!%%%%!!?!%%!!%!%!?!?%!%??!??!!!?%%%?%%%!%%?%?!%%??%!!?!%!%!!???!%?!!!!%?%%!%!%%%%!%%%?%%%!!?%%%%?%?%!!%?%%%%?%%?%%?!!!!!%!!?%!%%%%%%%%??%!!%%%!%!!%%%!%%?!?%?%%%!!%%%!!!!%%!%!%?!%%%?!?%%!%%%%%%?%%%??!%!%!%!%%!!%!?!%%%%%!!%!%%!%%!%?%%%%%??%%??%%%!%%%?%!?%!%?%%?%!%!%!!!!!%!!!%?%%%!?!%!!%!%%!!!%?!%!%!!%%%!?%!%!%!!?%%?%!?%!%!!%!?%?%%!%?%%!%!?%?!%?!?%%%%%?%!!?%!!%!!!%!!%%%?%%?%%!%!!!!?%%!%!!%%!!%!!!!?%%!??%?%%%?%!!!?!!!%%!%???!%!!!%%%!!!?!!!%%%?!%!!%%!!?%%!!%%?!?!!%%!%?%!%%!!%%%%!?%!%%%%!!%%!?%!%!!%%!%%!!!?%%%%!%%!%!!%!?!!%?%!?%%!?%%%%%%%!%!!%!%!%%%%%%%?%?%!!%%%%%!%%?!%?%%%!%%%%!%!%?%%%%%%!%?%?!%%%%%?%%?%%%!!%!!?%?%%%%%!%%!!%%!%!%!!?%?!%%!?%!??%%%!!%%%%%!%?%?!%?!%!%!!%%%?!!%%%%%%%%?!!%??%!!%!%!%%!%%??%!!%%%!!%!%!%!%%%%%%!%%%%??%%!%!!!%%%%?%%!??%!!%?!?!!%%!%!!%!%?%%??%!!%?!%%!%%%%%?%!%%%!?%?!%!%%!!!%%%!?!!%%!!!!?%%?!%%%!%%%%%!!%!?%?%!%%?%!%%%?!!!%!%!!???%%%%%%%%!!!%%?!?!%%%%%%%!%%%%%?%?%%%?!!%%!!%!%!%!?%?%!!!!%!%?%!!%?%%%!%!!!%%?!%!!%!!!%?!!?%%%%%%%%%!%%!!%%%?%%?%%!!%??%%!!%%%%%%%!!%!%%%!!%!%!%!%!%!!!%!%?%%!?!!?!?!%!%%%!%!%%!%%!%!%%%!%!%%?!!??%%%!%%!!!%!?!%%!?%%%!!%%!!%%???%??!%%!!%?%%?%!!!???%%!%%??!%!!%%%%%%!%?!!%?%%%!??%!%!!%%?%%!!%%?!?%%%!!%!%%%!%!?!!!%%!!%?!%!!%%!%?!%%%%%?!%!%!%%%!!%?%!!%%%%?!??!%!!%?%!%!%%?%%%!?%!%!!%%!!!!%!%?!?%%!!%!!!!?%%%%?%%?!!%!!%?%%?!!!%!!!?%!!!!%%%?%%?%!%%%%?%%%!!??!%?!%%!?%%%??%%%?!!?!%!!!??!%%%%%?%!%%%%%%%%%!!%!%?%!%!?!%?!!%%?!!%%?%%!!%!%!%%?%?!!!!!%%%%%!?%?!?%%%?%!%!%%%!!??%%?!%%%?!?!%%!!!%%%??%%!??!%%!%%%%%%!!!?%!%!!!?????!!%!%%!!!?!!%!?%%%!!?%%%%!?%!!?%!%?!%!!%%%%?!%%%??!!%!!%%!%%!!!%!%%!!!!!%%!!%!%!%%%%%%!%?%?%%%!%!!!%!%%%%?!?!%%!!%?%!%%%!%?%%%!%??!%%!!!%%!!!%%!?!!%!???!%%!%%%%%?%!?!!%%!?%%%?!??!%!%%%%!%%%!%?%%!%!?%%%!%!!%!%%%%!%%%!!%!%%!%%%!!%%%!%%%%?%!?%%!%%!!!!%?%!?!!%%!!%!??!!?%%!??!%!!%?!%%?%?!!!%!!!%%!!%!?!%!!?!%%!%?!%%!!%%!%?!%%!%%%!?!?%!?%!!%%!%%%!%%?!%%?%%?%?%%?%%%!!%!%!!?%!%%!!%?%%?!!!!!%%%%%?%%%!!!?%!%!!%%%%!%%%%%%!!%%?!!%!!%%%?%%%!!%%%%!??%!!%??%!%%!%!!!%!!!?%!!%!!!%!!!!?!%!%?!%?!%!!%!%%%%!%?%%!!!%%!!!%!%%!!%%?%%!?%%%%%?!!!%?%%!%%!%!%?%!%%%?!!%?%%%%?%%???!?!%%!%%%??!%?!!!%%?%%!?%!%!?%!??!%!!%!%%%%!%!%!?!!%!?%%%%!%%??%!%%%!%%%???!?%%%%?!?%%?%!%%%%%%!?!!%%%!%!!?!?%!%%?%%!%%%%??%%!?!?%??!%!%!%?%%?!%%%%%!?%%!%%%??%%!%%?%!?%?%%!%%??%%!!?%!%?%???%?!%!!%%!%%%%%!%%%!%!%%%!%?%!%!%%?!%%?%?%!%%%%%!%%%!%%?!%!!%!%%!%?!!!%!%!%!?%?%%%%!!!%?!%!%?%%%%?%?%%%!%%?!!!!??%!%?%!%%?%%%%?%!%%%!!%%?%%%!!%???%%!%!!%%%!%!%!??!!%!?!%%?!!%?!?%?!%%%!?%%%%%!?%!%%!%!%%%%%?!%%!%!?%%?!%!%%%%%%%!?%%%!!!%!%!%!!%!?%%?%%!%%?%?!%%???%!%%%%?%!%%%?!%%%!%%%!%%?%??%?%?!%%%!?!%!!%%%%!%%%?%!%?!%%%!%%??!%%!!??%%?!%%%!!!%%%!!?!%%?!%!?%!%%!!%!%?%!%!%%%!%?%%!!??%!!%?%%!!?%!%%%%%!!!????%%%!%%!!%!%?!%%!?!!%?%%%!?%!?!%%?!!%!!%!%!%!!%?!%%%?%%?%!!%!%!%!%%%?!%!?%!%?!?%!?!%%%%!%%%%%!!!!??!%!%%%?%%?%%%?%!%?%?%!!%!%?%%?%!!!!?%!!!?!!!?!!?%!%%%!%!!%%%!!%?%?%?%%%?!%!!!!?%!?!!%%%!!!%%%%%!?!%!%!%%%%%%%?!?%?%!!???%%!%?%%?!%%%!%%!%?!!??%%!%%%%!%?%?%%!?!!%!?%!%%%!%??!%?!%!%%!!!!%!!%!!!!%%!!!%%!%%!?!%%!???!!%%%%!?%%!%%%%%%?%??!%%!%%%!%!?!?%!%%!!!%%%???!%!%%??%%%!%%!!!%%?!%!?%%!!%%!?%%!!%!%%!%%!%!%?%?%%!%!%?%%%!?!%%%?%?%%!!!%%!!?%%%??%%!!%%??!?%%!%%?%?%!%%?!%%?!!?%%!?!%%%?!%%?%!!%%%?%!!%%%!!!%%%!!!?%??%%!%!!?%%!!%!!?!%%%%?%??%%%%!%!%!??%!%%%%%!%%!?!%%%%%??!%%%%?%%%%%%%%!%!!!%!%??%%%?%%!%%????!?!%!%!?%%!!!?%!%%%?%?%%?%?%!!??%!%!!!!?!%!%%%%!%%?%%??%!?%!!?!%?!%%!%!%!%!%%%!%%!!%%%%%!%!!!%%%!!!?%%%%%?!%!%%!%??%!!?%!?%?!!!%?!!?%%!!?%!%%%?!!%!%%!%%%!%!%%?%!%%!!!?%%%%%%!%!%%!!%%!%%!%?%!%?%!!%!??%?%??%%?%%%%%!%%%%?!?%%%%%!%%?!?%%%%!%!%??%%?%%?!?%?%?%?!!%%!%?%!!%!%!%%!!%??!!!%%%!?%!%!?!!%%%%%!!?!%?!!%!?%!%%%!%!!%%%%!!%!%?%%!%!%%%!!%%%%%!!%%%!!%%%!!%?!%?!%%%?!%!%%%%%%?%%!!%!!%!%%%%%%!!!!%%?%%!??!!%%!%?%%%!%%!!%%%%%%!%?!%%%!%%%%%?!%?%%!%?%?%!%%!?%!?!%%!!%%!%%%%%%%!??!!?%%%%%!!!%!??!%!!%!%?%%?!%!?!%%%%!!!%%%%%!%%!?%?!!?%%%!!%%!!!!!%%????!!%?%!%?%%%%%?!%%%%?%!%!%!?%!?%%%%%!%!%!!%%%!%%!%!!%???!??!%%!!?%%%!%??%%%%!%%?!%%%%%!%%%!%%%!!!%%%%!!%%%%?!%%!%%%%%!%!%!!!!!!%%%%!%!%?!%%!%%!!???!%!%%!%%%?%!%!%!!%!!%%!?%?!?%?!!!%%!%%!%%%%!!%?%!!%%!%?!%%%%%!%%!%%!%%!?%%%%?%!%!%%%%%?%!%!?%?%??%!%%%?!%%!%!!!%!!!%!%!%%%%%?!%%%%%!%!%%%%%?!!!%%%!%%!%%!!?%%!%%%%!!!%!?!%%%?%?%!%%!!!!?!!?!%%%?%!%%!?!%!!%!%%%!%!?%?%!!%%!?%%%%%!%%%%%%?%%%%%!?%??!%%!!?!%?!!%%%%!!?!%!%??%%%%!!%%%?!%!%%%%!!?!!?%%!%!??!?!?%?%?%%%?%%!%!%%!!?%!!%!%%%!!!!%%%%??%?%!%?%?%??!!!?%?%!!!%!%?%!?!%%!%!!!%??%%%%%!!!??%??!!%%%!%%%%%%%%%%!!!%????%%?%%!??!%!%!?%!!%!!%%!??%?%%%%?%!%%%!%%%%!%?%%?%%%%!%!%!!!!?%%%%!!%!!?%%%%!??%%%!%%!!!%%%%!!?%?%?!!%%%?%%%%?%!%%%%%?%?%!%?%%!%%%!%!!!%!!!%%%%?!%!?%!?%%!%%!!?%%!!!%%?%?%?%%%!%%%!%%%%%%%!!!%%%!%%!!!%!%%!%%!%!?!%!!!%%%!%%!!%?!!%!%%%!!%%!%!%%!%%!?%%%??!???%!%%?%%%?!%%%%!%??!!%%!%!%%%%%%%%%%%!!!!?%?!%%!!?%!?!!?!!!?%%%%!!%!%%%%%?%!%?%%%%!%?%!!%%%!?%?%%!%!?%%%%!!!%!??!%%%!?%!%%!%%%!%!%!%?%%%?%%%!!%%!%%!!!!!!!!%%!%%%%?%!?%%%!?%%!!!%!%!%!%?!%?!!!!?%%!!%!%??%%!?%%!%!!%%!%!?!%!%!??%??%??%%!?%%%?!!!!!!%!%%?!%!?%?%%!!!!?%%?%%%?%!!%%%%%%%%!?%%!?!%%!?%%%%%%!%%??!%!%!%%!!?%%%%?!%!%%?%?!!%!!!!!%!%?%!%!%!%!!%%?%%%!!%!%!?%?%%%%!%!??%!%!!%%!!%%%!%?%%%!!?!%!%!%%!%%%%%%!%%%%%!!!!%%!!%!!%!%?%!!?!?%%%!%?%!?!?%!?!%%!%%%!%%!%?!%!%%%!%?!?!%%!!%%!?%%%!!%!%%!?%!%%%!?!%%%%?%!???%!%!%%!%%%!??!??%%%!%!%?%??%?!%!%%!?%%!!%%?%??!?%%%%??!%%!?%%%%%!?!!?!%?!%%!%!!!%!?%%!%!%%!!??%%%??%%!%%!!%?%!!!!%%%%!!!!%%?%%%%%%%%%?%%%%%!%%?%%%!!?%%%%%%!%!%?%%!%%%%??%!%?!%%?!?!!%%!?%!%?%??%!%%!%%!%!??%?%%!??!!%%%!%%!!%?!%%%!%%!%%!%%%%!?%%%%%?%%%%%!?%%!?%!!?!?!%!%?%?%!%%%%%??%%!%%%!%%!%%??%!%!%%?!%%!%%%%!%%%%!%!?!%?!!!%?%%%%!%!%%!%?%%%%%%%!!%%%??!!%!%%%%!!!%!!%!!?%%!!%?%!!%!%%!!%!%%%%%%%!%!%%!%%!%!%%!%%!%%%!%%%!!%?!%!!!!!?%%!%!%%!!%%%%!%%!%?!%%%!%!%?!!%!!%%%!!?!%%?!!?%%?!%!?%%%!!!%!!!%!?%??!!%%!%!!%!%!%!%!?!%%%!!!!%?%!!!%!!?!%%%%?!%!%%!%%%?%%%%%%?!%%!??!!?%%??%%%!!%%%!!%!%%%%%%!%%%!%%%?%%%!!??!?%%!!?%%!!%%!%%!%%%?!%%%!%!?!%?%%!%%%!?!%!!%%%%!%!%%%!?!%%?%%!%%%!%!??!?%?%?%!!%%%%!%!%%%!%%%!%?%%!?!%!%%%%!%%%????%%%%??%?!!???!?%%%%%%!%%%?%%%%!?%%%%??%%!?%%%%%??%%%%!%!%%%!%%%?!!!%%!%%%%%!!%%!!!?%%!%!!?%%%%!?!%%!!!%!%%%?%%!?%%%%!%!%%%!%%!!%!%%%?%%%!%%!%%!%!!%!%!%!%%%%%!!%!%?%%%!%%!!!!!!!%!!%%%%!%%?!%%?%!!%%!!!!%%%!%%!???%%%%%%!%%%??!%???!!!%%!%!!!%%%?!%%%%!!%!%%!%%%?%!%%%?!!%%?%%??%!?%!%%%!!!!!?!%%??!%?!%?!%%%!!!%%?!%!?%%%%!?%!?!%%%%%%!%%%??%%%?%!!!!!??!%!%!%!%?!?%%?%%%?%%!!%!!%!!!!!%!!!%!%%%%%!%!%%%%%%%!%%!!?!%%!!!%?%%%%%!!%!%!?%?%!!!%!%!%%%%!!%%?%!%!%%!%!%%%!%%?!%!?%%!%!%!%%!?%%%!%%%!%!??%?%%!%?!!%%%!%!!!%!!%%%?!?%%?%%!%!%%%?!%??%!!!!%!%%!%?%%%%%??%!!%?%!???!!!%!%!??!%!%!%%!!!%?!%!!%%!!!!%%%!!%?%%!!!%%!%%!%!%%%!%%!??%!!!!%?!!%%%%%%%%%!!!!%!%%%!%!!!?!%%?!!!%%%!%?!%%!%%!!?!!%%??!?%%%?%%%%%!%?%!%%?%%%%!%!?!%%%!!%?%?%!!%%%?%%%!!%!!!?%%?%%!!!!%%!!%!%!!!%%%%!!!!!%!!!!!?!%%!!?%!%%%%!!?%!%??!%!%!%%%!!%%??%??%%%%!?%%%%!?!%?!%%!!!%?%%?!?%!%%!!%?%%!!%?!?%%!%!!%?!%%!%!!%%%?%%!%%!%!%%%%!%?!?!!%%!%%%%??!%%?!%!%!%!%!%!?%?%!%%!%!!%!!!%!%!!?%%%%%%%%!!%!%?!!!??!%!!!%%!!?%%!%%!?%%%!%!%%%!%!%!%%%!%!!?%%%%!%!!!!%!?%!%%%%%?%!!!!!%%%?!!!%%%!!?%%%%!??%%%?%%%%%%%%%%?!%!%!?!%%%%%!%%?%!?%%?%%%%!!?!%!?!?%?!?!!%%!%%%!%%%%?%%%?%%???%%%%!%%%!!%!!%!!%!%!?!?%%%%%%?%%%%%!!%!%?!!%!%!??!%!%?%!%!?!!!!?!%?!%%%%%%!%%!%?!%!%%?%!%%!%!%%!%!!%%%%!%%?%%%%?%%%%%%%%%?%%!%%?%%!%%!??%!!%!!%%?%!%%!%%?%!?%%%!!%%%?!?%!!?%!!%!?!!%%%!%!!?%?%%!%?%%%!!!%%%?%?!%%?!!!!!%%!?%!!!!!%?%%!%???%!!%%%%!!%!%%!?%!?%!?!!?!%!%!%?%!!%!!%%%%%%!%%?%%!!!%%!!?%%%%??!%!!%%!!!!!%%%!%%%%%!%?!%??!!?%%?!%%%%?%%%!!%!!?%!%?%%?!%%%!%!%!%%!!%%!?%?%%%!%?!!??%%%%%?!!%!%%!%%%%%%?%%!%!?!%%?!??%%!%%!?%!?!%!!%?!%!%%?!!%!%?%!%?!%%!%%%!%%%!%%?%!%!!%%!!%%??%!%!?%%%%%%!%%?%%?%!%!%%%%%%!%??%?%%%!%!?!%%%!!?%%!%%??!%%?!!!!%?%!%%?!!!%!!%!%%?%%%?%%?%?!%!!!!!!%!??%?%%%!%%!!??!%!!%!%%!%%!%!!%%%%%!%%!%!!%??!?%%%!%%?%%!%%!%%!?!%?!!?%%%??!%!?!!%%%%???%%!%%!%!%%%%!%%%?%?%!!?%%??%%!%%%!%%%%!%%%%?%%!%%!!%%!%%%%!%!%%%?!%%%?%%%?%?%!??%%%!%%%%%%%!!!!?!!!!?%%%%%!!%?!!%%%?!!!%%?!?%%?%%%%%!!!?%?!%%!%!!%%!%?%!?%?!%!!?%%?%!%%%!%%%%%%!%%%%%%?%%!!?!%%!%!??%%!%!!%%%%?%%?!?!!%?%%?!?%!!!?!%%!!%%!%%?%%?%??%?!%!!%?%!!%!%%?%!%?%%%!?%%%?!!%%?!?%?!!!%%%%%!!%!?%!%!%%%!!%!%!%%%?!!!!!!%?!?%%?%?%?!%%!%!%%%!!!%%%%%%%%??!!%?%%%%%?!%?!?%!%?%!!!!%%%?!!%!%!%%%%!%?!%%%!%!!%!%!?%%%%%%%!!%%%!%!%!%%%?!%!!?%!%%!%!?%%!%?!%!!!%%?%%?!?!!!%%!%%!!!%%!%?%!!%%!?!%?%%!%!%%%%?%?%?%%%%%%%%%!%%%%%!%%!!%!%!!%%??!%??%!%%!%?%%%!?!?%?%!??%%?!!%%?%%!!!?!%!!?%!%%%%!!?%?!%?!%%!%!?%!!%!!!!!!!!!%!!?%!%!%%?%%?%%%%%%%%!?%?!?!%?!%%%?%!%%!?%!???%%?!!%?%%%%%%%%!%%%?!%%%!%!%%!%%!%!%!%%%!!%%!%!!!!!%!%%%!!%%%%%%!!!?%?!%?%%!%%%!%!??!%%%%!!!%%%?!!?!%%%!%%%?!%%%!%%%%!!?!%%%!%%!!!%%%?%%?%!?!!%!!!!!%%!%!?%!%%?%%!!?!!%%%!%!!%?%%%!%%!%%!%!!!%%%!!!!!?%!%%%?%%!%%?!!!?%?%?!!%!!%!?!!!%%%!%!!!!%%!%!!%!?!?%!!%%%%!%!%%!%!!%!%!%?!%%%%%!%!%%?!%!%%!%%%?%?!%%!!!%??%!?%%%%%%?%%%!?%%?!%%!%%?%!!%%!?!%%%%!!%%!%??%%%!%!!!?%?%?%%?%%?!%!?%%%%?!!%%!%%%!%?!%%%%?%!!?%%!%?%!?!??%%%!??%%!%?%!%!!!!%%?%%!?%%%%!%%!%%%!!!!!%!!?!%%!!%%%!!!!%!?!!%%%!%?!%?%?%%%?!%%%!%%!%%%%!!%??%%??%?!%%%%??!?!!?%%!%%%?!!%%!%?%!!!!!!%%%!%%%!%!?!%%?%%??!!%%??!%%?%%?!%%!%?%%%%%!%!%!!%!!!%%?!%%!!?!!????!?%%%!%%%!?%!!?%%!%%%%%!!!%!!%%!%!%!%%%%%%%%%%!?%%!%??!?!!%%%%?%?!!!%%%%%?!!%%?%?%!!?!%%%%!!!!%%!%!%?%%!?%%%%!!%%!?%!?%%!%%%%%%?!%!%%?!%!!?%!!!%!!?!?!%!%%!!%?!%%%%??%!%%%?%!!%%!!!!!%%%%%%%%?%!%%%!%!!%!?!%!%%%%%%%!?!?%!%!?!!%%%!!?%%%%??%!!%!%!%%%%%?!!!%!%%!%!%%?!%?!!!!%!!?%%%%!%!%!??!!!%%?%%!%%!!%!!%?%%!%%!!!!%%?!%?%!!%%??!%%?%%%%%!%?%%?!%!!%?!!!!%%%?!%!???%!%!!%?%!!!%!%??%!!!!!!???%!%%%!%%%??%!%%!?%!%%?!%%!%%%%!%??!%?!%!!?%%%%!!%%?%%%%%!!%!!??%!%!!%!?%!!?%?%%%?%%?%%!?!!?%%!%%%!?%%%!%!!?!%%?%!??!%!%%!?%%%%?!%??!%!?%?%!!%%%%%!!!!%?%!?%%!!?%%%!%?!%%%%!%?!!%%%%?%%??%%?!!?%!!!%%%%!!?!?%%%%!%!!!%%!%!!!%%%!%??%!!%!%??!%?!!!%??%?!%%!!?%%%%?%!?%%?%?%%%%?%%?%%%!?%?%%??!!!!!!%%!?%%!!?%%!%?!%?!%!!%%!%?!!%%%%!!%!!%%!%?%%??!%%%%?%%!!%%%%?%%%%%?%?%%?%?%%??%!%%%!%?!!!%?%%!%%?!?!%%%!!%!%%?%%!%%!%%%??%%%%!?!!%%%?!%?%!%%?%%%!%!%?%!!%%?!!!!?%%%?%%!?!!%!%%?!%??%?%%%%!%!!!!%%%%%%%%%?%!%%%?%!?%%%%!%!%%%!%?%%!?!%%%!%%!%%%%!!%!??!%?%%???%%!?!?%?%%?!?!!?!!!%%?%%%%??!%%%%%%%%!??%%%?%!?!%%%%!%!!%!%%%%!!%%!!%!!%?!%%!!?%??!?%%%%%%%%%%?!%?!%%!??%%%!?%!?%!!!%%!%!%%%%!!%%!!%!??%%!%!!%?!!%%!%%?!%%%%%%%%!%!%?!!!!%?!%%!!!%%???%%!%?%???!%!?!!?!%%%!!!?%%!%%?!%%?%%!%!?%!!%!%%!%!%?%!!!?!!%%!%%%!!%%!!!!!!%%%!%%%%%%!%!?%!%?!!%%%!%%%!!%!%%!%%!!?%!?%%!!!%%!%%%%%%?!?%%%!%!!!!??!%%%!?%%%!%%%%%%%%?!%%!%%%?!!%!!%%%?%%%%!?!%%!?%!!%!!!%%%%%!%!!%%%%??%%?%%%%?!!?%%%%%?%%%???%!%!%!!%?%?%%!?%%!%!!!%?%%%!%%!!!!!%!%?%%!%%!%%%%%!??!%%?%%%!?!??!!?%!%%%!%!!!!!%!!%!!%?%%%%?!!%!!?%?%%!%!%!%%?%!!%!%%!!!%%?!!!!!!!!????%?%%%%!?!!?!!?!!!%%%%?!%%%!!%%!!!!%%?%%!%!%%!!!??%%%%%!%%!%%?%%%%?!%?%%%!??%%?%%!?%%%%%!?!%!!%!%!?!!%???!!%!!?!%%?%%%?%%%%%%!?!!%%%!%!?%%!!%%%!%%%!%%?!%%!!?!%%?!%!!%!!%?!!%%%!%!%?%%%%?%%%?%?%%%%%!%%?%?%%!%%?%!%!!!%%!!%%?!%!?%?!?%!%?%!!%?!!%%%!!%!%%!%!%%!%%!??!!%%!%%?%%%?!?%!%%%%%%!%%!%%%%?!%!%?!?%!!!%%!!%%%?%!%%%%%%%%%%!%?!%%%%?%!%?%%%%!!!!!%???%!?%!%?!!!%%!%!%%?%!?%%%%%?%??%%%%!?%!!%?%!?%%?%%%?%%?%!%!%!%?!%!?!%%??%!?%%?!!%!!!?%!%!!!!%%%?%%?!%%%!?%!!%%?%!%!%%%!?!%%%%%%!%??!%%!!!%%%!!!!%!?!!%!%%%%?!%%%%!%!!!!!??%!?%%%%???%%!%!%%%%!%?!??%%%!%%%!?%%!%?%!%%!?%%%%!%!!%%??!!!%%!!%%!?%%%%!%%%%!%%%%%%%%%!!!%%!%?%%%!%!?%%!?%%?%%%!!?%!!!%?%%%%%%??%%%?%%!%%!%%%?!?%%%%!%!??!?%?%!!!%!%?!%?%%%%?%!%%!?!??!!!?%???%!?!%??%!?%%?%??!!!%%%%%!!%??%%%???%%!!%?%%%%?!%!!%!!?!%!!!%!!!!?%?%%%!%%!??!%%!!%?!%%?%%%!!!%!!%!?%%%?!!%%%%!%%!%!%!!%%%%!%%!!?%?!!!%!!!!?%?%!!%%%!%%?%!%!%%??%?%%%%%!%!!!!%!%!!%%?%%%%!%%%!!!?!%%!%%%!!%!%?%!!%!?%!??!!!!%%%%!!%%%%?%!%%!%!%!!!%%%?%?!%%!!%%%%%!??!!??%?%??%!!%%!%!%%%%!%!!!%!!%?%%!%!??%%%%%%?!%%%%%!!!?!?%!!?!%%!!??%%%%%%%%?!%!%%!!!%%?%%!!%!%!!!%??%!!!%%%%%?%%%%!!!!?%!!%%?!!!%?%%!!!!%!!%!!!!%%?%!%!%%!!%%!%!!??%!?%!!%%!%%%!?!!%%!%!%%%%?%!!?!!!%!%%!%!!%!%%%%!%%%%%!!?!%%!%%%%%%%%!%!%%%%!!%?%%!%%!?%%?%%!%!!%%%%%!%%!%%?%%%!%%?%!%%%%%!%!%!!?%%!!%%!!!!%!%??%%!!!%%??%!!%%%%%!%!!?%!!%%!%!!%!!%?%!?!!!!%!%%!%%%?!??%?!%?!!%!%%%?!%?%!%!%%%?!!!!%!!?%%!%!%%%%%%%!%!%%%?!!!!%?!%!!%!%%%%%%!!??!?%!%%%%%%%?!?!%%!%!%%!%%%%%%!%%%!?%%%%!%%?!?%?%!!!!%!!%!??!!%!%%%!?%%!!!!?%%%!!?!!?!%!%??!?!!%%%?%%!%%!!%%?%!?%?!!%%%%%%%%!%?%%?%%?%!!%%!%%%%%%%!!%!!%%?!!!!!%%?%!!?%!??%!!!!%?%!%?%%%%%?!!%%%%!%?!%!%%%!%%%!%?%!!!?%!%%%!%%%%%%%!%?%%??%%!%%!?%!%!%%%!?%%!%!!!%%%!%%%?%!!%%%?!%%%!!?!?%?!%%?%%%!%!%%%!!%%%%!!%?!%%%!%%!%!!%!?%%%%%%!%!!%%%%!?%!!!?????!?%!%!%?%%!!??%%!%!?%!%!!!?!%!!%!!?%????!!%!%%!!!%%?%%%%%!!%%!%%%%%?%!!%?!?%%!?!%%?!%%%%%%?%?!%!!%%!%??!!%!%!%%%%!%?%%?!%!?%%!!%%!%?!%%!?!%%%%%!%????!!%%%??!!%%%!%%!!%%?%!%%!%%%%?%%!!%!!%!%!%!??%?!!%%?!%!!!?%%%%%!%!!!%%?!%%%??%%?!!%%!%!!?!%!%%%%!!%%%%%%?%%!!%!%!!!%%!!?!!%?!!?%!!%!%%!%%!!!%%!?%!!?!%%!!%!?!!%!!%%%%!%?%%!!%!%?%%%%?%!!%??!%%%!!!%%!!%!%!?%%!%%!?!%?%%?%%!%!!!%%%%!%%%?!%?%%?!%%%!%!!%?%%%??%!%!!?%%%!%!%%!!%%%%!?%%%!?!!?!%%!%%%%?%?!!%%%%%!!%%%%!!!%!%%!%%%%??%?%!%!?%!%%?!%??%%%!%%%?%!!%!?%?%!!!!?%?%!%!!%%%!!%%%!!!?%%!?%%%!!!!!?%?%?%!!%!??%!???%!?!!!%%%!%?%%!!!%%%%%%%%%!!?%?%!!!!%%%!!%!%%%!!%?%?!%%%!%?!%?%%?!%%!%?!!%%%!!!%!!%%!%%?%!!?!?%?%%!?!%%?%%%%!%!%!%!?%!%%?%!?%!!%%%?%!%?!%%%???!%%%!!%%%!?%%!%%!%%%%?!%!!%%%%!%?!%%%!%%%!!!%%%%%!!!!%%!!%%?!!!!??!??!%!!!%%!%!%!!?%??!%?%%!!%?%%?%%%%!!%?!?%%!!!!!?%%%!!!%?%%%!!%%%!?%?%!%%%!%!!%%!%!%!%%%%!??%%%!?%%!!!%%%%%%?%!!%%%!%%%%%%!!%!%!%%!%?!!%%%!!%%%!??!!%%!?%!!!!%!%%%??%!%!%%!%?!%%%?!%%!!%%%%%%!!!!%%!%%?!%!%%!!%?%!?%%??!??%%%???%?%%????!%?%%%%%!%%?%%%!%%!%%%%!%!%%!!??!%%?%%!!%!!%?!?%?!?!??%!%??!%!?%!!!!%?%!!?!%!!!!?%%?%!%%%?%!%%??%!!!%!!!%%%!%!%%%!%%%%%!%!!!!!!!%%%%!%!?!%%%%!!%%%!!%!!%!?%?!!?%!%!?!!?%?!%?%%!%%!%%%?%%?!%?%?%%??%!%%%!%!%%?%%%!%%!!%!%?%%%%%%!%?!%%!%%%!?%!%%!%!??!%%%?%!%%!!%!?!?!%??%!%%??!?!%%?%!?!!%!!%?!%?!!!?%!?%%!?%%!%!%%!%%%!!%%!%!?%%!%!!!???%%%%%!%%!%%%?%%%%!!!!!%%%%%%%%%%%%!!%!%%!!!%!!%!%!!%%%!%!?%%%%!!!!!!??!%!?!!%%%?%!%!%!?!%!!%!?!!?%!!!%!!%!%!%%%!%!%%%?%%%?%%%%%?!%%??!%??%%!!?%!!!!%!!%!!%%!?%%%!!!%!?!!%%!!%!?%!%!!?!%%%%!?%!??!%%??%%%?%!?!%!%%%!!%%?%%%%%%?!%%!?%%%!%%%%%!?%!%?%!!!%!!%%!!%%%%?%!!%!%%!%%%%%%!?%?!%%!?!%!%%!??%%?!%!%%!%!!?!%?!%%?!%%%!!%%%??%!!!!!%!?!!%%??!!%%%%!!%%!%!%?%%%%%%%%%%?!!!!%%!%%!!???!%%!%!?%%%!!!%%%??%%%!!%%?!?%!%%!%%?!!?!%?%%%!%?%!%%%!?!!??!!%%!%?%!!%?!%!%!%%!?%%!!!%%?!%!!?%%?%?%%!!%??!%!!%?%%!%!?%!!?%!%!%%?%?!!%!%!%%!!!%%!%%?!%!%?%%?!!?!!%%%%%%%%!%!%!?!%%!%?!%?%%!?!!!%!!!?!!%%?%%?%?%?!!%%??!?%?%%%%!%?!%?%!!!%%%%?!%!%!?!!%?!%!%!%%!?!!%%%%!%!!%???%!???%!!%%!!%!!!!?%!!%!%!%!%!!?!!?!%!!%%!?%%%%?!!!?!!%%%%!?%!!%!!!!?%%?!!!!?%?%%%!%!%!%!%%%!!?!!%%%?%!%!%!?%%!??%?%??%!%??!%%%%%?!%!%!%??!%?!!%!%?%!%!%?%!%!!?%!%?%%!%%?!!!?!!%%%?!%%%%%%%!??%%!??!%%???%%?!!?%!!%%%!%?%!?%%!!!%??%%?%%!?!!%?%%%?%%?%%%%!!?%!%??%%%?%%%!!%?!%!%%%?!?%%%!!!!%??!!?%%!!?%%??!%??%!%%%?%%?!%!!%%%!?!!%%%%!!??%%!!!?%%!%!!%!!%!%%%%!%%!!?!%%%!%!%%?!%%?%?%%%?%!%!%!?%!?%%%%!!%%!!?%???%!%%!?%%!!%?%%!%!%?%!!?%!!??!?%%%!%?%??%%!?%!!%!%?%?%?!%!!!!%%!%%%?%?%%%%%%?%?%!?!%%?%!!%!%%%?%%%??%%!!?%!!%?%%%?!%%%%!%??%?%?!!!!?!!%%!??%!%%%%%?%??%!%!!%%!?%!%??!%?%%%!!!%?%%%!%?%!%%!!%???!?%!!%%%%!!%!%??!%?%%%!!%%!%%?%%??%%%%%!!!%%%?%?%!%%!%?!?!%!%%%?!%%!%%%??!!!!!!!!!%%%%%!!!%!?!!%!!!%!?%%%%!!%%%%!%%!!%?%%!?%%%!%!%?%!%%%!!%?%%%%!%%!?%%!?!!!?%?!?%%?!%%?!%%%%%?!%!%?!!%%!%%!?%!%!%%%%??%%%!%%%!%%!%%%%?!%%%?!!!!%!?!%?!%!!%%%!%!%%!%%!!%%!!%%?%%%%%!%%%!%%?%!!!%!%????%%%%?%%%%?!%%%%%!%%!!%%!%%%%?!!%%%?%%??%?!%%!!%%%!?!!!!!%!!!?!%!%%!!%%!!%!%%%%%%%%%?%?%!?%!!!!%%!!%%%!!?!?%?%%!%!%%?!?%%%%!!!%%%!!!%%!!!?%%%?%!%!%%%!?%?!%%!%%!%!!%%%?%%?%!!%?%!!%%%%!?!?%%%%%!?%!%!!%%%%%!!%%%%%%%%!???!%!%!!?%!?%%??!!!%?%?%%%%!%?!!%!!%!%!!%!!!%%%%%%?!%?%!%!%%!!%!%%!!!%!!%%?!?!!??%!!%%%%%%%!%%!!%?%?!!%?!!%%!%%%!%%!%%!%%%%%%%%!!?!%%!%!%!%!?%!????!!?!%%?%!!%%%%%?%?%%!%!!!!%!%%?!%%??%!%%!%!%%%%???!%%!%?%!%%%%!%!%%!%!!!%%%!?%?!%%!%!%%%%!?%%%%!?!!%!%%!%%%%%?%%!%!%%%!%%%!?!?!!%%!%!%?%!%%%!!!?!?%%!%%%%%%%?%!%%!???!!!?%%?!?!%%!%!%?%?%?!!!%!!!%%!%%!%%?%%?%!???%?%?%!!?!%!%!%%!!!%%?%!!?!!?%!%?!!?%!%%%!!!!%%%%%%!%%%?!!%!?%%!%%!!!!%?!%%!!%%!!%??%%%!!!%%%!!?!%?%%%!%%%%?%%!?%%??%%?%%!%?!%!!%!!!!%!%%?!!!%%!!%!%?!%%?!!?%!!%!!!%%%?%!%%%!%!%!%!%%%%?%???%!%!%!!!!?!%?!%!%!%%%?!%%%!!??!%!!%!%!?!!?%!%%%!%%?%!!%%%!%%%?!!%%%%%%!%!%?%!%!!!%!%!%%?!%?!??%%%%%?!!!%%!!?!%?%%!!%!%!%%%%!%!!!!!!%%%%%!?%%!!!!!!!%%?!!%?!%!%%!%!%!%?%!?%%%%!?%?%%%!?!!%!!?!!%%?%%!%!!!%?%!%!%??%!?%!%!?%!%%%%!%!!??%%%%%!?!%!?!%%?%!%?!?!%?!?%!?%!?%%?%%!%???%!?%%!!%!%%!%%%?!%%?!%!%??!%?!%%?!%!%!??%!%%??%?%?!!%!%!??%!!%%%?%?%%!%!%%%!%?%!!%!?!!%%!%?%%%%!?!%%!!!%%!!%!?!%!!!!%?%?%%%?%!!%!%!%%!!!%%%??!!?!!!%%%?%!??!%%!!!%!%?%!%!??!!%!?%?%!%!!%!%!!%!??%!!%!%!%!%!%?%!%?%%%%%!%%%%%%?%!!?%?%%%!!%%%!%%%!!%!%!%%!%%%!!%!%%%%!%%??!%%%%%!?!%!?!%%?%?!!?%?%%%%?%%!%?%!?!%!!!!%!%%%!%%?%!%!!!?%%!%%??%%!%?%%%!?%%%%%%%?%%%%%%%!?%%%%%%?%%%%?%!%%!!!%%%%%%%?!?%!%!!?!%%!%!%%!?!%%%%%!!%%!!!%!!%!%!%!!!%%!?!?%%%%%??%?!%%!%!%%%%%?!%?%%%%!%%!%!!%%%!%!!!?%%??!%?!!!%!!?!%%!%%!!%%!?%?%%!%%%!?%%?%!%%%?%%%??!%??!%%!%%%!%%%!!%!!?%!%?%%!!%?%%%%!!!!!?%%?!!?!%!??%?%%?%%!%!%%%!%%%%!%!%%%%!%!!?!%%%%!%%?%!?%!%%%!!%!%%!%!!%%!!!?%%!%%!%%%%!%!%%?%!!?%%!%!%%!%!%!?%!!%??%%%?%!%!!!!%!!%!!!%!%%%%!%%?%!?!!!%%%%%!!!%!%?%??!!%?%%%%!!%%?%?%%%%!?!%!!!%?%!!!%!!%!%?%!!??%%!!%?%%?!%!%!%%!?%!%?!!!%%%?%!!!%!%%!??!%%!%?%!%%!?%!%%%%%!%%!!%?%%!%%!?%%%!!%%!%!?%?%!%!%%%!%%!!%!%??!%?!!%%!!!!!%!?%%!?%!!%??%%%??%%?%?!%!?!!%%%!%%%%%%%???%?%!%%!%%?%?!%!?!?%??%%?%%!%%!?!%%!%!%%?%!%!%%%%!!%!!%%!!%!!!!!??%!!!%?%%!%!!%%%!%%%%%%%!?%%%%!!%%%%!%?%?!%%%%?!%!%%%!%!?%%%!%!!!%?%%%!!!??!!!%!?!%%!!!!%!%%%%!!%%%%!!!??%!%!!!!%!!!?%!!!!!%!!?%%%!???!?%?!!???!!?%!?%%%!!!?%?!%%%%%%%!!%%%%%%%!%!%!!%!%??!!!!%!%%?!!!!!?!%!%%!!%?%!?!%%%!%%%!!?!%!%?%%?%!!%!%%%%??%!!%!%!?!%%%!%!%%%%??%?%%%?%?!???%%!%!%%?%!%!%%%!!!!%?%%?%%%!!%!%?%!%!?%%%?%!%!?!!%!??!?%!%%%!?%!!%!%!%?!!?!!!!!!%%!?%??%%!!!?!%%!!%%%%?%!%%%%%??!%?%%!!%!!!%!?!??!!%?%%!%%%!%!%!%?%?%???%%%!%%!%?%%%%!%%%!%?%?%!??!%!!%!!!%!!%%%?%?!%!?!%%%%%%%?!%!!?%?%!!%!%%!?%!%%?!?%!%%!?%%?!!?%%%%!%%%!!%%?%!%%%%?!!%!!%%%%!!%!?%!!!!%!%!!%%%%%!!%!%%!?!?%?!%!%%%!%%?%%%!?%%%?%%??%?%%%%%?!%%?%?%!?!!!!%%?%%!!%?%!!!?!%!?%%%!%!%!!%%%%%%%?!?%!%%%!?!!?%!!%!!!%?%%?%?!%??%%!%%!%%%%!%!%?%%???!!%%%%???!!!%%%%%?%?%%%%!%!%!%!?!!%%?%!%%!%%%?%%!%?!%%%%%?%!%!%!%!%!%%!!!?%!!%%%!!%%%%%%?%!%!!!?!%!%%%%%%%!?%%!?%%!!!%!%%?%!!!!!!%%%%?%%!%%!!%%%%?%!??!?%%?!%?%?!?%%%????%%!%%%%%%?%%%!!%%%%!%??!!!!!?!?%!%%%!%%!?!%?!%!?%?%%%!!%!?!?!!%%%!%?%!%!!%%%!%%?!?%?!%%!%?%!%!!%!!!%%!!%!%!%%%!%%?!%%?!%!%%!%%%%!!!??%?!%!%%!!?!!%%%?%?!!%!!%%%!??%%?!??!%%%!!%%??!!!!%!%?%%!!??!!%%%%?%!?!?!%!!?%%??%!%!%%!%!!%!!%!%!???%%%!%!%!?!!!?%%%%%%%%!%%!!!%!!%!%!!%%??%%!!%%%%%?!!%%%%%%%!%!!%!?!!%?!!%%%??!%%!%%!%%?!!!%%!%%%%?!!?%%!!%?!!%%%!!%!%!?%%!?%%!%!%?!?%?%!?!%%%!!?%!%!!%%!%?!%?%%?!!!%%!!%?%%?%?!%?%%?!%%??%%%?!%%?%%!??!!?%%%%%!%%!%%%!%!%%%??%!%%%!!?!%%%?!?%!%%!%!%?!!%%!%%%%!!?!%!%!%%%?%?%!%!%%!!!%?!!!%?%%!?%?%!?!%!!%%!%%%%%!%%!%%!!?!!%!!%%%!%%!!%%!!%!?!%%!?!?%??%?%%%%!!%!??%%%%%!%?%%!!!!%!%?!!%?%!!%?!%%%?%%%!%%%?!!%!%%?%!%%!%?!%!?!!%!%%%!%?%?%%%%!%%%?%?%%%%??!??!!%!%!!%?%!%%%%!%%!%!!!??%%%%%?%%?%!!?!%%%!!%!%!%!%!%%!!??%%!!?!!!??%%%%%%%%!%!%!!?%%!?!!!!%?%%!!%%%%?%%?%%!!%%%%%%%!!%??%%%%!??%?!%%?!%%!%!!!!?%%!?!%?%%!!%!%!!%%!!!%%!%??%%%!%%%!!%!%!%%%%%!%%%!%?!?%!!!?!!%%!%%!?%!%%!!%%%%%%!!%!?%%%!!%%%!!!%%%?!!%!!!%%!%%%%!?!%%?%%%%%!!%?%%%!?%!%%%!%?%?%!%!?%%%%%!%%%!??%%!%!!%%%?!%!%%?!%%??!%%!%!%??%!%?!!%!%!?%???%%!?%!!!!!%!%??%!%%!%!%!%!%%!?!%!!?!?%!%%%!%%%%%%%!!%%%%%%!!%%%%%!!%?!?%%?%?%%!%%?%!!%%!!!!!%%!!!%%!%!!%%%%%%!%%%?%%?%?%%!?%!%!!?%!%??%%!%!%%!%%?!%%!!!!%!%!!!??%%%%!!%%??!%??!%!!!?%%!!%!!%%%%%%!!%??!!!%?%%%%%%!!%%%%!%!!!%!%!%%!%!?!??%?%!%%!?%?!!!%!%!%!!%?!%%%!%%!%%!%%%!!?%%%!!%%%!!!!%!%?%!%%%%?%?%%!%!?%%!%??!!%%!!%!!%%%?!%%%!!!%%!?!!!%!%!%%%%%?!%%%!%%?%!%%?%?%!!%%!%%%%!%?!%%%!%%?%!??%!%%%%?!!?!?!?!?%!%!%?!%%%!%%!?%%%%%!%%!%%%%%%?!!!%%%!!%%%!?%!!!%%%%!?%!%?%!%%!%%%%%%??!?!%?!%?%!!%%%!%%%%%%%%%!!!%%%%!%!%%%!!?%!!%!?%!!%%%%!!!%%%!%%%!?!%?!%???%%%?%%%%%%%%%%%%??!%?%%!%!%%%%!%%!%!?!??!%!%!?!%!!%!!?%%!!%!!%!?!?%!%%%!!%?%%!%!!%!%%?%?!???!?!?!!!!%!%%!%%?%?%!!%!!%!%%%%!?%!%%%%%%!%?%!!?%!%!%%%%?!!%!?!%%!?%!%%!!%%!%%%!%%%!%%%!!!%%%%!%%%!!%%!%?!%!%%%%%!!%%%%%!%?!!!%!!!%!!%!!%!!%?%%%%?%!?%!!%!%%%!%!!!%%%!%!!!?%%%%!%%%%%?!%%%%?%?!!%?%%%?!!%??%%%%%%?%%!?%%%%!??%!!%%!%%!!%?%?%%%!%!%!!??!%%%!%%%%!%%%!%%%%%%%%?%?%?%?!%%%%!%?%!%%%%!%%!!%!!%!!!%!??!%%%!!!!%??!!!%%%!%%%!%?%!!!!?!!%%?!%?%!!?!%%!!%?%%?%??%??%!%%!!%%!!?%!%!%??%%%!%?%%%!!%%!%!?!!!%%%%%%!!%?!!!%%%!?!?!?!%%?%!!??!?%!%?%%?!?!!%%?%!%%?!!!%%%?!%?%??%%!?%%%!%%%!%%!!%!??%!%??%!%%?%?%?%!!%!%%!!%%%?%!%%!!!!!%!%!!?!?!%%%%!!%?%%?%?%%?%%?!%%?%!%%%!%%%!?!%%??%!%%%?%?!???%!%%%%?!!!!?%!%%!!!?%%???%?!%?!%!%??!%%%!!%%%!!%%%%%!??%%?%?!%%%%%%%!!!%?!%?%%%??%%!!!!%!%!%%!!!%?%?!!!!!%%%%!%!%?%%%!%%%!?!%!%!!!%%%%?%?!%?%!%?%%?!%!%%%%%%?!!%%!?%%!%!%!!!%%!%!%%%%%!?!%%?!?!!%%%%??!%!%%!%!%!%!%!!!!%!%?%%!%!!!%!?%?!!%%?%%%!%!%%%!??!%%%%!%?%%!!%%%?%%!%!!!%%!%%%!%!!!!%!%%!%%%?!!%!!?%!%!%%?%%%!!%!%!%%%%!!%?%!!!!%%!!?!%%!%!?%%%!!!%!!%!!%%!%!?!%%??!?!%!%%%%%!?%%%?!!%!?%%!?%%%%%%?%?%%!!!!??%%%?%%!!?%!!%!%%!%?%%!%%%%?%!!%?%%!?%!!%?!%%?%!?!%%!!!%?%%%?!!?!?!%%%!?%%?%!!?!%?%%?%%%%%!%!!%%?!%!%%%%!%%!!!!%???%%?%%%%%%?%!?%?%!!!!?!%%%?!!%!%%?%%??!%!%%!???%%?%!?%%%!%%!!%!%%%%%%?%??!%!!!?!%!!!!%!%%%!%%?%%!!!%%%%%?%!!?!%%!%%%%??%?%%%!!%%!%?!?%!!!%!!!%!!!%%%%%!?%%!%!!%%%?%%!?!!!!!?!!%!!%!%%%%!!?%%%%%!%!!!!!%%?%%%%!!?!%?%%%!?%%!%%%%?%%!?%%!!%!%!%%%?%!%%!!%!!?!!%!!%%!%!?!!!?%%%?%%?!!%??%?!%?!!!!!%%?%!%%%?%!%?!%%!!%%?%!?%%%!%%???!?%??!%%%%%%%%!%!?%%%%%%??%!%!!%!%!%%?%%%!%%!?%%?%%%!%%!!%%?%!%%!%%%%!%?%?%!!?%!!%%!%!%%%%??!!%??%%%%%!%%?!%%%%%%%%!?%%%!!%!%%!%%?%??!!%%!%!!%?%?!%?!!%%!%!?%%%!%!%!?!%%%?%%%%?%?%!%%%%!!%%%??%%%%?!?%!!!?%!%!!%!%!!?%!??!%!!!?%?%%%%!?%!!!?!??!%!%%!%!%%%!%!%!!!%%%%%%%!%%!%%%!%%%??%%%%?%%!?!%%!%!%%?!%%!!%!%!%%%%%%%%!%%!%%%%%%!?%?%%%%%%%%!%?!%%%?!%!!!%%%!%!%%%!%!%%!%%?%!%!%%%!%!?%%%%%?%!%%?%?!%?%%%!%%!%%!!%%%!%?%%%%!!%%?%%%%?!!?%!%!%?%%?%%!!%!!??%%%%!%!%%?%%!?%%?!??%%%!!%%%!?%!?%!!?!%%!!?!!%%!%%%!?%%?!!%%!?%%!%!!%!%??!?%%!??!?%%%%%%%!?%%!%???%!!%!??%%!%%%!%?%!!!%%!%?!!??!%!!!!?%!!%%!%%%%%%%%%!?%!!!%%%%?%!%!%!%%%%%!!!%%%?%?!%%??%!%!%!%%%?%%??%?%%%%?!!!%!%!?!!%!?%!?%!%%!%!!!%%%!!%%%%%%%%?!!!!%!%%!!??%%?%%?%%!%!%!%%%%!!%%?%%%%!!!%%?!!?%%!?!%%%%!!!%%!%%?%%%%!%?%!?%!!!%!%!!%!%%%!%?!???!?!!%%%%!%!%?%!!%!??%%?!!%%!?%!!!!!!%!!%%%%?%!%!?%?%%!!%?%%?%?%!!?!%!!%%!!%!%%%?!!%%!?!!%!%%?%%!!?%?!%!!?%!%%%!!?%!%%%!!??!?!!?!!!%%%%!%%!%%!%!!%%!?%!%%%%!!!%!%%%%%?!!!!!?%%?%!%?!%%!%!%!%!%?%!%?!%%!!!%!!%!!!!?%%!%%%%!%%?%%!%!%!!!%%%!!!?%%?!%%!!!!%?!%!%%!!?!?%?%%%!!!!!%%%!!%%!%%%%%%%%%%?%!?%!!%%%%!!%%!%%?!%%%!%?!!??%!!%%!%%!%%?%%!%%%!%%!%%!!!%!?!!?%?!%?!!%%%??%%!!!%?%?!%%?!!?%%%%%%%?%%%%!?%%!%%??%%%%%!%%%%??%%!!!!???%?!!%!%%%%%?%!%%!?!%?%%!%%!%!!%%?!!%%!%!!%!!%?!??%?!%!!?%??%!!%???!%%!!!%!%%!%%%%?!%!!!%%%!%!!!%%?!%?!!%!%!%%%%?%?!!!!%%%!%!%%!%%%%!??!?%%%%?!!%%%!%%%!%!?%%!??!!%%?%!%!!!!?!?%%%!%%%%%%%%%%%%!%%%%%%!%%!?!!?%%!%%!%!%%!!!%%!?!!%%%?%!%!??%!%%!%%??!?%!!%?%%%%!%?!!%%!%%%%!%%%!!%%%?%?%?!!!??!%%%%!%!%%!!%!%!?%?!%!?!!?!%%!?%%%!!%%?!!%%!??%?%!%%!%%%!?%%%??!%?%!%%%%%%!?%%!%%%?!!%!!%!%!%?%?%%%??!!%!!!%!%%%%!!%%%%%%!!%!%%%%%%%?%?!%!?%!%????%!!!%%?%%?%?%!%%!?%!%!%!%%?%%%%!%?%!%?!%!!%!!%%%%!?!%%!%!%!!!?%%%!?%%!%%??!%%!!%!%??!!%!%%%!%!?%%%%%%%!%?%!%%%?!%!!%?%%!!!%%%!?!%%%!%%?!?%!!!%%%%%%%!%!%!%!??%%?!%!%%%!%!%!%%!%%%!?%!!!%%?%%!%%%??%%!?!?!%!?%%%?!%?%!?%??!?%?!%%!!?%?%!!??%%?%%%!!??%?!???!?%?%%%!!!%!?!%%%!%!!!!%!!%%%%!%%%%%%%??%%%%%?%?!?%!%!%?!?%%%?!%%%?!?%!?!!%!!%%??!%%%?!%%!%!?%!?%%%!%!!%%!%%%%%?!%?%%?%?%!%!!%!%!%??!!%%!%%%?%!!!%%%%!%!%!%%%?!%!!%%!!%%!!%%%%%%!%!!%?%!%?!!%!!??%?!?%%%?%!!!%?%%!!%!!!%%!%!!!%%%!%%%%%%%%%!%%!%%%%%%?!%!%??%%!!!%%%!%%!%%!%%%%%!%%%%!%%!%!!??!!!%%!%?%!%%%%%!%%!%?%%?!%!?%%!!%%?%%%!?%%%%%?%!!?%?%?!!?%?!%!%!%!%%%%%%!%%!%!%%?%%!?%!?%!!?%!!%??%%?%!!?%!%%%?%%?%!%!!??!!?%?%!?%%%?%!%%%%%!%!!%%!%?%%%!?%!!?%!%?%!!%%!%??%!%%!?!%%!?%?!%%%%!!%!%!%%%%!!%%%?%%!!?!%%!%%%%%%%!?%%%!!%!!!%%!%%?%%!?%%%%!!?%%!?%%!%%!!?%?%%!!%%%%%!!%!%?!?!%%!??%!?%!!%!!!!!!%%%%!!!%%%??%!?%!!%!?%%??%!!?!!!!%!?!?%%%%!?%!%%!!!%%%%%?%%%%!%%!!%!%%!%%!%%%%%?!!?!!%%!%!%%%??%%%%!%!%%!?%%!%!%%?%%?%%%%?!??!!%%?%?%%%%!?!%%%%?%???!%%%!%!%?%?%%%%!?%%%%%%!!%!%!%%?!!??%!%%%%%%!!%%%%%?%%%%!!!%%!%!%%%?!%%!%!!%!?!%!%%!!%%%%?%?%%%?%%?!?!%%%%!?%!??!?!%!%%?%!%%%%%%%%%?%!%%!%%!%!!%!!?!%!!%%!%%%?!!?%?!%%??!%!!!?!??!?%??!%%!%%!?!?%!!!%%%%?%?!!%!!%%%%%%!!!%!?!%!%?%!%?%%%%!%%?!%!!?%%!?!!%!%!%!%%%%!%!%%!%!!!%!?%%%!!!!?!%%%%%%%!!%%%!!?%?%%%!%%%!?!%?%!?!%!!%!%%%%!?!%%!!?%%%%?%%!?%!!%%%%?!!%??!!!%%%!?!!?!!%%!%!%%!!%!!%%%%!!%%%?%%!%%!?!%!%??%!%!%%%%%%!%%%!%!%??%!%%??!?%!%!?%%%%!%?!?!%!%!%%%!!?!?%%%?!!!%%%%!%%%%?!%%?%%?!%!%%%!%??%%%%%%%?%%??!%??!%?%%!!%?!%%!?!!!%?%%%%%%%%%!%%%?!%%!!??%%!%%!%%?%%%!?%%!%!?%%%?%!?%%??!!%!%%!?!!!%?!!%%!%%?!!!!%%!%%!%%%!!!%!%%%%!!??%!%%%%!%?%%%%%?%%%%%!?!!!%?%%%?!%%%%%%%!%!%%%%%!%!!?%!!%!!%%%?%%?!%%?!%%%?!!!!!%!!%%%?%!%%!!!?!%%??%!%!?!!???%%!!%%%?%%?%!%%!%%!%%%!!%%?%%!??!%%?%!%?%?!?%%!%%!%?%%!!%%!%!!%?%!!%!!%%?!!?!!!%%%%?%!?!%%%??%!%??!??%%!!%%%%!?%!%!%%%!!!?%%!%%%%!%??!%?!!%!!%%?!%%!!%%%%!!!!!%?%!%!!%%!%!!%!!%!%?%!%%%!!%!!!!?!%!!%!??%?!%?%!%%%!??!%%!!%?%%%!%%%%%!?%?%!%%!!%%!?%?%!!!!%?!%%%%%%%%!%!!!!???%%%?%%??%%!!%%?!%%!!!!%%!!?%!%!%!%%!?!!%!%!%%%?!?%%!!?%%!?%!%!%%?%%%!%%%!!%!!%!%%?!%%%%%%%????%!%!!?%%?%!!!!%%%!!!!%!!%!!!!%%?%%?!%%!%?!%%!%!!?!%%!%?%%%!%%%!?%%!%!%!%?!??!?!%%?%%%%!!!?%%%%%?!%%!!%!?!%%%?!%!%!?%%!!%!!%%%%%!%!?!!%!%?!!!%%%!?%%!!!?%!!?%!!!%!%!!%%!%!!!?%%!%!%%%!!?%!%%?%%%!?%%%%%%%!??!!!%?%!%%%!%%%%%!%!?!%!?!%%!%!!%%!?%%!?!!%%!%!?!%%%!!!?!!%%%%%%%!%%!!?!%?%!!?%%!?%!!%%%!%??!!%!?%?%?!!%%?%%!%!!?%!!%%!%!%%%!!%!??!%%%?!%!%%?!!?!%?!%!!?!?!%%!!?!%!!!?!%%%%%%%%!%%!%?%%%%%%!?!%?%%!%!!%!!%?!!!%%!!??%%!?!?!%%!!?!?!!!?!%!?!%%!!%%!!%?%%%%!?%%!?%?%!!%!%?%??!%!%%%%!?%?!!??!!%%%%%!!???!%?%!!%%?%?%%!%%%!%%%%?%%%%%!!%!??%%%?!?%%%%%%%%%%?%%!!!%?%%%%%???%%%!%%?%!%%%%%?%%!%!!%%%%%!%%!%??!!!!?%!%?%%?%?%!%%!%!%??!%%%%%%%!%%%!%!!?%%!!!!%!%?%%%?%!%%!!%?%%!%%%?!%%%!%%??!!%!%!%%%%!%!%!!%!!%!%%%!?%?%?%%%%!%?!!%%%%!%?%%%?%%%!!%%!!!?%%???%%%%!%%%!!??%%!?%!%%%?%%!%!%%?!??%!!!!%!%%!!%!%%%?!%!%%?%%!!?%?!!%!%%%!%%!?%%!!?%%%!%%%%%%%?!%%%%%?!!%%%%!%!!%%?!%%%!%!!!%%!%%%!%!%%%%?!!%%%%!!?%%!%?!!%%%%%?%%%%%!%%!!%!%!%?%%%%%!?!%!!?!!%%??%??%%?%?%!%!%%!!!%!!%!!??%%?%%%%%%!%?!%%!%?!%%%!%%!%!%!?%?%?%!%%%%%%??%!!%%!%!%%%!?!%!%!%%!%!%!!!!%??%!%%!!!!%!%%!%%%!%%?!!?!!!%?%%%!??!%%!%?!!!%%%!?%?!%!%%%!?%!%%!%%%%%!%!!%?%!?%%%!?%%?!?%!%!%!?!%%!%%%!%!!%%?!%?%%??%%!%?!%!!%%??%%??%?%%?!%!%!%%%!!?%!%%%%??%%%!!!%%?!%%%%!!%?%%?!!%?%%!%?%?%%%!!!%!%%%??%!!%%%!!!%?%%!!%%%?%!%!%!%?!%%?%!!!%%!%?%?!%%?%!%%%!!!%??!!%%?%%%!!!%!!!!%!!%%%?!?%%%%%%?%%%!%%%!%!!?%!%?%?%%%??%??%%%!%%?%?%!%?%%%%%?%%!?%!%?!!!%!?!%!%%!!!?!!%!!?!%!!!!??%!%!%%!?%%%!%!!!!%%!!%%!??%%?!%!!%%!??!%?%%!%?%?!!!?%?%%%!!%%%%!!!%%!?%!%??%%%!?!%?%?!%!%%!?%!?%%?!%%?!%?%%%??%%%%%%??%!!%%!!!%?!!%!!%%?!%?%%!!!!!%??%?!!%?!%%%%%%%%!!%%?%?!%?!%%?%!%??%!!%!!!?%?%!%?!??!%!!!%%%!%?%?!%%!?%%?!%!%%%???!?!%%?!%%!!?%%%!%%%%%?%!?%%!%%!%!!%!%%%%??%!!!%%?!%%%%!!%?%%!%!%%!%?%%%%!!?!?%%!!!!%??%%%!?!%%!%!???%!%!!?!?!!!?%%%%%%%!!?!!%??!%!!?%!%%??!??%!%!%!%%%%??!!%!!?%%!?%?%%%%!!%!%%!%!%%??%%%%!%%%?%!%%!!%?%%%%%?!%!%%!??%%%?%%%%!%%!!%!%?!?!%%%!?!%!?%!%%?%!!%%!%%%?%%%!%!%%?%%%%?!!!%!%%!?!!!%%%%!%!%!%%%?%%??!%%?%%!%%!%!?!!?!!%%%%%%!!%!%!%%!!%%?!?%!!?!?%?!!!?!!%?!%!%?%!%%%!%!%!%!!%!%!%%??%?%%!%?%!%%%?!?!!%%%%%%!%%!!!%!!%?%%%!!%!%!!%%%%%%%!%!%%!!?!%%%%%%!%%?!?!!%%?%%?!%%%!%%%!!!?!%!%!!%!?%%?%%!?%%%!%!%%%%?!!!%%?%%!%%?%!%!!%!%!!!%%??%?!%%!%??%%%!??%!!!%!%%%!%%%!%?!?!!%!%!%?%!%%??%!!!?%??!%%%%%!%%%!%!%?%%%%??%%!!%%%!!%%%%%%!%%%%?%%%?%!!%%%%%%?!%%%%%!!%%%%?%?%%%%%!%!!!%%%%?%%%!?%?%%?%%!!%%%%!%??!%!%%%%%%%%%%%!%!%%!!%!%%??!!?!???!%?!??!%%!%!%!!%?%%!%!!!%%?!?%%%%!?%%?!%%?!%%!%%??%!%?!!%?%%%!%%????!!%%!%!!%!%%!!%!%!!!!?!%?%??!%?!%!!!!%!?%%!!%%!%%!%%!%!!!!%%!!!!%%!%?!%%%%!%%!%%!%?!!?!!%!%%!!!%%?!%!!!%%?%%%%%%?%??!?%?%%!?!%!!%!!!%%%%%%%!!%%%?%?!%?%!?!%%!%%!?!!!!%%?!%!%!???%%%%%!%!%%%!!%?%%%%%%%!%%%!%%?!%%%!?!%?%%%?!!%%%%%!!?!!%??%!%?!%?!%%%!!%%%!%%%%!%!%%???%%%!%%%?%!!%!!!%!!%%!%%!%!%%?!%!%!%!%?%%%?%!?!%!%?%%%%!!!!%%%?!%%!?%%!%%%%%?!%!!%%%!%%%%!!?%!!%%%!%!%%%%!%??!!?!%%!?!???!?%%!%!!%%?!%?!!!%%%!!%?%%!?%!%?!%%%!%%!!!%%%%%!%!%%?!%!%?!!%?!%!!!!!%%!%!?!%%%%?!!!!?%%%%%%%%%%!%%%?%?%?%!?!%!%??!%%?!!%%%?%?!%%%%?%?%%!?!!%%!%!%?%?!?%!!%%%%!%%!!%!!%%!?%%!!!%%%!?!%!?%?!%%%!!?%!!!%%%!%%!%%!%%!%!%!%!!%%!?%!?%!!%!%%%!!%%%?!%%!%%!%!!??%?%?!%%%%%%%!%%%!!!%!%%%%!%!%%%%!!?%%%!%!%!!?%?!%!%!%?!!%%%!%%!%%!!!%?%!!%%%!!%!!!%!?%%%%!%!%%%%%%%%!%?%?!%!%!?!%?%??%%!%%!%%?!!!%%?%!?%%?%%%%%%%%?!%%%%%%?!!?!!!%?!%?!%!!%?%%%!!?!?%%%%?!?%%!!%?!?!?%!%?%%!?%?!?%%%%!%!?!%!?%!!%%%%%?%?!!%!%%!%!%%!%%!?!%?%!!!%%?!%%%%%!?!?%?!%%?%%%%!?%%%?%%?%%%?%%%%!!!?%?%%%!?%!%%!%!%?%!%%%?%%!!!%%!%%?!!%!?%!!%%?%!%!%%%%%!%%%%!!%?%?%%?!%%!!!%!%!%%!!?!?!%%??%?%%!!%%%?!%!%!%%%!%%?!!?%!%?%!%%%!%?!%%%!%!%!%????%%%%!%!%!!!??%?%%%!%!?!!!%?!%%!??!!%%?!%%%!%%!!?%%%%?%!%??%%%%%%%?%%???%?%?!!%%%%%!!%%!!?%%?!!?!%%%!??%%?%%!%!!?%!%!%!%!%%!!?%%!?%%!?%?%%!?%%%%?!!%!?!%?%%%%%???%???!%%!%%!!%%?!?%!%!?%?%???%!!?%%%%?%%?!%!%%!%!%%!%%?!%!%%%!%%%!!%!%!!%!%!%?!%%%%???!!!%%!%!%?!%%%%%%!%??%%!%?!%???%%%%%?%%??%%%%!?!!!??!!%%%!?!%%!!%%%%?!%%%?%%%!%!%%%%?%%%%!%%%!!%!!!!??!%!?%!!!?%!!!%%!?!?%%!!??!%%%%!%%%%%%?%?%%!!%!?%%%%%%?!!!?!?%??%!%%%%?%%%%??!%%%%%%%?!?%%%%!%!?%%?%?%!%%%!??!!%!!%%%%!!%!!!%%!%%!%!!%?%%!%%!!%%%%%!%%!?!!%!!!%?!!%%%!!%%?%!?%%%%%%!%?!!%%%%%!!!%!!?!%!?%%??%?!%!%%!!%!!%%?!!!!!!!%!%%%%?%!??!!%!%%%%?!%%%%?%%%%!%!%%%!!!%%!%!%%?!%%%!%%%%%%!!!%%!%!!%!%%%%!%%?!%%%!%?!!?%?%!%%%?!!%%%!%%!!!?%!%%!!%%!%%!%%?!%%!!!!!%?!%%%!!!%%%!!%%!!?%%!%%%?!!%%!%!%%%!!!!%%%%!?%%!!%%!!%!%??!%%!%%?%%!%%?!!?%%%!!%%%!%?%!%?!%!!%!!!%!?%%!%??!?%%%!%!%%%!%%!%%%%!?%%!!?!%%%%%%%!%!!%%%%?!%?%%?%!%%?%!!!!%?!%%%!%!%%%%%%%!!%%%%%%%%!!!%!!%%%!!%!!%%!%%%!%!!!%%%?!?!!%?%!%!?!!%%!!%!??%!!%!%!?%%!?%%?!!!%%%!%%!%?!!%%!%%%%!%!!%%%%!%%%%%%%%?!!!%!%%%!%!!!%%%%!!?!!%!%%?%!%%%!%?%!%!%%%!!%%!!?!!%%?!?%!?%%?%?!!%%%!?%?%%!%!%!?%!!!!%!!%%!%!%%!!!?!%%!%%!!%!?!%!?!%%?!!!?!!%!%?!!?!!%!!%%%%!!%?!!!?%%%!!%!!??!%!%?%%!%?%?%%?!%%%%%%!!%%?%?%??%%%%%?%%?!%%!%?!!%%!!%%%%%!%%%%%!%%?%%%!!%%%%?%%?!?!%%!?%%%!?!%!%!%!%%?%%%%%%??%!%!!%%!!!%?%%%%%%%?!%?%%%%%%!%%!%%%?%!?%%%%!%!%%%!?!%!%%!%%%%?%!?%%?!%%!%!?!%%!!!%!!%!%%%!?!!!%%!!%%!?%!%%%!%!%!%%%%!%%!!?%!%?%%%%!%!!!%%!!!!%?%?!!%%!%%%!%%%%%?%!%???%!%??%!%%%!?!!!%%%%?%!%!%?!%?%!%?%?!%!%%!%%%%!%%!?%%%?%?%%%%%%%!%?!%%?!%!!!!%!%%%%%%!%?!!?%???%%!!!%%%!!%!%!!?%!?!??!!!!%!%%!?%!!!?%!?!?%%%?!?%!%%%%%%?%%?!%%!?!!%%!!!%%!%??!%%%%!!??!%!%%%%%%%%%!?%%%%%%%!!!%!%!%!%!%!%%??%?%%%%%%%?%%%!!%%%%%!%!%%?%!%!%!?%%!!?%%%!%%!!%?!%%%?%!?%!!?!%%???!%%%%%%%?!!!%?!!%%!%!%%%%%!!?!?%?%%!%?!?%!?!?%%%!!!!%%%!%%%!!?!!%!!%!%%?!?%!%!!%?%?!??!!%%!%%!%?%!%!?!%?%!?%%?!%!%!?%!!!%!?%%%!!%%%%!?%!%?%%!!%?!!!%!!?%?!%%!%!!%!%%!!%!?!%?%!!?%%%!!!?%%?!?!%!??!?!%??%%%%?%%%!!%!!!%!!?!%!%!?%%!%!?!%%%?!%%%!%!!%!%?%%?!%%%!%%!%?%%!%?!%?!!%%?%%!%!!%!%!!!?%%!%!!%?%%%!%?%%%%!%!!!%%%!!?%%!%?!%!%!%??%%?%!!?%!!%?!!%%!?!?%!!!???!??%%%%%%%%?!?%%!%%?!!!!!?%%?%!%!%!%%!%%%?!%!%%!%%%%%!%%!!%%?!%?!%%?%!%!!!%!?%%%%!%%!?!?!!%%?!!%!%!????%?!%!%%?!%%%%%%?%%?%!?!!%?%%?!!%%%%%?!%!%!!%!%%%!%!%?%!?%?%!!%?!%!?!!?%%?%%!%%!%!!!!?%%%?%%!%?%%!!%!%%!%!%!?!??%!%!??!!!!!?!?%%%%%%!?!!%%!!%!%!%%%%?!%%?!??%%%?%!!!?%?!%%%%%!%!!%%%??!?%!!!%!!%!%?%%%%%!%%%!%%%!!!%%!%??%%!!%!%?%%?!!!%!?%?!%%%%%%%%!!%%!!?%%%%%!?%%?!%!%%%!%!!?%%%%%%%!%?%%%%%%!%!?!%%!!%?!??!!?%%!!%!%%%%%%?%!%!%?%!!%%?%?%?!!%%%%!!!%!%!%!%?!%??%%?!!!!%%%%!!%%%%%!!?!%!!!!%!%!%!%%%%!?%?%%%%%!%%?!!!%%!%%!?%%%!%%!!%??!%!%%%!?!!!%%!?%?!!?!!%!%!!%!?%%!%!%%%%?%!!!?%%%%%%%?%!%%%%%?%%?%%%!%?%%!!!%??%!!%%%%%!?!!%!!!?%!%?%??%!%%!!%?%?%%!%%%%%!%?%%??!!!!!%!%!!%%?!%?%!%%%%!%%!%%?%!!?%!%?%?!%!%%!%%?%%!?!%?!%%!!?!!?!%%?%!%%!%!%%!%%%%?!%%!%%%%!??%%?%%!%%!%%!%%%%!%%%!!%!!%%!!%!!!?!!!?%%!?%%%!%%%!%!%%%!%?!%%%?%!!%!%!?%?%!%!!!%%!%%!%!?!%%!!?!%%%%!?!!%%?!%%!%%!%%!!?!?%!%%%%%!%?%%!!%!%%%%%%??!%%%?%%!%%%!%%?%!!%?!!!!?%%%%!%?!!%?%%%!%%??!%%%!%%!%!?%%?!!!!!!%!%!!!%%%%%%!!%%%?%?!??%%!%%%!%?!%!%?%!?%%?!!%%!%!!%??%%!%%!%!%%!%%!?!%%%!!%%!%!?%!%!%!?%!%%!!%%!%!%??!%%%!%!%!%???%!!%%!!%?%?%!%%%%%%%%%?%%!?%!%?%%!!!%%%!%%%!!!!%%%%%!%!??%!%%!!!%!?!%?%?%%%%%%%!%?%!!!?!%!!%!!%%!!?!%!!?!!%%%%%?!%!!%%%%?%?!%%%!!%?%!!!?!?!!!%!!?%%%!%%!!!%!!%?%%%%!!!?!%%!?%%%%%%?!!!!%!%%!?%%%?%%!?%!%%%?!%!%!%!%%?%%!!?%%!%%!%!%%%!%%!%%!%%!!?%??%%%%!%%!%!!%%%%%?%%?%!?%?%%%%!%!!??%!??%%!!%%?!%!!!!%%%!!%!!!?%?!%?!%%?%%%%!%%?%%%%!?%?%%!%!%?!??%!%%%%?!%%!!%%!!!%%%%%?!?%%!%%!?!?!%%!?!!!!!%%%!!%?!?%%%%!?!?!%??%%!%!!%%%!%%!??%!%%%%%%%%!%%%!!!?!?!!?%?%%%!%?!%!%!??%!%!!%???!!!?!%%?%!%!!%%%%?!!%?!!%%%%%%%%%?%?%!?%?!%%!!!%!!?%!!%!!%!%%!%!??%?%!!%?%%%%%%!%%%%!!!!?%%%%%???!%%!%%%%%!%!%%???!%!!%%%%%%!%!!%%!%!%%!?!?!?!???!%%%!%%%%!!?!%?%!%%!%%%%%!?!%!!%%!%%%%%?!!!%%%?%!%!?%%?!!!!?%%!%!?%!?!%%!!%%!%%??!%%!?!%%%%%!!%%?%!???!!%!%%%!%!!%%%!%%%!!%!!!%!%%?%!!?!!!?%%!%???%%!%!%%?!!!%?%!%!%!%?!?!?!%!!%!%??!%%!!?%%!%!%%!%%%!%%%%%%!!?!%%!?%%%%?!!%%%%%%%%%!!%%%%%%!!%!%!?!%?%?%??!!?%%%%!!!!%%%?%%%%!!%?%%!!?%%!%%!?!!!?!%!!%%!!?%%%%?!%%!%%?%%%!%%%%!%%%%??!!?%%!!%!!%!%?!?%%%!%%%?%%!!%!!?%%%%%?%%%!!%%%!!%%?!%?%%%!%%?%%?%%%%!%%%%%%%%%!%%!%?%%%%?%%!!%!!%!!%?!!?!%%%!%%%%%%%%!!%%%!%!%!??!%%%!%?!!%?%%!%%%!?%%%%%%%!%%!%?!%!?!%%!?!%%!!%!?%!%?%!?%%!%%%!%%!%?!%!?!%%?%!!%!?%%%!%%!!%??!!!!??%%!%!%?%!%?%%%%!!%%!%??!%!?%%?!?%!%%??!!!%??!%!!%%!!!?%%%%?!%!!!%%%!!%?!%%%%%%!!%%%%%%%%%%%!%%??%%%%%%%?!!!%%%%%%%%!!!!%%%%%%!%!%?%!?!!?!%%%?%%%!%%%!!%!%!!%!!%%!%!?%%!!%%%!%!!!?!%?%!%%%%%%%%!%?%%%?%!!?%%!!%!%%??%?%?!?!?%%%?%%??!%!!%%?%?!!?%?%%%%%!%!%%!%!%%!%%%?%?!!%!%!%!%?!?!%?%!!%%%%%%%%!!%!%%!%?%%%%%?!%%%%!!%!!%!!%!!%!?%%??!!%!%!%!!!%%%?!!%!?%%%!!%?!!%!%?%%%%?!!%??!%%!!%%?!%?!?%%!!%!%%!!!?!%%?!%!!%%!!?!!%!!%%!!!?%?%%!%%?%%%!%%%!%????%!!%%!??!!%!!!!!!?!??!%?%!%?%!!!?%!%%?%%!?%%%???!!%%?!%!!!!%%!!?!!!?%!%%!%%%%%%%%%!%?%%!%%%%%%?!!!!?%%%!%!??%%%?%%%%!%%!%?%%!%%%%!%!%%%?%%!%%%%?!%!%%?%%?%?!??%?!?%?%%%!%%??!%%%%%!???!!%!???!%?!!?%%?%%!!!!?%!?!%!!%%!%?%%%?!!%%!!%!?%%!%%!?%%%%%%?%!?%%?%!!%%%?%%!%%%?%%%!?!%%%%?%!%??!!!!%!!%!!!!%%%?%%!%?%%%?%?%!%%%%%!%!%%%%?%??%?%%%%%!!%%!!!%!%%!%?%!?!%%!!%%?!%!%!!%!!%%!%%!%%%%!!!!!!?%!?%%%?%!!%!??%%?!%%%!!?%!%%%?!!?%%?%%%%%%?%%%%!%%%%%!%%!?%%!!?%%%!%!!?%!!!!!%??%%!!%!!%%%!%!?%%%%%?!?!%%%?%%%!!!!%!%%%%%?!%!%%%?!!!!!%%?!?%?!?%!!!%%??!??%%%?%!!!!%%!!%%!?!%%!?%!?%!!?%!%?!!!?!!%%!%?%%%%%?%?%%%%%%%!!!!!?%!!!%%%!%%%%!!?%%!%%%%?!%%!?!%!%!%!%!!%!!?%!!%!!%!!%?%%%%%!!?%%%%%?%!%%?!%%%%!?%!%%%!?!%%!%%%%?%?%!!!%%%%%?%%?%!?%?%%!?!??!?%%!??!%??!!%!%!!%!!!!??%?%%%%%%%%%!!%?!%?!?%%??!!%!%!%!?%%%%%%%?!!%%!%?%%%!!%?%%%!%!?!%%%%%!!%!%!%%%%?%%%!%%!%%!%%??%%?%?%?%!%!!%%%!!!%%!!!%%??%%!??%%!?!!%%!!%?%%%!%%!!!!%?%!!%!%!%?%%%?!!!!%%!%%%?%!!?%%%%%!!%!%%!!%%?%%!%!%??%!!!?!%%%!!!%!%%%!%!!%%?%%%!!%?%%%!!!!%%%?%!%!%%!%!%%%?%%??%%?!?!%%!!%%%!!%?!!!!%!!!!%%?!%!!%?!??%%%!%%%!?%!!!?!%%%!!%?!%%!%?%!!%!%%%%!%%%!!!%!%%%%%!!?!%%!%!!!%!?!%%!%%%!!%%!!!!?%!%?!%!??%!!%%!%%?%%%!?%?%??%%!%%!%?!!!%!%?%%%!%!!%!%%?!%%!%?%!%!!%!!!!!%!%!?%?%!?%!%!%?%!!!%%%%!%%!!?!%%!?!?%%%?!!%%%?%%%%%?%!!%?%?!!!%!!%!%?%?%%%%!!%!%%!!%!%%%?%!!!%!%!!%!!?!%%?%!!!%%%%%???%!?!%!?!!??!%%%!%%!!??%?%!%!?%!%%%!%%%%!!%!!%%!%!%%!!%!!?%%%!?%??%?!!%%%%!!%%%?%%%!%?%!!%%!%!%!%%%!!%%%%!%?%!!%%!%%!!!%!!!%?!%??%%%?%%%%%!%!%!!%%!%%%%%%%%!!!%%%%%!%%%!%%?!?%?!%!!%!%!%!%!?%!%!!!!%%??%!?%!%%!!!!!!!%%%%%%!%!%%%%?!%%!!!!%%!%!!%%!?%%!%%!!%!!%!%%?%%%%!%!!%!%!%?!!!?%!%?!%!%!%!?!%%%!%??%%%%%!!%%%%!??%!!?%?!%%%%!%%%%%%?!%?%!%%%?%!%!%%!!!%%%%?%!%?!%%!%%?%!%!%!!%?!%!%%%%!%%%?%%?%%%%!!%?!%!%%%!%%%%!%%%?!%%?%%%%%!!!!!%%!!%%%%!!??!%%%!??%?%!!?%%!?%%?%?%!?%?!!?%!??!%%%%!%%!%%!??!!%%!%%%!!%!!?%%?!%?!!!!!!%!%%%?!%%%%!%%??!%!%%!%!%%%%%?!!!%%%!?%%%%%%?%!?%!!%!?!!%!%!!%?%!!%%!!%!!%!!%%!%!!?%%%!?%!!%%%!%!!%%%%%!%?!%%!%%%%?%%!%!?!!!%!%!%%%%%!%!%?!%%%!!?%%!?%%?%?????%??!!!!%%%%?!!%%!!!%%!%%!!!%?%%?%%!%?%%%%%%%%!%?%%?!!!%%!%%!?%!!!%%!%?!%!%!%%!!%?!?%%%%!%!%?%!%!!?!%??%!%??!%!%%%!!%!%%%!!%%%!!%?%%%?%%!%%!%%%%%!?!%%%?!?!%%!?!%%!%?!%?!%??!%!%%!%!!%%%%%?%%?!?!?!%%!!%!!!??!%!%%!!!%%!?!!?!?!?!%%%%!%??%?!%?%?!!?%?%?%%%???%!%%%%!%%%!%%%%!%%%%%!%!%%?%?%%%%%%???%%%?%!%!!%!%?!%%%%%%!%%!!!!%!%!%%%?!!%%!%!?%!!%%!!!?!%%%%?%%%!!?%!?!!%!%!!%!%!!!%%!??%!!!!%%!?!?!?%!!!?!%?%?%?%%!%%%%%!!!%%??%%!%??!!%!!%%%!%!%!%!%%!!%!%%%%%%%%!%%!!%!%!!?%%%?%%?!%!!!?!%!%%!!!%!!!%%!%%!!!%?!!?%!%!%?!%%!!!%%!%%?%%!%%!%!%???%?%?%?!%!!!%!!!%!%%!??!!%!!!%%!%!!?!?%!?!%!%!!%%%%!%%!!?%%??%!%%%%%%!%%%%%!?%%!!!!!%%!%?%!!?%%?%%%%%%?!%%?%!%!%%%?!%!!!%?!??%?%%%%%!%!?!?!?%%%?%?%!%!?%!!%%??!!!%!%!%?%%%%%!!%?!!%??!%??!!%?!%%!%%%!?%?%!%?%!%!!%%%%%%?!?%%!!?!%%%??!%%!%%%%?%!%??%!%%!%?%%???%%%!!%!%!%!!?!!!??!!%%%%!%?%!%%?%%!!!%!?%!%%%?%?%?!!?%!!?%!%%!?%!?!!%%?%%?%%!!%!%!!%%!%%%!%%%?%!???%?%%%%!!!%%%%!?!?!!!!?%%%?%!%!%!%%%%%%%%!%!!!!%%%!%!!%%%!!%%%!%%!%%%!!%%?%?!?!%%!???%!%%!!!!!!?%%!%%%%??%!%?!%%!%!!%!?%!%%!%%!%!%%??%%!!%%%!%%!?%%%%?!%!%!%!!%%!%?!!%%%!%!!!!!%?%%!%%?%%!!%%%%!%!%%%%!%!!?%!%?%%?!%%%!!?!%%%!%%!%%!!%%!?!%%%!?%%!%%!%%%?%?!?!%%%!%!%!%!!%%!%%??!%%!!%!!?%%?%!%%!%!!!!!!?!!!%%%!%!!%%%!?%?!!%!%!??!?!%!%%%!!%!%!%??%%!%?%!?!!?%%!!%%%?%!%%!%%!%!??%%!%%!%!%!%!!!%?%%??%?!%%!%%?%%?%%%%?%%%%!!!?!!?%!!%!!!!!%?%%%%%%%!!%%%%!?%!?%!?!%!?%!?!%!!%%%!?%%!%?!?%%!%%%!??%!%%%!%!?%%!!%%%?%??!%!!?!!%!!%?!%!%%%%?%!%?%%%%!%!!?!?!%!%?!%!!!%!%%%%?%%%%?!?%!!%?!?%%%?%!%!!%%!!!?%%%%%%%%!!%?!!!%??!!%??!!%%!?%%%?%!!%%?%%%%!%!?%?!%%%?!?%!%%%!%!!!%!%!?%!!%%?%!!%??%%%!!!%!%!!???%?!?%!%%?!%%!%!!%?%%!%!%?%%!!?!!%%?!!%!%!%%%%!!%%%????%%?%!??!!!%?%!!!!%%%!?%!%%%%%!?!!!!!%!%!?%!%%!?%%!%!!%!%%%%!%!!%?!!?%!%%?!%?%%!!%%!?!!?!%???%!!%%%!%?%%?%%%%?!%%!%!%%?!!?!!%!!%%%?%!%!!?!!?%%%!!??%%!??%!%%??%?!%%%%!?%?!%%%!%%%!%%%%!!!?!%%%%!%!%%?!!?%%%%!!!!!??%!%!!%?!!%!!?%!??%?%%%!!%?%%%??%%??%%%?!%?%?%%!?%%!?!%?%!%!%%%%!?!!%!!%%!!!%%%%!?%!%%%%%%%%%%!?%%%?%%!%!%%%?%%!%%!%!!%!%!!%?%%?!!%?!?%%%%??%!%!!!!?%%%?!!?%!%%%!%%%!!%!!%!%?%!%%%!?!!%%%%%!%!!!!!!!%!??!?!%%?!!%!%%?%!?%!%!%??!!!!!!%!?%!%!?!??%%%!%%!!!%!%!%%?!%%?!%!?!!%!%%!%?!!%%!%%!%%!?!%%!%!!??%%!%%%%%%!!%%!?%!!%!?!?!%%%%!!!??!%!?%%%!%%?!??!!%??%!%!!%!%%%%%??!%%!!%%?%%!%!?%!!!!%?%%%%!?!!%?%!%%%?!%%%%?%%%!%%!!!!!%%!%!?!%%?%??!%%!%?!%%%!!?%??%%!%!!?!?!%%%%!?%%%%%%!%!!!!!!?!!%!!%!!!%%%?%?%?!%%%%%!?%%%!!?%!%%%%!%!?%?%%%!!%%%?%!!!%!!!!%!!%?%%!%?%%%%%%%%!%!%!%!%%%%!%%!%%%%!!%??!!%%?%%!!%%%!?!%?!?%!?%%?%!%!%!!%?!%%%!!%!%%%!%%!%?!%%!!%!%!%!!!!%%?%%!??%%?%%%%!%%%%?%?!%%%?%?%%!!??%%?%?%%%!%%!!%%??%%%!?!!%%%!!%!%%%?%?!?%!%?!%%?!%%!%%!%%!!%!%?%!!?%!!!%%%!?!%?%%%!%%!??!%%%%%%%%%!?%%?%!%%%%!%!!%!?%!!!%%??!?%?!%%%!?%%?!?%%%!%%!%!?%?!%!%?%!%%?!?%%%?%%%!%??!%%%%%%%!%%%%!%%!%!?%%%!?!!!!?!%%%%%!??%?%%%!?%%??!!%!%!%%%!%%%?%?%%!!!%%?%%??!!%%!!!%!!%?%!?%?%%%!%%%%%%%??%?%?%!!!%?!%!%%%%!%!!?!%?!%!!%%!%%%%!%%%%!%!!!%?!?%!%%?!%!%%!!%%%%%%%%!%??!%?%!%%%!?!!%!!!%%%??%%!%%!!?%%%??!?%!!%%!!?%%%%!%!?%%!??%!%%%!!!?%%%%%%!!!???!!!!%%%!%!?!!%%!!!!??%%!!!!!%%%%%!%%%%!?%%%!?%!?!%??%!%!!%!%%%?%%!!!!%?!%!!%%%%%!?!!!!!!%%%%%%!?%%!%%!%%!%!%%%%!%%?%!%!%%%?%%!!%%%!!!!%%?%?%%%!!%!%%?!%%!?%%%%!%%!%%%%!%!!!!%%%!!%%%?%%%%!%%%!!%!!%%!?%!?%%!%!%%?!?%!!!??!%%!?%%%%%?%?%?!!!?!?%!?%%?%!!!%%!!?!%%!!!?%%!!%%%%%%!%%%!!%%%%?%%%%%!%%%!!!!!%%%%!%!%%%%?!!%%%!!!%!%?%!%%!%%?!%%%?%!%%%%%?%?%%%%%?%!%%%%%!!%!?%!??%%!%%!!!!%%%%!!%%?!!%!%!!%!!%!%%!???!%!%%!%!%%%%!!%?%%!?%!%?!!!%?%!!!%!%!%!!%%??%%%%%!!%?!%!%!%?!%?%%%%%%%?%??!!%??!%?!!?%!!!%%!!!%?%!%%%!?%%%!?%??%!!!%%%%%%!?%%!%%!?%%%%%!!%!?%%!%%%!%?!?%%??%!!%!!!!!!%%!%%!%%?%!%!%?%%?!??%%!%?!?%%!!%!!%!!!%!?!%%%!!%!?!%%!%!%%%%!%!%%%%!?%!!%!!!?%%!%%%!%??%!??!!??%!%%?!!%%!!!%%%%?%!%!!?%%?!%!!!!!!%???%%%!!!!%%%%%?%!%%!%%!?!!%?!!%?%%%%!%%?%%%%!?!?%%!%?!%%%%%!?!%!%!%!!!!%%%!%%%%!!?%??%!%?%%%!%%%!?!!%?!?!%%%%%!%%%%%?%%!!??%%%!%%!?%!!!!%!%!%%!???%!%!%%%?%?%%?%!!!%!%%%?!%???%%!?!%!%!%%%%!%%%%%%!%%%%%%?!%!%?!%%!!%%%?%!!?!?!?%%%%%%!%%!%?%?!?%%%%%!%%%!!%%?%%!!?!?!!%??%?%%%%%!%%!???%?%!?%%%!?%!%!?%!%!?!%%%!?%?%?!%%!!!?!!!?%?%!!%?!%!%!%%%?%!%?%!%!%?%?%!!?%%%??!%!%!?!%%%%?%%%?%%%%!!%!%%!!!!?!!%%%!%?%%!!!!!%%?!%?!%%!!%%?%%%%!%%!%!%%?!%!?!%%%!!%!!!!?%%%???%!!%??%!%%!!%!%%%!!%?!%%%?%?%%!%!!!?%%%!%%%%?%?%%%%%%%!?%%!!!?%%%%?%!%%?%??%?%%%%!%%%!%!%%!%!?%?!%!!!%%%%%!?!??%%?!?%%%%%?%!%!?!?%%?!%!%%!%!%%%%%%?%?!%%%%%%%%?!?!%%!!%%?%!%!%!?%%?!?%!!%?%%?!%%!%%!!!%%%!?%!%%%%!%%%!!!!!!%%%??%!!!!!%%!!%!%!%!!?!!!%!%%%!!?!?!%%?!!?%%%!!!%%%!%%%%!%??%!%%%?%?%!!%!%!!%?%!%??!!??!!%!!!%%!%!!%!%%%!?%!%?%%!!%!%!%%?%!%!!!%%%!!!?%%%?!?%%%!!%%%%?!!!%!%%%??!%%%!%%!%%%%%!%%%!!!!!%!!%?%%?!!%%%?%!?%%!%?!%?%%!!?%!!%?%!%!!???!%%?!%%%!%!!!!?%!%!%!%%%?%!%!%%!%?%!!%??!%%%%!%???%%!!!%!%!%%%%???%%!!!%?%?%%%%%!%%%!!%%!?!%%%!%?%%%!%?!%%!%!%!!?%!%%%%%%!%%%?%%%%!%?%!%%%%%%%%!%%%%??%%???!%%%%!%!%?!!?%%%?%%!%!%%!%%%!%%%?!%!!%!!%?!?!%%!%%%!%!%%%%%%!?!%%??%%!%!%%%!%%%%!!%!!!%!!!!%?%!?%?!?!!?!!%%!%!%?!!%%%!%%?%%%%?%%%%!%??%?%%%%!?%%%!?%?%%%%%%%!%%?!%%%!%%%!!???%?!!!!?!%!?!%!!??%?!!!?!%%%%!!%%!!!!!%!?%!!%%%!%%%!?!!!%%!%%%?%?%%!%!?%!%%?!!%%!%??%?!?%!!!%!%?%!%%%!?%!!%?%!?%!!%%%?%!?%%!%%%%!!!!%!?%?!??!%!!?%%%%%%!%%?%!%%?!?%%!%!?%!?!!%?%%%!%!?!!%%%!%%%%%%%%%?%!%%!!?%%!%%??%%%!!!%%?!?%%%!!!!%!%!%?!!!!!!%%!%%%%!%%%?!%%!%?!%!!!!%%%%!!?%??!?%%?%!%!!%%%??%!%%?%!!%!%?!?!!!!!!%%%!?!!!!!%!!%?%!!%%!!!%%%%!%?!?%!%!!?!!!?!%%!%!%%%%!%!!!?!!%!?!!!?%!!%?%%?%!%%%!%?%%!%%!?!!!%!%%!!%%!%?%!%!?%%%??%%?!%%%%?!%%!!%?!%?%!%%%%!??!!%!?%?!%%!%%%%%%?%?%%%!%%!?%%!%%?%!?%!%??%!%!!%%%!%%%!%%%%%!%??%%?!%%%!!!%%%%!?%%%!%%!!%%%?%%!?%%?%?%%!%%!%%!%!??%%%%!?%!!?%%%%!!%%!%%?%%!%!!%%?%!%%!!!?!??!!??!!?%?%%!!%%%!%%!?!!!%%%!%%%%?!%%?%!!!%%%!!???!%%!!!%!!%?%!%!?%%%?%%!%%!?!%%%%!%%%%%?%%?%%%%!?%!%%!%%!%%!!?%!!!!%%!%%%!!!%%!!!%?%!!%!!%%%%!!!???%%???%%!%%%!%%%?!!%%%%!?!%%?!%%?%%%%%!%%%%?%%!%%%?!!%!!!!%!!%%%%!!!!?!!!?!%!%%!!!!%%%?%%%%%%!?!%??!!%%%%%!!%!?%?%%?%%%%!%%!!%?%!%!%%%!!%?%???%?!%%!!?%%%%%%!%??%%%!!%?%%?%%%!?%!%%!???%%!%!!%!!%!!%??%!%?!%%?!?%%%%!??%%!!??%%%%!??%?!%!?%!?%%%%%%!!??%!?%%?!!%!%?%?!%?%!?%!%!%?%%%!%?%%%!!%%%!%!?!%!?%?%!%!%%%%%%?%%?%%%%%%%%%!!%%!!!!?!!%?%?%%%?!%?%%%?%!!%%%?%!%%%?%%%!%!%!!!?!%!%!%%!%!!%!?%!%%%!%!!!%%!%%!%!!?!%%!%%%!???%!?!%%%?%%%!%%!%%%%%??%%%?!!%!?%%!?%!%%??%!%%%%??%?!???%%!!!?%%%?!!%%%!%%%%%?!%?!!%%%!?!%%!??!!%!?%!??!!!!!%%!!?%!!?%%%%%!%!??!?%%!%!!%!%%%?!%%%!%%!%%%%!!?%%%!%!%%%%!%!%!!%%%!?%!%%%%%!?%!%%!?%!%!%%!?!%!!!%%%!?%%!!%%?%!?%%!%!!!!%!%!!%!!!%!%%?%!%!%%?!!!%%!%%!??%???%%%!?%??!%%%!!!%!?%%???%!%?%!!%%???%%!!%%!%?%%%!%!?!%?%%!?%%%%!%?%??!!!?!?%!!%!%!!%?!%!!?%?%!%!!!%%%??!%%?!%%!!?!%!%%!?%!!%%%!!%%?!!!%!%%%%%!!%!?%!%??%?%!%%!!??%!!!!?%!?!!%%!%??!?!%!!%%?%%%%?!!%?%!%!%%%%%%!?%?!!%%%%%!%?!!%%?!%!!?%%%!%!%!%%%!?!?%!%?!%!!%?%%%!%%%?%!%%%%?!!%?%!!?%!!%!%%%%%%!!!%!%!%%%%%!%%%%%?!!%?!%?%%%!?!!!%!%%%%!!!%!?%!?%%%?%%%%!%!?%!%%%%!%!!!%!%%%%%%%??%%%!%!%!%%%!%%%!%!%%!%!?%!%%%!%?%!?%!!!%!!!!%!!%!?!?%!!!!%%%!!%%%!?%%!%!%!%%%!?!%%%%?%%%!%!!!%%%????!!!%%??!?!%?!!??%?%%?%!!%???%!%%!!%%?%!!%!%%!%%%!%?%%%!%%?%%%!%%%!?!%!!!%%%%?%%%?%!!?%!%%%!%!?%!%%%!%??!!?%?!%%?!?!?!%?!%?%!%%!?%%!!%%%!?!%%!?%!%?%%?!!!%%%%%!%%?!%%%%!%%!?%!%?!%%?!?%%!!!%%?%%%?%!??!!?%%!!?!!%??%!%?!!!%%%%!!%!!%%!%!%?!!%?!%?%%%%!%?!%!%%%!!!%%%%%%%%%%?!?%!%%%%?!!%%%%!!%%%%!?!?%%?%?%%???%?%%%!%?!%%%!!%%%%?%!%%%%%%?%!!!%%%?!!!%%%!?%!%!%%?!%%%%!!!!!%%!!%%??!!%!%%%%%%!%?%%%??%%!%%%%!!%%!!?!??%!??%!!!%%%%??!!%%!%!!%?%%%%%%!%!%%!%!%!!%!!%%!!%?%%!!!!!!%%!%%?!%%!!!!?%%!%%!%%?%%%?%%!?!%%!!%%!!!%?!%!!%%!!%%%?%!?%%%!%%?%%%!%%!!!%!%?%??%?%%%%?%%!?%%?!?!?!%!%?%!!%%%%%??%%?%%?!!%!%%!%%!%!!%%%%%?!%!!%!%!?%%%%??%%?!!!!!?%?!!!!%%!??%!!%%%%%%%%!%%??!?!%%%?%%!%!%%%%%!!%%!%%%!%!%%%??%!!!%!%!!!%!%!?!%%!!%!!%?!!!!!%?!%??%?%!%%!%%%?!?!!?%!??%%%%?!%%%?%%!!%%%!!?%%?!!%!%!?%%%%!%%%!!%%!!%?%?%%?%%!?%!?%%%!?!!%?%%!%%!%!%%!%%%!%!?!%%%%!%%!%!?%?!!???!?%!%%%%%!!!?!%?%!?!%%?!!%%%%%%!%%%?%!%%!%!%?%%!%?!!%%?%%%%!%!!!!?%%!%!%%!%%%!%%%!%%%%!!%%?!%!%%?%!%%%%!!!%%%%%%!%%?!%%%%%%!!!%?%??!?%%%?!%?!%%!?%%%!!%%%!?!%%%%%!?%!%%!!!%%!%%?!%?!%%!%?%%!!!!?!!%%!?!%!%!%!!%!%%!!%%%!%%%%%!?!!?!%%%??!??%!%%!%!!%%%???!!!%!%%%%!%%?!%%?%%!%!%%!!%%%%!?%?%%%?%!?%?%%%%%%%!?!%%!%%!!!%%%!!%%%%%!%!%?!%%!%%??%%!!!!%!%%%?!%%%!!%%%%%!%%%!!%?%%!%?%!%!!%??!%%%%!%%?%%!%!%??!?%%%?%%%%!%%%!?%%!%!%!!!%%%!%%!%?%??!%!?%!%%?!%%!%%%!!%%!!!!!%!%%%?%!?!!%%%%%?%%%!!%%?!%%!!?%!?!?%!!!%?!!%%!%!%?!?!%%%%%%%%%%%%%%!?%%?!%!!!?!%??%!!?%!%%!!%!%%!%%?%!%%?!%!?!%!!%!!%?%%%!%%!%%%%%?!!%!%!?!%%%!?%%!%%!%%%%%%!?%?!????%!!%!%!!??%%%%!%!!?!!%!%!!!%%%%%%%%?%!%?%!!?%!%!%%!!!%%!!!%%!!%???%%?%%%?!%%?!%!%%?!%!!?!?%%%%!?%?%%%?%%!%!%!!%%!%%%!%%%%%%%!!?%!%!%!!?!%?%?!!%!%%%%%%!%!?!!%%%?%?%%%!!!!%%%%!%?!?!%%!%%%?%%%!??%%%!%!%%%%!%%?%?%%!%?%!%%%%!%%%%%????%!%%!!%!!?%%!!?%?%!%!%?!!!?%?%?!%!%%!%%%%%!%%!!!%!!?%%!%%%!?%%!%%!%!%%%!!%%!%%?%!!!%%?!?%%%%%%!!%%?%%?!?%?!!!!%!%!%%%!%%%%!?%?%%??%!?%%%%%%!%%%?%?%%%!%???%?!!%!!%%?!%?!!!!!?!!!?!!%!!%%??!%!%%!%%%%!!%?!%%%%?!%!%?!%!%%!%%!%%%%!!%!!?!!!!!%!%%%!!%!%%%%!?!%%%?%!?%!????%!!%%?!%!%%!%%%%%%!%%%%?!%?!??!!%??!%%!!!%%%!?!%!??%!%%%%!?!%!%!!!!???!!%%%%?!%%%!???%%?!!!%%%%%%!%?!%%!??%%%%?!!!%%!!%%!?!%!!%%!%!!%%!!!!!%%!%%!!!?!?!%!?%!%%%%!%%!%%?!!??%%%%%?!?!%!%!%!%%%??%%!%!%!!!!%!%%%!!!?%!%%%%!??%?%!%%%%!??%%%?%%!!!?!!%?%?!!!!%?%%?!%!????%%%%%?%%!%%%%!!?%%%!??!%?%!?%%%!!%?!%?!!%!%!%!!!?%%%!??%!!%%%!%%!%!%%!?!?!?!?!!?%!%%%%!!?%!!%??%%%!?%!?!!!!%%%!?%!%?!!%?%!?%!!%!%%!%!?!%!%%!%%%!%%?!%%%!%!%!?!!%%?%%!%!!%?%%!%!%!!?!%!?%!%??!%!%!!%!?%%!!?%%!!!!!!!%!%%!%%!!?%%%%!!!%!?!!!%!%%!!%!%!!!!%!!%!%%?%%?%%?%%!%!%!%!!%!!?!!%%%%?!?!%!!%!!%???%%%%?!%%?!?!%!%?!?%%!!%!%%%!!?!%?%%??%%!%!!%%%?!!%?%?!!%!%!!!!%%%!!!!%??!?%?%%?%%%%!!%!?!%%!%%!%!%%%%%%!%!%?%%%?%!%!%!%%%!%?%?%?!%?%%%!%!%%%%%!?!%%?%%??%%%%!?%%!%%?!?!%%%!%%%%%!%!%?!%!??%%!%%%!!%%%!%%%%?%%%%!%!%!!!%%!!?%%!!%%%?!!%%?%?%%%!%!!%%?!%??!%%!!%%%!!!%%!!!?!%!%!%!!%!?%%%?%%???%%!??!!%!!%%%%!!!!?!%!!?%%!!%%%!%%%%!%%!%?%%!!?!%%!!%!?!!%!?%?!?!%%%?%!%%!%%%??%%!!%%%!%!%?%%!%%!?!%%%!%?%%!%%%?%%!%%!%??%?%%%%!??%!??%%!!%?!!%%!%!?%!!!%!%%%!%!%%!!%?!%!%!%%?!!!?!%%??%%!!%!!!?%%!?!%%!%!?%!!?%!?%%!%%?%%?%!!?%%%!%%%%!!%!!!%%%%%%%%%%%%%!?%!?%!%?!%%%%?%%%!%%%?%????!%%%%!!!!%%%%%!%!!%%!?%!%?%!!?%%!%%!?%%?!%?!%%!!!%%%%%?!%%?!???!%%???%%%%%!%???%%!%!%!%!%%!%?%!!%%??!%%%!%!%!%%?%?!!%?%%!%!%%%%!%%!%!!!%%!%%%!%%?%!%!!%!%?%%%!!%%!!%%!%%%%!!??%%%%!%?!%!!?!!%!!%%?%%?%%%%!?!%%!!%%%%!!!!!%!?%%%%%%%!%%%?!%!?%%!?!%?!!%%!%?%%%!!!%%?%?!!%?%%%?!%!!?!%!!!!%%?%%%%!?!!!%%%!%%!!!%%%%%!%%!%!%!!%%!?!!%?%%%!%%%%%!!%!%!!%%%%!!?%%!!?!!?!%?%!%!!!?%!?%%%%!%!?%!%%%%%%%!?%%!!%%!!%%?%%%!%!?%%!?%%%%!%%%%%??%%%!%!%%!!!!!%%%%%%?!!%???%%%%%%?!%!%??%!!?%%?!!?!!?!%%%!!?!?%%?!!!%%%!%!!%%!%!%!%%%%?%!%!!%?!!!?%?%%!?%!%%%!%!?%?%%%%%!%%!%%!%!!!?!%!%!!%?%?%%%!?%%!??!!%?!%?%!!%%%%!??!%?%?!!%?%??%%%%!!%!%%%%??%!!!!%?!!?%!%%%!%%%%!?%!%!%!%!%!%%%!?!%?%%%%%%%!!%!%!?%%!%%!!?%%!%%%!%%!!?%!!%?%%%%%!?!%%!?!%!?%%!%?!!!%%!%?!%%!!!%?%!!%%%!%%!?!%%!!?%!??%??%%%?%%%!%%?%!%!%%?%%!!!?%?!%%%%%!%%%!%!?%!!?%%%%%??!%%!%!%!%%!%?!%%!!%!%%%!?%%!!!!%%%?%%%!%%???!!!%%!!%%%%%?%%!%%%%%??%?%%%%%!%?!%!%!%%?!??!!%%%!%%%!?!%!?!!%%!%!%!%%?%?%%%!%!%!%%??!%%!?%%!!!!%%!???%%!%!!!!%%?%!%%!%%!%?%%?!!%%%%%!!%%%%%%%%%%%%!%?%%!!%!?%?%!??%!?%!%!%%%?!??%%?%!?%!!!!!%%%%?%!%%%%?%!%?%%%%?!?%!%!?%%!%!%%%!!%?%%!?%%????%?!!%?%?%!%!%%?!%%%%%!?%%%?%%%!??%%!%!?!!%!!!!%?%%!%??%%%%?!%%%%!!%??%?!%%%%%%%!!?!?%!%%?%!%%?%!??!?%!!!?!!%!?!%!%!!!?!%%%%%!!%%!!%%!!!!%!%!%!?%%%!%%!!!%!!%%%???%%!!%??%!%?!%%%%%!!!%!!?!%!%!!!%!?%!!%?!%%!%?!%%%%%%?!%!!%!%%%%%!%%%!!!%%%!%%!!%%%%%%!??%%!?%!%%%%%!!%%!%!!?%!%!%!?%%%%!%%!!?!%%?%%%%!%!%%!%%?%!%%%!%!%!!!%%%!%??%%%%?!%%!%?!%!%!?%?%!!!!%%!%%%%%?%?!%!???%%!%??%%%%?%!!?%%%%?!!%?%!%%%%%%!!%?!?!?!%%%%%%??%%%%!%%!!%%%%?%???%!%%?!%%!%!%%%%%!??%!%%%?%%!!%%!%?!!!??!%%%!%?!%%%!?%%!%%!?!!%%%!??%%%!%%!!%!%?%!!%%!!%?!%!!!!%%?!!%??%!!!!?!?%?%!!%%!%!%!!%?%!%%%!!!%%%!?%%!!%?%%%%%!%%!!!!!!%%?%%?%%%%%%!%%?%?%%?!!?%%%%%%%%!?!????!!%!%?!%%%!%!?%?!!!?!%%!!%%?%!%!!!%%%!%%%%%?%!??%?!%!!%%!!?%%%%!??%%?%!%%!!!?%%%!!!!!!!!!!%?%%!!%!%%%?!%?!?%!!%%%!%%!?!?!?%?!%!!%!%!%!%!?%%?!!%%%!?!!?%!!?%%??%%!%!%%%!!%%!!%%!%!?!%!%%%?!%%%!%%?%%%?!!%%%%%%%!%!?!%%!!!!%!%!!!%%%%!!?%!%%!!!!%!!%%%%%!%%?!!!!?%%%%!%!%%%%%!%!%!!%!?%!%!%%%???!?!%%%!?%!!!%%?!%!%%%!%%!!!?!%%?!!!?!!?%%%%%%?%??%?%%%%%!!%%!%?%?%?!%!%!%?%!%%?%???%!%!%!%%?%%!%%%%%!%!!%%!?!!?!!%%%!?%?%?!%%%%!!??!%!?%!%%!%!%%!??%%!?%!%%!!%%%!%?!!%%!%!!!%%%!!%%!!%!%?%%%%%%!%?%%%%%!%%%!%!!%%!%%????%%!%%%%%!%!%?%%!%%!!!?%!%%!%%?%%!%%!!!!!%!!?!?%!%!!?!!!?!!%!%%%!!?%%?%?%%!%!?!%?!!%!%%%?!!!!!!%%%%!!!!!!%?!?%%!??%!?%%%!!%?%%%!%%%%!?%%%%?!%!%?%?%!%?%!%?!!%%%%%?%!%%%%%%??%%%%%%?%%!!%%%!%%%!%%%%?%??!!%%%%%!!!%%%!%%?!%%!%?!!?%!!!%%%?%!?!%?%!%%!%!%?%%%!%%%?!?%!%!%%%!!%%!%?%%%!?!!%?!%%!%!%%%%%%??%!!%!?%!?%%?!%!%%%?!%!!%!%!%%!%%?%!%!!?%%!%%%!%%!!%!%!%%!!%%%%%!%%?%!!%%%%!!%!%%?%!%%%!%%%%??%%%!%%!!%%%!%%?!!!%!%!%%%!%!!%!%%%!%!%%!!!%!%%%?%!%!?!%!%!%%%!!?!%??%%%?%%%?!%%?%%!%%?!%!%%!!!%%!?%%%!!!?%?%%%!?%!%%?!!?%%?%!?!!%?????%%%!!??!%!%?%%%!?!%!%%?!?!?%!??%!!%%%%?%!!%!!?!?!?!%!!%%!%%%%?!!%!%?!?%!!%%%?%%?!?!%!%?!!%!%%%!%!%!!!??%%%!%%%!!!!%!%!?%%?%!%%!%%%%%?%!%%%!!%?%!%!!%!??%%!%%!%!!%!%!??!!?%?%%?%!%%%%!!!!??!??%?!%%%%!%!?!!%!%%!%!!%%%!!!%%%!!!?!!!%%%%!!%%%?%!%%%%%%?%?%?%%?!??!%!!%%!%%%?!?!%%?%%%%%!%%?%%!%!%!%?!%%??%!!%%%?%%?%!???%!?%!!%!?%!!?!%!!%!!%%!%?!%!%!!!%%%%%%%%%%%!%%!%!%!%!!%!%!%!!?!%%!%!!?%!%!!%?!%!!%%!%!%!!?%!%?%!?%%%%%%!!?%%%!!?!%%%%?%?%%!%%??%!%%%!%?!!%%??!?%?%?!!!!??%!!?%%%%%%%%?%%%!%?!%%%%%%%%%!%?%%!%!%%!!%%%?%%!!%%??%%!%%%?!!!!%!%?%!%!?%!%?%%?%!?%!%!%!??%%%!?!%!?%%!%%%!%%%??!%!!%%!%!%%%%!!%!%?!?%!%!?%%%%!%!%!!%%?!!%%%%%!%%%%%!%%%%%%%%%!?!?!%!%!!%!!%?%!%%%%%!!%%!%!%!%%%%?%?%?%?%%?%%?%%%%?%%!%!!!%%%??%%!!!!!%!!!?!%?!%%%%!!%%!?%!!!%%%!!????%!!%%!!%!%%!!%%%?%!!%!%!%!%!%!%!!%%%%%!!!%?%!!%%%!%!!!%%%?!%%%%!%!!?%?%%%%%!%%!!%!!?!??%!!?%%%%%%!?%%%%%!%%?!%!%%?!%??%!?%%!!?%!%?%?%%%%??%!%!?!%?!!?!!%%%%%%%%%?%%%?%?%!%!?%!%%!?!??!?%%!%!%?%%??!%%!%%%%?!!%?%!??%%%%!!!%%!%?%!%?%!%!?!%??!!!%!%%%%?%%!??!%%!%%%%!%?%%%!%%%!%!%?%?!%%!%!%!?%%!%!%!%!%?%?%%%??%!%?%%%%%%%!%%?!%?%%?!%?!%%?!%!%%%?!%%%%!%%!%%%!?%%?!%%?%%%%!!%!%!!%%%?%!%!!%!?%%%%%%?!!%%?!!%?%!%!!%!%%!%%?%!%%%!!!!%!%%!%%?%%%%%%%%%%?!?!!%%!!!!%%%%%%!%?%!!?!?!!!%%?%%!%%!%%?!%!%%!?!??!%?!%%%?!%!?!%%!?!!!!!!?%?!%%%%?%!!!!!?!!!!!!%!%%%!!%?%%!%%%%%!%!!%%%?%!?%%%%%%!%!%?%!%!!%!%%?%%%?%%%%!!?!%??!?%!%!?%%%!!%%!%?!%%?%!%!?%??!%%%!%?%%!?%?%%!?%!!%%?%!%%?%!%!!??%%%!%??%%%%%?%?%%!!%%??%%%!!!!?%!?%%%%%%!!!%%%%?!!%!!!!?%!!%!?!%!!?!!!??!???%?%%!%!%!%%%?%?%%%%%!?!%!!?!!!%%%%!%!!%!!?%?!???%%??%%%%!!!?%%%%?%%%%!%%%!!!!%!%???%%%!!!!%%!%!%%%%%%!%%!%?%%%?!!%%!%%%%!%%%?%?!%%?%%%%%!%!?%!!%!!!?!%!!%?%?%%?%!!%%!%%%!?%?%?!!!!!%?%!!%%?%!%%!!!!%!%!%%!%%?%!%!?!%%!%%%%%%%!?%%%!!?!%%!!?%%%%?%!?%!!%%%?%%?%%%%%%%%%!!%!?%!%?%?%%?!??!??!!?%!!%%%%%?!%?!%%%!!%!%!!!!%!%%%!!??!!!!%!%%%%!!%!?%!?!!!%%%!%!?!%%%%!?!%%!?%%!%%!%%%%!?!!!!%?%!!%?%%?!%?!%!%%!%??!!%%?!%%!%!%?!%%!%!??%%!%%!%!%!!%!%!%?!!%!%%%!?%?!?%%!?!!?%%%%%%%%?%%%?%!%%%?%%?%!!!!?%??%%!!%%%!%%!?!!!!!?!%!!%%!!%%!%?%!%?%!%?!%?%%!%%%%??!%!%%%%%%%?%!%!%!??!!%!%%%!%!%!%%!%%%%%%!%%%!?%!?!%%%!!?%%%!%?!%!!?%%?!!!%?%%%!??%!%?%!%%?%!%!?%!%%%!?!%%%%!!?%!!%%%!!%!??%!!%?%!%%!%!%%%%!%%%!%!!?%%?%%!%?!%??%?!?!%%%%!%%?%?%??%%%%%?!!?!%!?%%%%!!%!!%!%???%%%?!?%!%%%%%!?!%!!%!%%!%%!%!%%%%%%%%%%?%%%?!!!!!%!%%!?%%!!?%??%???!!!!%%!%?%!!%%!!%!%!!%?!!%??!%?!!!!%?!%%!%!!!?!!!!!%!%%!!%!%!%!%?%?!%%!%%?%%!%%%!%!!?%?%!%%%%%%%!%!!%%!%%%%%!!?!%%?%%%!!%!%%%?!%!?%!%!!%!!%%%!%%!%%%!!%!%%!%%%!?!!%%%%%!%%%!!!%?%!%%!%%!%%%?!%%%%%!!?%!!?%???%%%!%!%%%%%!%!!%!!%?%!%!!!%!%!!%!%!!??%!%?%%%%%%%?!!!%?%!!%%%%!!%%%%%%!!%%%%?!%%!%?%!!%?%%%%%!%!!%!%!%!%?%!%%%??%?%!%?%!%%?%!%%?%%!%!!!%!!%%%%?%!%%?%%%!!!%%%!?!%%%?!!%%%!!%%%!%%%%%?%%%?!?%!?%!!%%%%%%!%!!!!%%%!%?%?!!%?%???%%!!?%%%?!%%!!?!%!!%%!!%%%!%%%%%!!!??!!?!??%%%!%%!??!%?%!!!!%%!%%!%!%%%?!!??%!%%?%%!?%!!!!!!!!%?!%%!%%?%??!?%%%%%?%%!%??!%%%%!!%?!%!!?%???%!!?%!%?%!?!%%%%%!%%?%%!!%%%%%%!%%!%!%!%%!%%%%%%%!!%!%!?!?%%!%%!%%?!!%%!!%?%%%!%%!!%??%!?%!!%%%%!!?!%?%%%!!%!?!%%%%%%%!!?%!%%%%%%?!!?%%%%!%%?%!!?!%%%!%!%%%%%%%!%!?%%?%!%%%%%%!%?!!!%!%?%%%!%%%%%%!%%%%%!%?%?!!%%%??%!!%%%!%!!!!?%%!!?%%!%!%%!%%%%!%%!!!%%%!%%%%%%%!%?%%%!!!%?%%%%%!!?%%!?!%!!%!!?%!??!%%!!%!%!%!%%%?%%%!?%%!!%!%!%%?%%?!!!?%?!!?%!%%%%??!!%%%!!%!%!%%%%!!!%%?%%?!%%%%!!%%%?!!!%?%%?%%!%!%?%?%!!!?%!?%%!?%%%%?%!!!!%%%%%%%!%%!??%%%%!!?%!%%%?!?%%%%?%!!%!%%%%!%!%%!!!%%%?%%!!%??%!%?%!%!%%%!?%%!%?!!%%!!!%%!%%%!%%%!!!%?%%%!!!%!%!!%%??%%!%!%!%%!%!?!%!?%%%%!!%%%%!!?!!!!!%%?%%!!%???!%%?!%%%!%%!%!!!?%!?%!%?!!!%?%%%%%!%%%%!%!%%%!%%?%%!!%!!%%!!?%%!%%%!!!!??%%%?%%%%%!%?%%%%!!%%?!%?!!%!!!%%%!!!!!%%!!%%%?%%!!?%!%%????!%%%?!!%%%%!??%!!!!??!!%!?%!!%%!%!%!!??%?%!%!%!%%?!?%%?!!%!!%?%!%!!?%!!%!%%%%%%%?!%%%%%!%!%!%%%!%%%!!?%?!?%?%!!%!!!!!%%!!%%%?!%!?!?!%%%%%%%%!!!%%!%!%%%!%?%!%%%!?%!!%!%%%!?%!!?%%?%%%%!!!%!!!%%!%%%!%%!!%%%%!!%!!!!%%!%!!!%%?!?%%?%!!%%%%%?!%%%%%%%!%%!%!?!!!%!%%!!!!!%%%!%!%%!!!!?!!!%%??%?%!%?%!!%!!%!%!!%!%?!!%?%!%!!!%!%!%!!%%!?%%%%!%%%%%!%%%?%!%%%???!%?%%%!%!!%%%%!!%!%!!!!%%%!!%!?%!!%?%%%?%!%%%%%%%!!%%!!!!%%!!%%%!%!?!%%??!%%?!?!%!%%?%%!%%!%!!!!%%%%%%?%?%!!!!!%??%??%%!!?!%%!%!%?!%!%%?!%%!!!%?%%%%?%!??!?%?%%%!%!%!!?%!%%!%%%%!?%?%%%!%%%%?%!!%?!%%!%!%%%??!%?!?%!?%!%?!?%!?!%!%%?!%!%%?%%!%%%!?%!?!%??!!!%!%!!%%?%%%%%%%!%%!%!%%%%%!%!!!%?!!%?%?%%!?%?!%?!!%?!!!%%!%!%%!?%%%!%%!!!%%?%!!?!!%!%!?%%%%%!%%!%?%%!%%%!%%?%!!%%%!?%%!?!%%%!??%!!%!%!!?%!%!%%?%%%!!%?%%%!%%%!%%!%!!?!!%%%%%%??!?%%%!%??!%%%%!!?%%%%!%%??%!%%!!%!%??!%%!!%?!%%!%%%%%?!%?!???!!?!%!%!!!!%?%%%??%?!!!%?%?!%!?!%!!!%????%%?%?%!!%%%%!!!?%?%!%%%%!%!%%?%%%??%?!%%??%%?!%????%%%?%!!%?!!?%?%!?%!%!!?!?%%%!!%%%%!??%!%!%%!%%%?%!%!%!%?%%??!!!%%%%!?%%%!%!!%!!!??!%%%%%!%!%!%%%%!%!%!%%%%%%!%??%%%%?%!%%!!%%%%%%?%!%!%%!!!%%?!!%%%%%%%!!?!%%?!!%!!%%%?%%!%!%?%!?%%%?%!?!%%%%%!?!%??%!%%!%%!%!%%!%???%%?!?%!%%%!?!%%!!!???!!%!!?%!%?%!%%%%%%%%%%!%?%!!!%%%%%%%%?!%%!!?%!?%%%%??%%%%%%%%!!%%!!!!!!!!!%!!!%!!%!%?!%!%%!?!!%%?%%?%%%%%%!%%!?%%%!%%%!%!!%!%?!!%%!!!??%%%%%%%%%!?%%%%%%%%%%%%%?%??%?%?%!%!%!!!%!??%!%?%%%!!%%!%?!%?%%%%?!?!%!%%%!%!!??%!%%!!?!%!%%!%!%!%??!?!%%!!%!!?%%%%%%%%%%%?%!!!!%%!%%%?%%%%%!%!%%%?%?!!!!%!%!%%%%!%?!%%%?%!%?!%%!!?%??!%!?!!!%!%%%!%%%%?%!%%%%%%!!!!!!!!%%%!%!%%%?%!!?!??!!?%%%%!%%!!??%%!!%%%%%%%!?!%!%%%%%!?%%%!!%%?%!%%%%?!!?%!!!%!%%%%!!%%?%?%%?%%?!%%%!!!%%?!!%?%?!!?%!!!%%!!%?!!?%?%%!%?!?!!%%!!?%!!%%?%?!%%%!!!??%%%??%%!?!%!??!%%%%?!%%??!!%%%%!%!%%%!%%!?!%%!%%!!%%%!?%!!!?%!!%%!%!%!%%%?%!%?%%!%?!%%%?%!??!%%!!!%%%%!!!?%!%%?%%%!%%%??!%%!!%!!?!%%%%%%%!%%%%%%%!!!%?%%%%?%!%?%%%%%%%!%%%%%%!!%%%!?%%%!%?%%!!?%%%!%!%?%?!%!%%%%%%!!%%!%?!%%!%%%%!%?!%%%?%%!?%%%!?%%?%!%%!?%%!%%?!!%!!?!!!%!!!%?!%%?!%%??!!%?%%%??!!%!%!?%!%%!%%!!!?%!%!!%?%!!%!%!!%??%%!%!%?%!%%%%!!?%%?%?%%%!%!!?!%%%%%%%!!!%!%%%%!!!!%%%%%%!%%!%!%?%%%%%%!%!!%%!!%?!!%!%%?%!%%??%%!%%%!!%%!!%?%!!?!!?!%!%!%%%%%%%%?%????%%!%%%%?%!?%%%%??%%!%?!%??!!%%%%%?%!%?!!!!%!%?%?!!!%!!%?%%!%!?!!!!%!!!!%?%!%!%%%!%!%!%%%%!%!%%!%!%!%%%%%!%!%!!%%%%!%!%%%%!%?!!!?!%!%?%!!!?%!%!%%%%%!%??!!%!%%%%!%?%%%?%!%%%%!%!%!!!%?!%!%%%%?!%%%%!!%!!%%%!%?!!%!?!%?%%?%!!!%!!??!!%%!%!!%!%%!!?%!!%?!!%%?!%!?!!?!%%%?%%%!%!%%%!%!%?!!%?!?!!%%%!%?%?%!%!!%?!!%!!!%!!!%%%??%%!%%!?%%%?%!!?%%%?%%!%!!%?%%%%??%!!?!!%%?!!!%!%!!%?!%??%!%%%?!%%?%!!%%!%!%!%?%%?!!%%!%!!!%%%%!?%%!??!%!?%%%%!%?%?%!?%!??%?%%%!!%???%%%?!%%%%?%?%!%!!!%?%%?%!?!%%%%?!?%!%%?%!%!??!%%!!!!!%%!!!!%%??!?%!%!?%%!%%!?%%?%%!%%%!%%!!%!!!!?!?%%!!%%%%?!%%%%!%?!?!%%!%!?%%%%?%%?%%?!!%??%%!%%%!!%!?%?!%!%!%!!!%%%%%%%!?%%!!?!%!%%%%%?!?!%%!%%%%!!?%?%!!!?%%!!%%%!%%%%!%??!!!%???!%%%%%%%??%%?%%!%%!%?%%?!%!%%%!!!!%%!!%%%?%%%%!%!!%?!%!%?!!!!%?%!%%%?!%!%%?%%%%!%!!%!%%%?%!!%%?%?%%%%!!%%%%!!%%?%?!%!%!?!%!%!%??%!%!%%!%%%!!%%!!%!%%?!%!!!%%%%%?!%!%%?!!%%%%!%!%%?%!%!%%%%%%%!%%!?!%%%%%!%?!%?!?%%%!%!%%%!!%%?%!!%%!!!%%%%%%??!!%%!%?%%!%%?%!!!!%!%%%!?!%%??%%!%%!%%!!!%!!%?%!%?!%%?%%?!!!%%!!?!?%!%!!%%?%%!??!?!%!%!?!!%!%%%%!!!%?%!?!!?%%!!%%%??%!%?%?!%!%?!%%%!!%!!%%!%?%!%!!!!%!%!%%%??!!?!!%!??%%%%%!!%%?!%%?%!%!?%!!!?!??!%%?%%%!?%?!%%?!!%%??!!%?%%!!%!?%!%%%!%%%!!%!%?%%%%?%%?!??%%%?%?%!%!%!%?%%%%!!%%%!!%%!%?%?!!%%%%%%!%%%%!%%%!%?!%!?%%!!%%!!!?!%!!!!!%%%!!%?%%!!?%%%%!%%%?!!!%??!!!!?!!%!%%!!%%%%!?!?!%%%%%!%%%!%!!%!!!%%%!??!?%%?%%%%!%!%%!!%!?%%!%%?%?!%??!%!?%%?%%!%!??!%%!%%%%%!%%%?%!%%%%?%!%?%%%!!!!!!%???!!?%%?%!%!%?!%%%%!%!%%!%%??%?%%%?%?!%%?!!%??%!%%??!%%?%%!%!?!?%!!%%%!%%%%?%%?%?!%%%!%%%?%%%??!!!%?!!%!%!!%%%!%!!%??!%!%!!!?!!%!%!!%%??!%!!%!%!!%%!%!%%?!!!!%%%%%%!%!%%!%???%!%!!%?!%%!!%%?!?%%%%?%%%!!%%!!%!!%%%!%?!??!??%!?!!%?!?%%!%%%%!%!?%!!!!??%!%%!%%!%%!!%!!!?%!!?%??%%??%%!%%%?%%%%!%?%??!?%%%%!?%!%!!%!%!?%!?!%!%!?!%!?%!%?!?!%%%%!%%%!%!?%%!%!!%!%%%%?%!%%!?%%%%%%%%!?%%!%%%!%%%?%!!%?%%?%%%!%%%!%%%%!!%!%!%%%%!?%%%%!?%%!??%?%!!%%?!!!?!!!%%%%?!%%%!%%%?!??!?!%%%%!%!!!?!!%%!?!!!!!!?!!!%%?!!?%?%?!%!!%%%%%!%!%%!!!?%!??!%%?%!%%!%!!%%%?%%?%?!%%?%!%%%?%?%!%!!!!%%!%%?!%!%%%!!!%!!%%%?!?%?!!!!%!%!!!%!!%!%!?%?!?%%??!!?%!!%?!!!!?!%%%!%!%!%!!%!%%!%!%!??%%%%%?!!?%%%%%%%%%!!%%?!!%!???!%!%%%%!!%%%!%!!!!%?!%!!%!%%%?%?%?%?%%!!?%%?%%!%?%!%?!%%%!??!!%%?!!!!%%%%%?!%%!%%!?!?!???%%!!!%%?%!!!%%%%!%%!!?%%?!?%%%%?%%%%???%!%%%!%%!?%!%%%!!?%%%%?!%%?%%%%%%%%%%?!?%%%?%%?%%!%?%%?%%%%%%%!?!%!%!%%?!!!!%%!!%%?%?%!!%!%%?!%?!%%%%%%%%%%!?%?!%!!!!%%%!?%!!!%%!?%!%???%%!?!%?%%%!!!%%%?!%%%?!?!!?%?%?%%?!!%??!%!%%%?!%!!?!?!!%%??!?!%%!%?%??%!%?%!!!!!%%!%%%%%!%!%!?%%%%??%%?%!%%!%%!%%???%%!%%%!!%!%%%%%%%!!%!!%!%%?!%!!!%??%!%!%%!!???%!?%!%%%%%%%!!!%!!?!!!%%%?%%%%%?%!?%%%??!%!?!%%%!!%!!%!%%!%!!!%%%?!%?%%%?!%!?%%!%%?%!??!!?%?%?%!%?%!?????%!%%%!!?%%%!%!!??!!%!?!%%!!!%!%%!!?%!!!%%!%?!?!!%%!%%%!%?%%%%!!%%%???!?!?%%%!%%?!!%%!%!!!!!?%%%!%??%??%%%%?%%%%!%!%%%%%%??%%!%%%%%%%%!!%?%%%%%???%%%?!%!?%%%?%%%!!!%!!!!%!%?!!%%%%!!!??%%%?%%?!%%?!%!!%%%%%%??!%%!%%!!%!!%!%%!!?!!!!%%!??!?%?%%%%?%%!%!?!%!?!%%!!?%%%!%!%%!!!?%%?!!!%%!?!%%%!%!%!%!%%!!??!!%%%!??%!%%!?%!%?%%!%!?!%??!%%!%!%%%%!?%%%%%%%?%!??%%%!!!!%?!%%%%%%%!%%?%!!%!%%?!?%%%%!!?%!?%%!%?%%%!?%?%%%?%!?%%%!%?!?%?%!%%%%%!%?%!%%!%!?%%%%%!!!!%%%%?%%!!%!%%?%%?%!?!?!!!!%?!!?%!%!!%%??!?!!!%?%!%?%%?%%%%%?%?%%%%%%???!%?!?!!?%%%%%?%%%%%!%?%%%!?%!?%!%%%%%%!!%%%?%%!%?%%?!%?%%%%%%!%%%%%??!%%%%%%?!!!%!!%%%%!%%!?!?%!%?%!%%%!!%%!%!%%%%?%%%!%%!!%!!!%%!!%%%!!%%%%%?!?!%%!!%!!?!%!%!%%%%%!%%%%%?!%%%%!!%!!?!%%%%%%?%%%%%%%!%%!%!!?!??%!!%!!%%?%%%%%!!%!%%??!%!%!%%!%%%!%%!!%!!%%%?%%%%?!%!!??%?%?%!!!!%%?%%%%%!%%%!!%%%!%?!!!!%?%%%%%!%!%%??%%%!?%%%?!?!!%%%!!%!?%!!%?!%%%!%?%?%%%!%%!!%%???%%!%!%%?%%%!%?%!!?%?%!!!!!!!!%!?!!!!!%%%?!?!!!!!?%%%%%!??%!%%?%?%%!%%!!%%!%!!%%?!%%?%!?%!?%!!%%!%%?%%?%!%!%%??!%?%%?%%!!!!!%%!?!%!!!!%%%%!%?%%%?%?%!%%!?%?!!%%??%!%?%%%!%%%%!!%!%!!?!%%%%%%%%!!!?%!%!%?%%%%!?%%%%!%%!!%!?%%!%?%?!!%%%?%%%!!!?!%?%%%%!!%%!%!%%%!%!?%%%!%%?!!!%!%%%!??%%!%?%%%%%%%%!?%%!%!%%?%!?!%%!%?%!%!!!%!%!%!%%?!!!!?!!!%!!?!??%%%%%%%%?!%!!%%%!??%???!%%%%!%%%!?!??%!%%!??!%?%!%?!%!!!!?%%?%%%?!%%!%%%!%!!%?!%%%?!!%!%%%!%%%%%%%%!!%%%%%?!!%%%%%%!?%!%%%%%%%!%%?!!%%%?!%%%%!?%??%!%!%%!?%%%%%?%%!?!?%!?!%%%%?%%!!%%!!!!!?!%!%!%!??%%%%!?%!%%%%%!%%%%%%%?%%?%!%!?%%!!!%%%%!%%?%?!!!!?!%%%%!?!!%??%!%!%!%?!%%!%!!%%%!?%%?!%!?%%%!%?!!%!%!%!%%!?!%?%%%%?!!%%%!?!%%%?!!%%%%!%%!!!%%!?%%%!%?!%!%?!%%!??!!!%!!!%!%!?!!%%?!%%!%!%%%%%!?%!%%%!?!!?%%!!??%!%!%?!%??%!!%%?%!?%?%??%%%%!!!%?!!%%!%%!%%%!?%?%%!%!%?%!!!%!%?%!%!!%%%%?!!%%!%%%?%%%??%!%%%%%%!!?%%%!%!%%%!?!%!!?%%%!?%!%%!?%%!!!??%%!!!!!%%!!!%%%!!!!%%!!!%%!%%?!%!!!?%%%%%%!%!!??%%!%!?!!!%!%!%?%!%%!!%%?%!%%%%%%%?%%%!%??%%%?%%!%%%?!!!%%%%?%!%?!%%%%%%%%%%!%%%??!!%%!%%%%!!%%!%?!%%!?!%%!!%!!%!!%!%?%%%?!?%%??!%!!!!!%%!!%!?%!?!%!?%!?%%%?!?%?!%%?!!??%%%%?!!%%%%!%!!!!??!%!%!!??!?%!%!?%%%%%!??%?!%%?%!?%?!%%%!%!%!?%!!?%%?!!?%%!%%%!%!%%!?%!!!%!%%%%!%%%!%%?%%!%%%%%%%!%%%!!%!?%%?!!?%?%%%!%!%!%?!%?%%?!!?%%?!%!%?%%%???%!%!!!?%%!%?!%!%?!!%%??%%%?%%%!%%%%!?%%%%%%%?!%!%?%?%%%%!%%!!?%?%%!!%%%!?!?%%!?!!%%!%!%!!%%?%?%%?!%!%?!%%!%!!%%%%%?!!%!%!%%%%!!!?!!%?%!%%%%!%!%??!?%%%!??!%!%!%!%!!?%!%%%%%%?%!!%%?%?!%%%?%!!!%%!!!!!%!!?%!!?%!%!?%%%?!%!%!!!%!%%%%%!%%!%%!??!%%!%%%%!%%%?%%?%%!%!?%%!%!!?%?%?%!!%%!%%%!!%!%!%!%!%!!%!%%!%!?%?!%%%!%%%%!%!%%!%%!%!%%%%%!%%!%%%%???%!%!%%?!%%%?%%%!%!!%%%!!%%%!!!%!!!%?!%!%%!?%!%!%%!%%!%!!%?!%%%%!%%%%%%%%?!%%%!%%%%%??%!%?!%!%%?!!%%%%%%?!%%%!?!!%%%%%!?%!!!%%?!%%%%?%!?%!%%%%!!!???%!!%!%%%%%%%%!%!?!?%!%%%%!%%!%%%?%%???!%!!?!!!!!!!!%%%?%!!!%!?%!?!%%!!??!%?%%%!!!?%%%%!%!%!%%%!%%%%!%?!?!%?!?%!!??%!?%%!?!%%!???%%!?%?!%?%%%%?%!!!%%%%?%%%%%!%?!!?%%%!%%%%!%!!!%!%%%%!?%?%!?%%!%%%%%!!??%!%!%!%%%!%!?!!?!%!%%%?!%??!?%!%%!%%%%%?!%%!?%!%?%!!%!%%%!%%%%?%?%!?!%??%!%%%!!?%%!%%!%%?!%%!%!%???!!!!!??!%?%!%?!%!%%?%!%%?%?!%!%%%%%%%%!!!?%%%%?%%%!%%%%!%%%%%?%%%??%?%%!!%!!???%%%%%!%?%!%!%%%%%%%%!?!%%??%%?%%!!?!%!?%%?%%!!?!%%??%%%%%?%!?%!!%!???%%!?!%!!!?%%%!%!%?%?%!?%%!?%%?%%!%?!%%%!!!?%%?%%!%%!%%!?%?%%%%%?%!%%%!!??!%!??!!%%%%!%!!%!%%!?%%%%???%!!%!%%!!!%?!!?%%%!!!%%%!!%%!%!%%%%%!???%%?!%!%%!!%%!?%!?!?!!!%%!%!%!!%%%!!!%%%%%!%!%%%!%!%!??!!??%!?%%?%%!%?%%%%!??!%!?%?%%%!%%%%%!%%???!!!!!%%?%%%%%%%!!%!!%%!%%%?%!!!!%%!%%%!%%?%!%%!!!!%!!?%%!%!?!?!%%%?%!!%%!%%?!?%!%%!!!%?%!%!!?!!%%%?%%%!!%%%%%?%??!!!%%?%??%!%%%?%%??!!!!%!?%!%%%%%!!!!%%!?!!!%!!!!%!?%?!%!!!!%!?%%%%!!!!!?%%%!??%%%!%!!%!%%!?%!%!?%%?!!!%%!!?%%?%???%!%%%%%!!%!!%!%%%%!%%%%%!!%%?%!%?%%??!%!%%%!!!??%%??!!%%%!%%%?%!!%!!?%!!%%!?!%?%!?%??%%%%%%?%?!%!!%?!!%%!!%?!!%!?%!%%%!!!!!!!%%!!?!%!%!%?%!%?%%!%?!!%%!?!?%%%%%!%%?!?!%!?%!%%%!%%!!%!%?????%!%%!%%%!%%!%%!%?!%!?%!!%???!!%!%%%%%%!%??%?%%%!?%%!!%%!%%%%%%!%?!!%!??!??%!%?!!%%%!!!%?%!!!%%?!%%%%?!%%%!%!!%!%%%?%!?!?%%!%%?!%!%%!!%?!%!%%%%%!%???%%!?%%!%%%%!%%%?!!!?%%?%%!%%!%%?!?!!%???!%%!%%%?%%%?!!%??!%%%!%%%!%%%!%%%%!!%!%?!%%%?!!?%?!!?%%!%%??%%%%%!%!?%?!%%%%!%!%%??%%%%%!%%%?!!%%?!%%%!%!%%?%%%!%!%%%%?%%!%%%!%%!!!%%%!%!%?%?%!%%%!%?%%!%!!!!!%%?!%!%!!%%!%%!?%%!?%%!!!%%!%%%!%%%!!!%%!!!%?%?%!!%%%%%!!%%%%%%%%%?%!!?!%!!%!%%??!!?%!%!%!!!%?%!%%%!!%%%?%%%%!!%!%!%!!%%%%%%%%!%%??!!%%!%!!?%%!%?!!%!%%%%?%%!%!?%!!%%??!!!%%%%!%!!!%!%%%!%%!%!!?%!!?!!%%?%!???%?%%%%%?%?%!%!!!!!?!?%?!?!%%%!!%%?%%!%!!%%%%!?!%!%%%%!!!!%%?%!%!?%%%%?%?%%%%?%!?%%?!???!!!?%%!!!?%%!%%%!!%%!!!!?%!%%%%%?%?%%%%?!!?!%%?!%?%%!!??%%!!!%%%%!!?%%!!%%%%%%!%%%!??!%%%%?%%!!!%%?%!%!%!%!!!%%%%%%%!%%%%%!%!?!%?%%!?!!?%%?%!%%%%!?%%!%%!%?%!%%%%!?%!?%?%?!%!%?!??!!!?!%!??%%%%%?%%!!%?!%!?%!!%?!!!%!?%!!!!%%%!%??%?!!?%%%%!?!!!%!?%%%%!%!!%%!%!%!%!%%%%?!%%!%?%!!???%%!!%!%!!!!%%!!!!%%%%!!%%%?!!!%!%!??%%!%??%%!?%%!!%!?%%%!!%?%?%!%!!?%!%%!%!!!?%??!%%!%%?!?%%!%%????%!%%!%%%!!?!%?%%!!%%%!%!%!??!?!%??!%%!%%%!!%%%%%%!%%%%!%%%!!%%%?%!%??%?!%!??!%%%!%%!!!!%%!!?!%!!%%?%??!%?!?%!%?!!!!!%!%%!?%!%?!%!!?!%%??%%%?!!%?!%%%%%%%%%%?%%!%!!%%%%%%!?!%!!?%%%%%%%?%%?%%?%!!%%%%!?!%?!%%!!!%!!%%!%!%%!?%%%!%?%!!!!?!!%!?%%?%%!%!%%%%%?!!?!!!!%%!!?!?%?!%%%!??!%%%!?%!%!!!?!!%%!!%!!?!?%%!?%%!%??%?!!??!%?%%%?!!?%%%?!%!%%%%?!%!?%%!%?%%%%!?%?!%??????%%%%%?%%!?%%%?!%%%!%%??%?%?!!?%%%?%?!%%!?!!%!?%!%!!?%!!!!%%%%%?!%%!%%%%%?%%%!!!%%!%?%%?!%??%%?%!%%?%%!!!!%%!?!!!?%!!?%%!!%?!!%%?%%!!%%%?%!?%!!%%%%!!?%!%!%%%%%!!%%?%%%!%!%!%%!!%!%%?!!!!!%%?!?!!%%!!%!%%?!!!!%?!!!%%%?%%%%%?!%%!%%%!!!?!%?%%!?!%?!%?%!%%%!%?%%!!%%!%?!!!??!%%!?!%%!%%!%!%!!%%!%%!!%%%!%!?!?%%?%!%%!?!%%!?%!%!%%!%!?!%!!!?%!??%!%%%!!%%%?%!%%!%!?!%%!!%!%%!%%%%%??%!%%%%%%?!!?!?%%!%!!!%%!%%!%??%?%?!%!%!%%!!!%!!!?%%!!!%%%?%%!%%!%?%%%%!!%!???%!!?%%%%%%!%%!%%%!%?%!!?%!%%%!%?!%!!??%!?%!%%%!!!%?%!!%!?%?!%!%!%?%%%%?%?!?%%!??!%?!!!%?!!%%?!!!!!!%%%%!?%!?!%%!!!%%?%!%!!!?%??%!?%!!!!?%%!%?%%!!%??!!%?!!!!!????!?%%!%%?!%?%!%!?!%!?%%%!!%?%%!%%?%%??%%%%!%%!?!%???%?%?%?%%!?%?%!%%%%!%!!?!!!%%!%?!!?!!?%?!%!?%!%%!?!%?%!?%!%%!!%!!%!%?%!%%??%!%%%%%%?!%?!%!%%%?!%!!?%%%%!!%%?%!??%!%!%!!!!!?!%!%%!%!?%%%%%!%%%!%!%?!%!%??%%?%!%?!!%%???!%%%!%!!%%?!?%?%%?%%%!!%%%?%!%%!?%!!%%%%%!%?!%!?!!%%?%%%!%%%%!%!!!%!!!!%%%%?%%!!!%!?%%!?!%!???!%!?%%%!?%%%%!!?!?!%%!!?%%!!?%!%!%%!!%%%!%%%?%?!%?%%%!%%?%!%%%!%%!%%%!?%!%%%!!%%%?%%???%?%!??!%!%%%?!?%%%%%%!??%%!?!!?%!!%!%!!%!%%%!%%?%??%!!%!%?!%??%%??%!%!%%?%!?!!%%?!!?!!%!%%?!!%?%%??%!?%%%!??!%??!%!?!!!%%%%%%%!%!!%%?%!%%!!%%!!%!?%!%?!%!!%?!!!!%%%?%!?%!!?!%!%!?%%%!%!!%%%!%!%%%%%!?????!!%!?!!!%!%!%%%%!!%?%!%%%?!%%!%??%??%%%?%!%%!%?!?%%%%!!%???%!%%?%%!%%?!!!%%%!%?%%%%%!%!%!?%!%!!!%!%%%%!%!!??%!!%!%!%%%!%?%%?%!?%!%%!?%%!%%%%%!%%%%%!!%%%!%!?%!%!!%!??!%!!%%%?!%%!!!%%!!%!%!%%!%?!?%?!!%!!%??!!!%%%%%%!%?%!%!!!%%???%!%!!?!%!%!!%%%%%!%%%?!%%%%%%%%%!%?!%%%?!%%%%!%%!%%%!??%!?!%%!%%%%!!%!!!!%!?%%!%%%%!%!%%%!!!!%%%!!!%?%!??%%!!%%?!?%!%?%%%%?%%!%!!%%?!%!!!!%!?!%???%%%%%!?%%?!%%%%!%?%%?%!%?%%!!%?!%%%!?%%%??!%!%!%%?!?!?!%!%?!?!!!!!??%%%?!%%%!!%!%%%%%%%!!%?!!%!!!!?%!%%%!!%%%!%%%%?%!%%%!%!?!%!!!!%!???!!%?%%%?!??%?!!!!%%%!%%?%?%%%!%?%?%?%%?%!!!%%%!%!%%%!%%%%!%%!?%!!!!!%%%%%!!%%%?!%!%!!!%?%%%%!!?%%!!?!%%%%!?%%%!!!%%!??%!%%??%%%%%%%!!%!!%?!?%??%%?!%!!%!%!%!!%%?%%%!!?!?%%%!%!!?%%!?!!?%%!%%??%%?!%?%!!%%!%!?!?!?!!%%%??%%?%%%%%%%!%%!?!%%!!!?%%!!!?%!!%%!%%!%%!??!%%%!!%!!%!%!!%!%!%!%!?%%?%%%!!!!!!%?%%!!?%!!!!%%%%%%?%!%%!%?%%%!?%%!!!!!%!!?!??%!%?!%!!%!%!?!?%%!%%%%%!%%?!???!?%!!%!%%!%%%%%!%!%%!%%%%?%%!%%?!%?!%!%!%%!%%%!?%%%!!%!?%!?%%?!!?%!!!?%!%%%?!%%%%%%%%??!!!%!!%?%%%!!%%%%?%!%!!%!%!?%!?!%?%!!!!%?%!!?%???!!!%?%!%%?!%?%!!%%!!%!?%%%!%%%!%%??%?!%?%%%%!%!?!%?%%%%%%!!!%!!%!%?!%%!!%!%??!!!!!%%?%!?%%%%%!%?%!!?!!!!!%?%!?!%%!%%%!!!%?%!%!%!%%%!%%%?%%?!%?!!%!!!!!%??%%%!%%%?%%!!%%!!%?%!!?%%%%%!!%!!%!!!!%%!%!%%%!?!%!!%!!%%?%%?%%%?%%???!?!?????%%%%%!%!!?%!?%!%!%!%%??!!?%?!!!?!%%!%%%%!!%%%%%!?%%%%!%!%??%!%!%?%%%!!!%!??%!!%?%%%!!%%%%%%?!%!%??!%%?!%%?%!%!%%!%%!%!?%!%??%%%!%?%%%?%%?!%%%!!%%%%%%?%?!%%!%%%!%!%!!%%%!%?!!!%!%?%?!%%!%!%!%%!%?%%%%!%?!!%%%%%!%!!!%?!!%%%%?!%!%%%%%%!!%%%!?%%!!!?%%%%!??!!?%%??!%!!?!!!!!!%%!!%!!!!%%!!%%!%?!%%%%??!?!%%!!%!%!%!%!?!%?!%!%%%?!!%%!%%!%!!%%?%?!%%!%!?%!%%!?%?!!%!!%!!?%%%%%?!!?%%%%!?%???%%%!!?%!!%%%???!!!?!?%!!?!!!?%%%!%!%!?%?%%%%%%?!%%?%%%%!%!%%%!%%!!%%??!!!%!%?%????!%!!%%%?!%?%?%??!%??%!%%!!!?!?%%%!??%!%%??!!%%?%!%%!!%%%%!?%?!%%?%%!!%%%!??%%%!%!%!!%%!?%!%!!?%!%%%!%??%!?!?!%!%!!%%!%??!!%!!!%?%!!!%%%!%%%%!!!%%%%!?!%!%%??%!%!%!!%%!!%%%%%!%?%%%?!!%!!%%%!%%?%%%?!%!!%%!!!?%?%!?%%%!%!%!!?%%?!%%!!%??%?!!!%!!!%?%!!%%%%!?!%!!?!!!%%%%%%?!!!?%!!?%%!%!!%!!%%%%!!%!%%!%!??!!%%!%!%!%%!%%%?%!!!%%%!!?%!!?%!?!%?%?!%!%???%!!%!%!!%!%%!!%%?%%%%%%!%?%%%%?!%?!%!?%%!!%!%%?!?%%!!!%%!!?!%?!%?%%?%!%%%!%!%%%%%!%?%%%%%%%!!%???!%%%?%!%!%%%%!%!!%!%%!%%%%%!!%%%!%!!%%!%%%%???%!!%%%!!!??%!!!?%?!%?%%%%?%%?%?%%?!%%%!??!%?%!!%%!!%?!%%!%%%!?%%%%!???%%!!?!%?!%%!%?%%%!%!%?%!?%%!?!%??!%%%%!!!%!?%%%%!!%%??%%!!!??%!!%!%%%%%%%%!%%%!%%!?%%!!%%%?!?!?%%!!!?!?!%!!!?%%!??!!!%!!?%!%%?!%%%%%!%%%?%!%%%!%!!!!!?%!%%!?%!?%%!!%%%?%%!?%!!!%??%!?!%?!!?%!?!!!%!%!!%!?!%%!%%%!%%%%%%!%%!!!?%%%%!!!%?%%%%!?!%!!!!%!%%!!!%?!%%%%%!%!!%?%!%%%%%!!%!%?%!!%%!!%%?%!%%%!%%!%%%%%%??!!%%!!?!%?!%?%?!%%%?%%??!!%?%?%%?%%%%?%?%%%!!%!!????%%!%%!%%!!%%!%?%%!%%%!?%?%%%%%!%%%?!%?%!%%?!%%%!!!%!!%!%%?!%!?!%%!!!%%%%%?!?%%?%%%%%!%%%!!%?%!!%%?!%?%!%%%?!%!%!!!%%%%%%%%%%?%!!!!%%??!?%?%%%!%%%%%??%!%?%!%%!%?!!!%!?!!%%%!!%%%%?!%?%%%%%!?!!!!%!!!!%%%!!%%?%%%!!?%%%??!!!%%!%%%!%?%!!??!%!!%%?%%%%?%?%%!?%%%%?%!%%%!%?%%!!?%!?%!%%%!!??%!%!%%%%%%%%%?%!%?%%!!?!!%!%%%!!%%%%!!%%?!?%%%%???!!!%%%%%!!%!!%%%%?%?%!%%%%?%%%!%!%%%%!%!%%!?!%%?%?%%%%%%!!!%%%!!!?%!?!!?%!!!%?!%!%%%%!%!%?%%!!!!!%%?!%%!%!???!!%!%!!!%!??!%!!%!!%%!%%!%??%!%!%%%!%%%%%!!!!?!!!!!!%%!%?%%%%%%?%!!%%!%!?!%!%!?!?!!%%%!%!!?%%?!%!%!!?!%!?!!!%%%%%%%?%!%??!!%%!%%%!%!!%%%%%??%%%?!?!!!%%%%%!!%!%!?%!%!%%%%??!%%%!%!!%?%%!?%%%%%!%!!%!%!!%?%%%%!%?!!!?!%!%%%?!!%%?%%?%!%%%!???!!?%!!%%%%!!!?%%!?%%%%%!%%!??%!!%!!!!?%%!?!!%%%?%?!!!%%??!?%%?%!!!!%%!%?%%!!!%?!?!%?%!%!?%!!%!!?%!!%%!%!%!%!!%%%!%?%%%%!?%!%!!%%%%!%?%?%%%%%!%%%!!%?%%?!%%%%!%!!%%?!%!??%!!!%!%%!%?!?!%?!%?%%%%%!%%!!??!!%%%%%!?!%?%%%%%%?%!%!%%!!!%!%%?!%%!%%??!%!?%%!%?%!?%?%?%!?%%%!!%%%%??%%%!!!!%?%%%!!%?%%%%?%%!%!%!%!%!%%!%!!??%%!!%%%%!%!%??!!%%%%%%?%%%!!%!%?%?!%%%?%!%!%?!!%%?%%!%%%%!!!!!!!%!!%%!%%??!%%%%?%!?!!?%%!!%%!%%!%%???%%%%%!!%%%%%!%%!%%%!%!!%%%%?%!!?%!!%!%%!!!??!!%!?!%%%%??%!?%!%%%!!%%%?!%?%!??%!!%%!%%%!!!!!!%!%!!!%!%%?%%%!!%%?!%%%%??!!??%!%!%%%%%%?!?%%!!!%!?!?%%%%%!!%%%!?%!?%%%?%?!%??%!!!!%!%!?!?!!%%?%?!!!!%%%%?!!%!%!%?%!%?!!%!%%!%?!!%!!%%!%%!!?!!%!%!%%%!%%%!%%!%%%!!%!%%%!!%%%!%??%!%%!%%!!%%%?%%%%%!%%%?!?%!%%%!%!!!!?%!%!%!%?%?%!%%?!?!%%!%!!!?%%%!!%%%!!%%%%!!!!!%%%!?%%%%!?!%?%%!?%%!!%?%?%%%?!%%%!!!%%!%%!%%!%%%!%%?%!!?%%!%%!?%!%%!%!%%%!%?!!?%?%%!?%%!%%%%!%%!%!!%%!%%%!!%%%%%!%%?%?!%%%!?%%%?!!!%%!!%!%!%%%!%%%?!%%%%%%%%%!%%%%%?%!%?%!%?%%%?%?%!!%!%%!?!!!!?!%%%%!%?%%%??%!!!%!%!%%!?!%!%%!%%?!%?%!%%!!???!%%???!%!%%?!!%%?!?!%%?%%!?!!%!?%%%%%%%%!????%%%!!%!?!?!!!%?!%%%?%?!%%!!?!%!??%%??!%?%%%??!%%!?%?%?%!%!%!?%%?%%%!!!?%!%%%?%%%!%%!%?!!%%!%!%!!%%?%?%!?%!!!!?%!%!!!%!%%%%%%!?%%%!!!%%%%!!%%%!%?!?!!?!%!!%%?%!%!?%!%%%%%!%%!??!?%%!%!?%%!?%%%%!!%!!%?!!!%??%?!%%%?%!!!%!%%!%%%%%%%!!%%%!%!%%!%!!%!!?!%!!%!%?!!!!%%%!!%%!%?%!!?!%!?!%%!%!%!!%!%%%!%?!!!?%%%!!!!%!%%!%%%!%%%!%%%?%%%!%%!?!!%!?%!%!?%?%%?%!?!%%%%!%!%!!%%%?%!??!?%!??%%?%%%!%%!%%%%!!%%%%%%!%?!%%%%%!!%!%!?!!!%!?%!?!%?!?%?%%!??!%?!%!%!%%%!!!?%%!%%!%%%%!?%%!%!!%!%!!%%!%%%%!%%!%%%?!%!?!!??!?%?%!%??%?%!!%!!%!!?!%!?%%?%?%!%%%%?%!%!%!%%%%%%%!?%%?!%%%%??%?%!!%%%%%??%%!%!%?%%%%%!%%!%!%!!!?%%%%!!?!%???!??%?%!!%!%%%%%%%?%!%?%?%%%?%?!%!!?!?!!%!!%!%!!%?%%!?%%?!%?!!?!!%%?!%%?!!%%?%%??!!?!%!!%%!!%%!%%%!%%%!!!%%??!%%!!!%!!!%%?%%?%!!!!%%%!%%!!!%%%%%%!?!!?%%%?!!%!!!?!?%!%%%%!%%?%%!!%%%!!%!%%!!!%%%%!!%%%?%!%!?!!?!!?%!!%%%%?%!?%%!?!?%%%!%!%?!%?!%?%%%%?!%%%!%%%!!!??%%!%%%!%%%%!!!%%?!%?!!?%%%!%!%%%%!%%!%%!!!%!%%%%!%!!%!?!%!?%%%?!!%?!!!!!!!!%!%!%!!%%!?%?%?!!?%?%!%??!%?!???!%!!%!%?!%!%%!%!?!%%?%?%?!%!%!%?%!!!%!?%%%%!%%%!!!?!%??%!%?%!!!!!?%%%%%!%?!!%%%?!!?%?%!%%!%%%!!%%%%!%!%!!!?!%?%!%%!%%!%%!%?%!!%!%%!%%!?%!!!%%%!%?!%!?!%!%%%!!%?%!???!!%!%%%??!!?%%!%%!!!%%%!%%!!??%??!!!%%!%!%%%?!?%!!!%??!!%!%%%!???%%%!!!!!%!%%%!%??%!%?%%!%?!%%%?!%!!!%%!%%!!%%!?%%%%??!!%%!?%!!%%?%%!?%%%%!?%!!%!%!!!%!!??!!%!??!!!!%%%%!?%!????!??%%?%!%!!?%%!%!%?%%%!!%!%!%?%!%!!%!!!%%%!%!!%%!!!?!%!%!%!?%?!%%%%?%%?%%%%!%?%!!!%?!%%%%%?%%%%%!%?!?%!%?%%??%!%%!%%!!?%!!?%!%%%%%!?%!!!%!%%!!%%%!!!?%!%%%?!?!?!!%%??!%%%%!%%!!!%%!%%?%!!!%%!%%%%!%%%%%%%%%?!%!%?!?%?%%%?%!?%%?%!!%%!%!%!!!!!%?%%%%%%!!!%%?%%%?%%?%??!!!%%?!%%%%%!%%%?!%%!!?%%?!!!%!??%%%!!!!!%?!%%%?%%!!?!?!%!!!!%!!!!!!!!%%?%!%?%!%%%%%!!%%%!%%%!!!%%?!!!!?!!%%?%?!!!%??%?%%%!?%!%%%%%!%!!!!?%?!%!??%%%%?!%?!%%%%%%!%!%?!%%!%%%%%?!?!!%%%%?%%%%%%%!%%!!??%?%?%%%?%%%%%!!%%%%%!!?!!?!!%!%%%%%!%!!%%!!?!!%%!%?!%!%%%%?!%!?%?%??!%%?!%%!!%%%!!%%%!%%%%!?%%!%%!?!%%%!?%%!%%%???%!%!!%!!!?!%%%%%%%%%!%?!!%?%!%!!!%?%!%?!!!!%%!?%%%%%?%!!%%%%!%?%%%!%%?!%!%??%%%%%%!%%%%!%%%?!?%??%%%%%%%%?!!?!!!%%%%!?!?!%%!?!!?!!%%!!%%!%!!%?!!%%?!%%%!!?%%%%%%%?%!%!!??!%%?%%!!%%%!%????!%%!%%!!%!%!??%%!?!%%!!%%%!%%%!%?!!!??%?!%?%%?%%!!?%?%?!!?!%!%!%?%?%!!%!%!%%?%%%%?!!!?%!%%%?%!%%?!!%!?!!!%%!%!%!%%%%!!?%%%!!!%%%!%%%%%!?!%%!!%!!!!!%!!%?!?%!%%??%!%%!%?%!??!!%!?%!!%%!%??%!!%!%%!!?!!!%%!%!%%%%!!!%!%!%%?%!%%%%%!%%!%%??%!!!!%%%%%%%?!!!%!!%%%%%%!??%%?%%%!?!!?%?!%?%%%%!%%?%%%%%!!%!!%%%%%?%%?%%%%%%%!%!%!%!!!!%!?%%%?%%!%!!%%%%!?%!%!%?%!!%??%!!!%?!%%!%!%!%%!!%?!%%?!!%!%%!%%%!?!!!?!?%%!!!%!?%?!!!%%%%%?!!!?%?%%?%!?%!?%!?%%%%!%!!!%!%??%!%?%%?%?%!!?!???!!%%!%!!%%%!%???!?%%%%!?!%?%%!!!%%!?!%%%%%%%%%!!%!!?!%?%!!%!!!%!!%%%%%!!%!%%!%%??%%%!!%%!%%?!!%%??%?%??!%!%!!??!%!%!%??%%%!!!!%%%%%?!%!!%%!?!%??%!!?%%!%?%%%?%%%%%?!%%!%%%!%%?%!!%!?!!%!!%%%!%?%!%%%%!%?%%%%%%?%?%!%%??!?%%%%%%?%?%%%%?!%?%%%!%%%!!!%%!!!%%%!%%!?%?%%?!!!%!?!%%%%!!!%%%%%%?!%%?%%%%%%!!?!?%!!?%%!?%%%!%%%%?%!!!!%%%%?!!%%%%!!%!??%%??!%%!!%%%?!%%!?%%?!%!!%!%?!%%!%!%??%!%%%%?%?%?!!??!%!%%!?%!%%%%!%%%?%%%!!!%?!%!!%%%%!!?!!%%%?!!%!%%!%!!%?%%%!%!%%!!%?%!?%!%!%?!!%!!!?!!%!?%?%%!?%?!!%!%!?%!%!?%?%%%%!%!!!!!%%!!!%%%%%!!%?!%%%%%?!??!%!?%%%!%%%!%%%!?%?%%?!%%?%%%!%!!?%%%!%!?!??!!%!%%%%%!%!!%!%%!%%?%%!%!%%%%%!%!%%?!!%!%%?!!%%!%?%%%%%?%!!?%!%?!%%%%?%!!!%%%%%!?%%%%%%!%!%!?!%%?%?!!%!?%%%!!%!%%!%!?!%%%!%%%!?!%?%%!%%%%!?%%?!%%%%!?%%?!%%!!%?!%!%%%?%%%?%%!!!%!?%?%!?!?%%?!!%%?%!!?!%!?!%%%%%%%%!!%%%!%?!!%%!?%%!%?%%%%?%!%%!%?!??%%!%%!%!%!%!%!%!!!!?%%?!!!%%!!?!!%%!%%??!??!%%%!%??%!!%!%!!?%%!%!%!%%%!!%!!?!%%!!%%!%!%%%?%?%%%%?!!%%!%!%%%%?!!!!%%%%!?%?%%%%%!%!%!!%?%!%%%!!?%!%?!!%??!%%?!%!%!!!%%!%%!%%!%%!?%%%%!!!?!!!%?%!%%!%!%%!%%?%!!%%!%!%%!%?%%!!%??%!!%!?!!%%%%!%?%%??!!%%?%%!!%%!!!%?%%%%%%?%%%?!%?!%!!!????%?!?%%%%!!%%!%!!!%%%%%!?%!??!%%!%!!?!%%!!?%%%!?%?%!?!%?%%%%%!?!%!?%%%%%%???%%%?%?%!%%%%!%!?!!?!%%%%!%!%!!%%%%%!!!?!%?!%!?%!!%!%!%??!%%%!%!!%%%%%%!!!%%!%%%!!?%!%?!%?%%!%%%%%!%!%%?%%%?%%!!?%%%%!%%?%!!%%!%!%%%%?!??%?!!!!!%!?%%!%?!%%%%!!%!?%%?%%%!!?%%?!%%??%?%%%%?%?%%!!%%%!??!??%%%%!!?!%%!?!%%%%!%%%!!%%!!!?%%?!!%%%!%?!!?%%?!!?%%%%?%%!%%%%%%%!?%!!%?%!%%?%%!%%!!%%??%%!%%%?!!%%%?!%!%%!%%!!??%%%?%%%!!!!%!??%!!!%!%%%%!%!%!?!!??%%!%%?%%%!%?%!?%!?%%??%%%!%!!%!%??%!!%%?!%%!?%!!%%%!!%%??%%!!!%?%!%!!%%!!!%!!?%!%?%%%!?%%%%!%%%%!%!%%%%%?%%%?%%%!%!!%%%%%!!%?!%%!?!%%!%%%?!%!!%%%%?%!%?%?!?%!!!%%!!!%%!%%%!%!!!!%!%!!!?!?%?%%%!%%%!%%!%?!%%?%?!%%%!%!%%%!!!!?%!!!!!%%%%??%%?%?%!%%%%%%!!%%%%%!!?%%%!?!?%%!%!!!!%%?%!%%!%!!%%?!%!!%!%!%!?!!!%!%?!%??%%%%!%%!%%!?!%%!%%%%%%!%%!!%?%!?%%%!%??!!%%%%!?!%%%%!%?!%?%%?%!?!%!%!?%??%%%%!%%!%%%%%%!%%!%!?%!%!%%%!%%%%%!%!%??%!%!?!%%%!?%%!%%%%?%%!%!%?!%!?%%%?%%%%!!%%!?%%%!!!%%!%!???%%!%!!%%!%%!?!%!?%%%?!?%!%!!%!%!!!%!%%!%%%!%!!!!%%%%!%!!%%%!%!%%%!!!?%%%%%!%!%?%?!!!!?%%%%%!!!%%%?%%%%%%??!%%%!!!%!%%%%!?%%?%%%!%!%??!!%!%%!!!??!%%!!%!!%%!%%!!?!%!%!!%!%!!!!%%%?%%!%%%%!%??%%!!%?%%%!!!%%??%!!!%%!%!!!!%%%%!%%!%?!!%%!!!%%%!%?%!!%%%%%%!%!%!?%?!%??%%%%!%!%!%%!%?!%!%%!!%%%?%?!?%%!%%!%%!%!%?%%%%!!!!%%%%%!!!!?!%%%%!%%!!!%%?%!%%!!%!%!!!!?%%?%?%!%!%!?!!%%?%!%%?!%%?!%?%%%?%?!??%?!?%%%?%%%%!??!?!%?%?%!!%!?%!%%%!%%!?%?!!%%%!?%!%!%!%%%!%!%!%%!!!%!%%%%%!!%%!??%%!%?!!!?!%!%%%!?%%%%!!%!%%??%%!!!?%?%%?%!%!%%%%?!%%!%%%%%!%%!!?!%!%!%%!%!?%!%?!!%%!!!%?!%!!%%%%%!!?!%!!%??!?%?%%%%%%%%!%%!%!%%!?!!%%%!%!%?%!!%?%%?%!!?%%%!!!!%!?%?%!%%%!%%%?!%%%%?%!!%!!%!%!!%%!??!%!!!%%?%!%%%!%%!!??%!%%%%%%?%%!%%!%%%%%%%%!!%!?%%!?!!%%!!!!%%!!%%!?!!?%!?%%%%!!!%%%?!?!%%%%%?%%!%%!!%!?!!!!%?%?!%!?!%%%!!%%!%%%?%!?%%%!%!%%%!%??%%!!%?!!!!!%!%%%%%!?%!!%??%!!!?%!!%%%!%%%!%!%!!%!%%!!%%%%%%!!!%%%%!%%%?!?%%!!%%!%!?%%??!!%%%!!?%!!%%?!%%%!%?!!%!%!?!%%%!%??%!%!!%??!%%!%!!?!%!!!!!?!!!%?!!%%?%!%?%!!!!%%!!?%%%!%%%%!!?!??!%!?%%!!%%!%???%?!!!%?!%!%??!%!%%%%!%%!%%?!!!!!!%%%?%%%!?!!?%?%%%%?!%%!!%!!%%?!!%%??!?!%!%?%%%%%%???!%%%%!%%!!%!%%!%%!%!!%%%?%!!!?%%%%%%%%!!?%%%!%?!%%%???%?!%!?%%%!%%%!%%!%!!%%%!%%!?%?!!!?%%!%%?!%%!?%!%!%!%!%%?!%!%!%%!%%??!%%%!%%%%%!!!%!!!%!%%%%!!%%%!!!%!%%?%%??%!%%!%!%%!%%%?%%!%!%?!%!!%!%?!?!%%%%%?%!???%%??!!!%!!%!%%!!%!%%!%?%?%!!%%!%!%%%?%%??!%%?!%%%!?!!??!%!!%%?%!%?%??!%!%%?%!%%?%!%!%!?%%?%??!!%%%!!?!%%?%?!%%!%?!?!%?%!!%?!!!%%%%%%%!?%%%%!%%!%%!%%?%!%%?%!%!!%%%?%?!%%!!%!%%!!!!%?%%??%!!%!%%?%%!%?%!%%%???!%%%??%!??!!%!?%!%%%??%!%!%!!!!?!%!?%!%%?%%?%!??%%%%!%!%!!!%%!!?%!%%%%!%?%%?!%%%%!%%!%%???!!%%%%%?!%%!!%%%?%!%%%?%?%?!!!!%!!%%%%!?!!%%%!!!%!?!%%%%%%%!?%!%%%%!%%%%%!!!!%??%%%!!?%%%%!!!!%!?%%%%%?%%%!!%?!?!%%!%%?%!%%??!%?!?!!?!%!!!%%%?!%%%!%!!%%%!%!%%!%!!?%!%!!%!%!%?%!%%!%%!%%?!??!%!%%!!?%%%!!%%?%%!%%%%%%%!%!!%?%?%%!%%%%%?!!%%!!%!%!%%%!!%?!%%%%?%%%%?%!%%!!!%%?%%!!%%?%%!?!!%%!%!!!!%%??%?!?%??%?%!??!?%%??!?!!%?%?%?!!!%%%%?!%%!!%!?%%%?%!%%!%!%?!!!??%%%%!%!%!?!!%%%%!%!?!?%%%!%%%%!?!%%!%%!%%!%%%!!%%!%??!?!%?%%%!%!!!%%!%%!!!%%!%%%%!%?%?!%!?%?!%%!%%!%%?!%?!!%!!%!!!?!%%%%!!%!%!!%!!%%%?!%%!%%%%?%!!!!%%%%!%?!%!%%%%%%%!%%%%!?!%%%%%!!%??!%?!??%%%%!%!!!%%!?%!!%%%??%%%??%!%%%!%%?%%%%%%?!?!!?%%%!!%!%%%%?%%?!!%%!%!!%%!!%!%!!?!!?%!%%%%%?%?!!%%!?%!!?%!?!?!!%!!!!!?%%!%%%%??%%%%?%?%!%!%!%!!!%%%%%%!%!!!%!%?%!%?%!%!!%%%?%%%!!%%??%!%%%!?%!!%!!?%?%!!%!%%%%!%!%%%%?%%!%!%?%%%%%%!%%%!%!%%!%?!!!!%!?!%?%!%!?%%!!%%!%%!??!%%%%!?%%%?!!?%?!%%%!!%%?%!%?%!!!%%!%?%%%?!%%!%!%%%%%!%??!!%?%?!%!!!?%?!!%%%!!!%%%%%??!%!!!!%%%!%!!%?!!%%%%%!%%?%!%!??!?!%%!?%?!%!!%!!%!%%%!!!!!%%%?%!!!?%%!%!!%%%%!%!%?!%%%!?%?%!%%%?!%!%!%?!%%%!%%%%%%?!%%%%!!?!%%?%%%!!%%%%%%%!%%%?%!%!%?%!%%%%!!?%%%%!!!!%%?%%%%!%%!%%%!%?%%%?!%!!?%%%%%?!%%%%!!!?!%%%!%??%!!%%!%!!!%%!!?!%%%%!!?!%%?!%%%!!!%?%?%%?!!!%!!!!%?%%%%!%?!!?%%????%!!%%!%?!!!%??%%%!%%!!!%!%!%?%%%!?!?%%?%?%%!!%?%!!%%%!!!%%?!!?!%%%%%%%!%!?%%!!!%?!%%?!!%%%!%!%!%%!!%%%??!!!!%%%%!!%%!!%%!!!!?!%%?%%!%!!%!?%?%%%?!!%!%!%%?%%!%%%?!%%!%%!%?!%!%!!%%%!!!%!!%%%!%%!%!%!!%%%?!%!%%%%!%!!%!%%%%%!%%%!%%%!%!!?%?%?!!?!!%%%!%%?!!!!%%%%!!!!!%!!!?%!?!!??!%%%%?!%%%!!?%%%%%!!%%%%%!!%%%%%%%!%?!??%!!%%%%%%!!!!%%!??%??%%!%!%%!%%%!?%%!%?!!%!!%%!!?%%?!!?!!!?!?%!!%!!?!%!?!?%!!!%%?%?%??%?!!%!!?%%%%%%!%?%!?!?%%!!!%%!%!!!%?%%%%!!?%%%%!%%!%%%?!?!!!%%%!?%!!%!!%%?%%!!%!%%%?%!%!?%!!!?%%!%??%%!!%%!%!%%%?%?!%%%?%!!?%%%!!!%!%???%!%%%%%%?%!%?%%%!%!!?!%%!%%%?%!!%?!?%%%!?%?%%!?!?%?%!?!!%?!?!%?!%!!%!%!??!%%?!%%?!?!%%%%%%%%!!%%%?%!!!%%%%%%%?!%%%%?%%?%%%?%%%%?%?!%%!!!%%!%%!?%%%!?%%%%%!!%?!!!%???%%%!%?%!!%?!!%!%%%%%!?!%%%%%!%%%%%%!%%!?!%%%?!%%!!%?%!%!?%%!%%!%%!!%!?!%%%%?!!?%!!!%!%???!%%%!%%%?%%%?%!%!!%%%?!?!%%%??!%!%%%!%%%%%?!!?!!%!!!%???%%%?%!!?%%?%?!?!%!%%%%?%%!%!!?!?!!%%!%%!%%!%!%%%!%!%%%%!!?%?%!!%%%%%!!%!%%%!!%%%?%%!%!!!?%!%%%!!%!%?%?!%?%%%%?%%%?%!!!%%!!!???!%!!?%%%%!!%!!?%!%!!%?%!!!%?%%?%?%%%!!%%!%%%%?%%!%!???!%%!%??!%!%!!%%?%%%?%!?!!%%?%?!?%!!%?%%?%%%!%%!!!%%%%!!%%!!!%%%!?%%?!%!%%%!?%%%?%%?!?!%%%?!%?%?%!%!%!!%!!%%???%%!%?%%%?!%%%%%?%%!%%%?%!%%?%%%%?%%%%?%%?!%%?%%??!?%!?%%!%!!!%?%%%%!!!!!%!!%!%%%!!%!%%%!%%??%!%!?!!?%%%%!%%?!?%%%!!!%!%%!%!!%%!?%%!!!???!%?!?%???!%!%!?%!%??!%!%%!!%!!!%%%%!!%%%!?%%!%!?!!%%%!?%%!?%?%%%%%%%!!!!%!!%%%?!!%!!%?%!%%%%%????%!%%!%!%!%%%%!%%?%?%?%%?!?!%%%!?!%?!?%%!!%!%%!?%%%?%!%%?%%!%?%?!!%!%%%?!!%!%%?%!?%%?%?!%%%%!%!!%%%?%?!!%%!%%!!%?!%%%!!?!%!!!!%%!!?!%?%%%%!?!?%?%!?%!%!%!%%!%??%!%!?!%!%%%!%%%%%!?!?%%%!!%%!%!!!!??%%?%%%%!!!%!?%%%!%%%!%%?!%!%%%%!%%%%!!%%%?!!%%%?!?!?%%!%%%%%%!%!%!%%%!%%%?%??!%%%!%%%??%%%???!%!!!%!!!%!!!%!%%!%%%%%%%?%?%!!%%!%?%?%!%%??%?!!!%?%!%%%!?%!?%%?!!?!%%%%%%?!%!!%%%%!%?%!%!!%%%%!%!%%!%!!!%!%!%%%?!!%%!%%!%%%?!?!!!?%%!!?%?!?%!%%!!%%%!?!%!?%%?%%??%%!!!%!!%?%!%!!%%??%%%%%?!%%%?%%%%%?%%%!%%!%%?!%%%?!%!%%!!!?%%!%%?%!%%!!%!%%!%??%!%!%%%!%!%%%!%%!!%!!%%%?%?!%%%%%!!%!%!%%!!!%%!!?!%%%!?%!?%%!!%%%%!???!%%%!?!?!?%%!%??%?!%!!%!!???%!%!%!?%%%!%!!!%%%?%!%%%%%%%?%%%!%%%!%!!?%%?!??%?!%?%?!!%?%!%?!!%!%?%?!%!!!%%%?!%%!!?!%?%!!!%%!%%%%%!%!?!!%%%!!!??%!%%!!!%!?!!!?%%!%?%?%%%!%%!%%%%??%!%!%?!%%%%%!%?!%%!%%?!%?%!??!%%!!%?!?%%%%%!?!?!%%%%%!%!?!!?%?!%%!?%!%%%!%%%!%!?!%%%%?!%??%%?!%%%%?!%%%%?%%!!!?!!%???!!?%!!%!%?!?%!?%!%!%%%%%?!!%%?%!%%%%%!%%!!%%!?!!!%!!%%%%!%!%%!%%%%?!!!%%!?%?%%%!?%!%%%!!?!%!%%%!%%?%%?%%!?%!!%%?%%!!?%%%%?%!%%!%!!!%%!%%%?%%!!%%!?!!%??%%!?%!??%%%%%%??!%%%%%%!%%%!%!%?!?%!%!?!%%!%?%!!%!%!!%%%%%?!!!!!!%%%!!%!%!!%%%%%!%%%%%?%!%%%%!%!%%!?%%%!!%%!%!?!!%!%%%%!%!!%!?!%?!%!%%%%?!%%%%!!!!!!?!!!%?!%%%%?%?%%%!?%%!!%?!!!!!??!!%!!!?!?%%!!?!%%%!?%!!!!%!%!%!!!??%%?%%%%%%!!!%%!%%!%%%!%%?!%?%?%%!%%%!?%!!??!%%%%%%%%%%?!%%%?%%?%%??!%%!?!?%!!!??%!%%%?%!!?%%!%%!!?%?!%%?%%!?%!!%%!%!%%%!??%??%%!!%!%%?%%!%%%?!%%!%?%!%?!!!%!!%?%!%%%?%!!!%??%%%%!!%%?!%%!%%?!?%%?!%%%%!%%%!?%%?!%!!%%!%?%%%%%%%%!%%%!!%?%!%%!!%!%%%%%?%!!%%%%?!!%!%?%!%%%%%!%!%!?!!%?%%!%%!%%%%%!!?!%%%!%!%?%!!%%%%!%%%%%%%%!%!!!!%!%%%%?%%!!!!%!!%!%%??!!%!%%?%%!?%%?%%!%%?!!%!!???%?!!%!%%%!!!%!!?!%!?%!%!%%?!!%%%%!%?%??%!?%%%!!!%!%%!!%%%!%%?%!!!%!!%%%%%!!%%?!!?%%%?!!%!%%!%%%%%%%%%%!?%!!?%!??%?!%!%%!%%!%%%%%%?!%%%%!!!%%%%?%%%%%!%!%?%%%?%%!%?%%%%!!?!!%%%%!%!!?!%%%%?%!!?%%%?!?%%!!!!%%%?!%!%%!%%!!!!?!?!!%!!%!!?!?!%?%!%!%%%%%%%%!%%?!%%!!%!!?%%%%%%%!%%%?%%!?!!%!?!%??!!%!%%%%%%!?%%%%%?%!%%%%!!!%!!?!%%%%?!!!!%!!%%!?%!?%!!%%?!%%?%!%%%!!%!%%??%!!?!%?%!%??!?%%!%%%%!!!%?!!%%%%?!%%%%%!%!%???%%!%!!!!!%%%%!%%!?%!%%%!%%%!!%?%!!!!%!%?%?!%?%!%!%?%!?!!%%%%%%!%!!%%%?!%!!!!?%%%%!?!?%?%!%%%?!?!!!!?!?%???%?%%%?%!?%%%?%?!%%%!%%!?%!%%!!%%%%!!%!?!%!!!%?%?!!!?%%!!?!!%%%!!??!!?!%?%%%%?%%?!?%??%%!?!%%%%%%%%%%!%!?%!%%!%%%%!%?!%??%?%%%!%!%%?%%%%!?!%%%%?%!!??%%%??!%%!?!%?!?%!!!!%%!!%%%!!%?!%%!%!?%!%?%%?%!!?%!%?!%%!?%!%%!!?!%!!!!?!%%?!?%%!%!%%?!!%!%!!%?!?!!!%%%!%%%!!%!?!!%!%%!!!%!!!%!%?!?%?!!%%%%!!%%?%%!!%%%!?!!%!%??%%!%%?%%%%?%!!!!%%%%%%%!%!%!!!%%?%!%%!!%!%!%%%%!!!%!?!%!!!!?%!%%%%!!%?%%!!!!!!%?%%%%?%!?!!%%!%%%%%?%%%!?!?%%!!!%%%%%%???!%%%!%%!%!%%???%?!?%%%%!?!%%%!%?!!%%?%?!!%%%%??!%%!!%?%%!?%!%%%%%!!!???!!%%%!%%%?!%%?!%!??!!%%!%!?!%!?!%!!%%%%?!%!!!%!%%!!?!?%!!!!!!!!!!%%!%!!%%!%%!?!%!?%%%%%!!%!%%!???%?%?!?!!!%%!%%!!%%!%!%%%!%%!%!%??%%!%!?%?%%%?%!%%!%!?!%%!%%!?%?%%??%!%%!?%%?%%!!!!?!%!%!%!%%!??!!%%?%%!%?%%%%!%!%%!%!%%!?%!%%%%?%!!?%%!?%?!%%%!??%%%%!%%%%%%!%!%%?%%!!??%?%%!%??%%%%?%%%!%!%?%%!!%!?%??!?%!%!?!%%%%!!%!!!!%%!?%?%%%%%!!??%!%!?%%?!?%?!%!!%!%%%!%%!%%%%!?%??!%?%%!?!%!!%%%%!%!%%!%?!!!%%%%%%?!!!?%%??!?%!%%!!%%!!!%%!?%??%%!!!%!%?%%%%!%%!!%%!!%!?%?%%!%%%?%!%??!%?!!!%!!!%!%!!%%%?%!%%!!%%?%%?!!%?%%%!!%!!?!%!!%%%?%!%%?!!%%%%%%%%%%?!!%%!!!!%%%%%%!??%!%!?%!%!?%%?!%%%%!%%%%%%!!%!%%%%!%!!%%!%!%?%!%%%%%%!%%!!!%%!!%?%%?!%%!??!%%?!%!??%!%%?!?!%%%!%%%??!%%??%!!!%%!?%!%?%%??%!%!!?%%%%%?%?!?%!?!?%?!%%!%%%%!!?!%!%%!%!%%!%%?!%%!!!!!?!!!!%!!%%%!%%%!!%?!%%%%?!%!%%%%!?%%?%?%%%%??%!%!%!!?%%!%?%%!%%?%!%%%%%%?%%!%%%%%%%%%%?!%%?%%!!%!?%?%!!!!%!%%%%!%%?!%!!!%%!?%!%!!%%%%?!?%%%%!!?%!!%!!%!%%!%%%%!%?!!!!%!?%%!%!?%?%!!?%%!?!!%!%?!%!!!%%%%%%%!!%%%?%%%%!%%%%!%!!%%!!!!%!!%!!%%!!!%%!%!%!%%%%%?%!!?!%%%?%%%%%?!?%!%%!%%!%!%!%!?!%?!!%%%%?!!!%%%%%%!?!%!%!%!%?%?!!!%!!?%%!%?%%!%%!?%?%!!!%!?%%%%?%?!?%%?!%!!%?%%?!%!%%%%!??!!%!!%%%%%%?%%%?%!%!%?%%%%!%!!%%%%?!%?%%%%?!%%%%%%%!%!!?%?%%!?!!!!%!%%!%%%?!!!?%!%%?%?!%%!%!%%%%%?%%?%???!%%!%%!%%%!%!%%?%%?%%?!%?!%%%%%%!%%??%!!%%%%?%%%%!%%%!%?%?!??%%%%!?!%!!%%?%?%!%!%!%%!%!%?!%%?%%!?%%%!%%%?%%?%!%%%%!!!%%%%!!!%%%!!%!?!%!!%!%%%?!%%!?!%!%!%%%%%%!%!!!!!%??%%%%%%%!??!%?!!%%?!!%!%!!%?%!!%!!%%%?%%%%%%?%!%%!?%!!%!%%%!%%%%!?%%%???!%?!%?%!%!%%?!!!%!%!%%??!%%%%!!%!%!%%!!%%!!%!%%!%!%%%%%!%!%!%%!!%?!%!%%!%!!!?!!?%%?%%!?!!!%%!%%%%%?%%!%!!%!%%%%%%!%!!?!%%!%!%%%%??!%?!!!!?%?%!?%?%!!!?!?!!%!?%!??%!%%?%%!!!!!%!%%?%%?!?%%!%%%!!!%!%!?!!!!!!%!%!%?!!%!%%?%%%?%!????%%!!!%%!%!%??!!%%!%%%%?%%?!%?!!??!!%??%!%!%!?!?%?!%!!%!%%%%?!%?!??%!?%%%%%%??%!!!!!??%%%%%%!?%!%%?%!%?%??!!?%!!?!%!??%?!%%!!%%%!%%!%!%%!!!%!?%%!?!%!!!%!%%!?!%%%!??!%?%%??%%?%!!%!%!%!!!%%%?%!%%%%%%%%%?%%?%!!%%?%%%!!%?!%%%!%%?!%!?!%!%%!%%%%!%!%%!%%?%!!!%%%%!!?!?%!!!!%?!%%!%%%!!?!%!%%!!%!%%!%%!%?!!!%%%!?%?!!%?%%%!%%?%!%%?%!%?%!%%!?%??!%?!%%?!!%%!!!?%%?%%!?!?!?%%!!%!%%%!!%%?%!!%%??%%?%!!%%?!%%%!!%!%%??%!%!!%?%?%!?%?%%%%%%%%!%%!%%?%!!?%?%%%%%%%%%%%!%?!%%%??!%%%%!%!%!%%%!%?%%??%?%!%%%?%%%%?%%!!%!!%%%!!%!!%!%%%%?!?%%%!!%!!%%%!%!??%!%%%!?!!%!%!%%%%%%%!?!?!%?%!!!%?%!%%!%!%!%!%%!%%!!%!!%?%%%%%%%!!!!??%%%%!?!?!!?%%?%!%%!!%%?%??%!%%!?%!%!!!??!?%!%?!%!!!%?!!?%%?%!%%?%?%%%%!%?%%%%%%!%!!!%!!!%%!%%!?%!%!?%%%!%%?!!%%!%%!%!%!??%?%!?%!?!%!%?%%??%?!!%%!!%%!%!%%!!!!???%%%??!%!%!?!!%?!!%%!%%%%%!%?%?%!?%?!!%%????!%%!!%%?!%!%%???%!?!%!%!%%%!?!?%%%%%%%%!?!!%%?%!%!%%!%!?!!%?%!%%?!%!%%!!!%%%!%%!!?!?%%%?%!!%!?!?%?%%!%!!!%??%?%%%!?!%%%?%!!%!%%!!%?%%%%%!?!?%%%!!?%!?!%!%?%%!?%%%%??%??%?%!%!?%?%!%%%?%!%%%%!!%?%%%%!!%!??!?%%!!%!%%!!??%!?!%!!%%!!%%%!!%%%%%!?%%%%%%!%%!%%??%%!?%%??!!!!%?%%%??!%?%!?!%?%!%?%!%!%%%%%%%!?!?%!!!%%!!%%%!!!%?%??!%!%?%%%%!!%%%%%%!!!%!!%%%!!%%!!!?!!!%%%??!?%!%?!%%%%!%%??%%%!!%%?!!%%!%!%!?!??%%?!%?%!%!!%%%?!!%%%%?%%?!%!!!!%!!%%?%!??%!%!!?%!%%!%!!%%%!%%!%!!!%!%%!!!!!?!%!%?%?%%%%%%!%%!%?%%?!%%%%%!!??!?%!!%?!%%%%%!%!%%!!%???!%%%%%%%%!%!!%!%!%?%!!%?!!!%%!?%%%?%!!%%%!!%%%%???%%%!!!!??!%%%!%%%%!%%%!?!???%%!?%!!!%!!%!!??!%%?%!%?%!!?%!!!!!!?%!?%!%%%?%%!%%%%%??%%%%%!%!!!%!!?%!?%%!!%?!?%%!!%%%!%!!%%!%%%!!%%%!!?%!!%%%%?%%%?%!%!%!!%%%%%%!%%%%%%!?!!!!!%%%%!!%%?%%!!!%%!!%%?%%%?!!!!%%%%!!%!%%%!!%%%%!%?%!%%%%!!%!!%%%!!!?%%%%?%!!!!?%%%%?%!%?%%!!?!!%!!!!!?!!%%!!?!?%%??%%!%!%%!!!!%?!%!%%%%%%!%%%!!!!%!%!?%!%%%?!%!!%%%!?%%!!!?%!%%!!%!%!%%!%!!%%!!!?%!?%?!!%%%%!?%%?!!%!%%!???!?%?%?%!%!!%?!%!!%%%!%?%!???%!!?%%!!?!%%%!%?!%%%!%!%?%?!%%!!!%?!!!!!%!%%%!?%%!%?%?%!!!!%%?%!%%%%%%%!!%!%%?%%?!?!%!%%%!!!!%?%%?!!!%%%%%!%%!!?!?%%%!!?%%!!!!%%!!!%%%%!!%%!%??!!%!!!%?!!%!!%?%%%%%?!!%%!!!%!?%?%%%%%!%!%!%??!!%?%%%!!!%%%%%%%%?%!%%%!!!%!%%!%%?%%!?!%%%%!!%!??%%%%?!%%%?!%!%!!%%!?!%%%%?%!?%!??%%!?!!!!%%!?%?!%!??%%?!!?%%!??%%?%%!%!?%!%!!!%%%%!%!%%%!!%%%!?%%!??!%%!%!!%?!?%?%!!%?%!%%%%!!!!%%!%%%%%%!%???%%%%?!%?%!?%!!%!!?%%!!!%!%%!%%?%!%?%!!?%%%?!%!%!%%%!%%!?!%?!!?%!!%%%%?!!!?%!%%%%%!!!%!!??!%%!%!!!?%!%%%!%!!!?%%!%!!?!!!?%%%%!!?%%%%%%!%%!!%%!%%%%!%!?!??%?!%%%%%%!%?%%?%%?!%!?!%?%%%?!!!%?!?%%%%%%%?%%!%!%!!!!!?%!%!%%%%!?!%%!%??!!%?%%%%%%!%!%%%!%?!%!??%!%?%%!!%?!!%?%%!%%!!!%%!!%%%!%%!%%%%!%!%!!%%!?!%%%%%!?????!%!!%!?!!?%!%?%?%%!%%%!%%!!%%%%%?!!??%!!?%!?!%%?%?%%%%?!%?%%%?%!?!%%%%?%%!%??!%%?%%?!!%??!%?%%?%!!?%%!!!!?%%?%?%!%!?%%?!%?%!%%??%!!%?%%!?%?!!%%%%%%%?!%%%!!%!%%%%!%?%?!?!!%!?!%!!%%%!!?%%!%?%%%%!!?!?%%%%%?%!?!%%%%%%?!%%?%?!?%?!%%!?%?%%?!%%!%%%%!%%!%?%%%?%%%%%%!!!!!%%%??!!!!%%%%?!!!!%!?!%%!!!?%%%%%%!%?%??!%%!%?%%!!%%??!!%?!!!%!?%%%%%!?%%?%%%%%!%%%??!!%?!!%!%%%!%???%!?%!%%!!!!?%?%!!!!!%%!!!?%!%%%%!%%?!?%%!?!!%%%%%!%?!%%!%!%%%?%%%%!!%??%!%?!!%???%!!%%%!%!!?%%%%%%%%??%%!%%%!!%%!!!%!%!!!%!!!!%%%?!%!%?%!%%%!%?%??!?!??%%!!!!!!%%!%%!!%!!%%%!%!%!%!!%?%!%%%!!%%?%?!?!%!%%%!%%%!!!%%?!!%!!%!?%!!%%%%!!%?!!%%%??!!?%%!%%!!%?%%?!?!%%%!!%!%!%!%%!%?!%?%%?%%!%%!%?%?!%!%%!!%%!%?!!%%!%%!!%%??%!%%!!?!%?!%%%???!%%!%!%!!%%%%?!%%?%%!%?%!%?%!%?!%%%%%%%?%!!!%!!%%!??%%!!!!!%%%%%%%!%!%%?!!!%!%?!%%%?!?%!%?%%!%!%??!?!%%!!%!%?!%%!!!?%%!%!%%??!%!?%!?!%%%!!%!?!%%%!%?!%%???%%%?%?%!%??!!%%%%%%!%%%??%%%!!%!%!!?!??!??%%!%!%!??!%!%!%?%?!!%!%?%?%!??%%%!?!!%%%!%%%!!?%!%%!%!!???!%?!?!%!!!!%?%?%!???!%?%%!!%%%!%%!?%!%%%%!!%!!%!!%%??%???!!!%%!%%?!!!%!!!%%!%%%%!%!!%!%?%%?!!%!%%%%!!%?!%%?%%%!!%!!?%!??!?%!!!!?%%!?%%?%%%%!%%!%%!%?!%!%%%!?!!%!!%?!%!!!%!%%!!!%!%%%%%!%%%!%%!%?%%%!%%?%!!!!!!!%%!%%%!%?%?%!??!%??%%!%!%%?%%!%!%%%!%%!!!!!%?%!!%!%%%%%%%!!!???%%!?!!%?%%%%?!%?%%%%!%%!?%?%!?%%!?!%!?%%!%!??%!%?!??%!%%!?!!!%?%%%!!%!%!?%??!!%!%%%%%%%%!!?%!%%!?%%%%%%!%%!%%!%%%!!%!?%%%!%%%%%%%!!!!%%%%?%%!!!%!!%!!%%%%%!%%%%!%!!?!?%?%%?%%!!!!?%%!?!?%?!?%%!%!%!%%!?!%!%%%%%%!%!!?%%%%%%?!%!%?%%%%!!!?%?%%%?%??!%!%!%!%%!%?!%%!%%?!!%%%%%%?%%%%%!%%%%?!%%!%%%%%%%%%%%%!!%?%%%?!?!%!!!?%%!!%%!!%!%!%!?!?!?%!%%%!%!!?!%%!%%!%?!!!?%?!??%?%%?!?%%?%!%?!!!%!!%%?%%%%?%!%%!%??!?!%?%%%!?%%%%%%?%%%!?%%?!!%?%!?%%!%%%!!!%!!%%!%!!!?!%!%!?%!!%%?%!%!!?!!%!%%!!%%!%%?!!%%!!%%!!!?%!%!!%%%%!%?%!%?!%%%?%%%%?!??!!%??%%?%!%??%%?%!?!%%!!%%%!?%%%??%%!!!%?%?!?%?%%!??%!%%%%!!!!!%%!%!!%!%%%!!%%!!%%!%%!%%%%%?%%!!%%%%!?%%?!%%!?%%?%!%%%!%%%!%%?!%%!?%!%%!%%?!%%%%%%%!!%!?%!!%?%%%?!%%?%%?!?%%!%%%!!%!!!?!%%%?%?%%!%%!!%!%%?%??!?!%%!!??!%!?%%?!%%!%!??%%%%%?%!%%!%%%!!!%%!!!!!!%!!!%%?!!%%??%%%!!%%?!%%!%%%%?%%%%%%%%!%!!%%%%%%!%!!!%%%%??%%?!!?!%%%????!%%!%%?!%!%!%%%%?!?!%?!!%!%!?!%!??%!!!%%!%%%%%!%%%%%?%%!%%%!%%?%%!?!%!!%!!!!!%%%%?%%%!!!%%%?%!!%?!%%%!%!!!%%??!%?%%%%%!!!%?!%!!!!%%!!%!%%?%?%%!%!?!%%%%!?!!!%%!%!!%%%%!%!!!!%!!!%?%%!!!%%!!%%?%!!%%%?%?!%!?!?%%!%%!%!???%%!!?%%!%!%!!%!?%?!!?%!%%?%??%??!%%%!%%%%!!%!%%!!!%?!%%!!%%%%%%%!%!%%!%%??%!!%!%?%?%!!!?!%%%%%%%%!%!!%?%%%?!?%%%%%%!%%%!??%%%!!%%%!%!!??%!%!??%%%!!!!%!??%%!%?%!!%!%!!!%!%?!%%!%!%!%?!!%!?%!!%!%%%!!!%!?%%%%!!%!!!!%%%?%!%%%%%%%!%!!%?%!%%!%%!%%%??%!%%!%?%%%!%%%%!%!!%%%??%%%!!%!?%!%%!???!?%!?!%!%%?%%%!!!!?!%%%!?!%!!!!?!%!%!%!!?!!!%!?%!%%?!!%%%???!%?%%%%!%?!%?!!%!!%%!!%%?!%%!%%%?!%%%%!%!%%!?%?!%!!!%%%%?!?%?%%%!%!?%%%%!?%%%%?%%!%?!?!?%%!%%!!%?!!?!!%%%!!%%!%%!%!%!!!%!?!!%!!%%%??%!??%%!%?!!%%!!%%!%!!!!%%!!%!%%!%!!!%!%!%%!%%%%%%?!?!%%!%!!?!%%%%%%%%!!%%%%%!!!%!!!!%!???%!?%?!%%?!%%!!!!%%%%?!!!!??%%%?%%!!%%%?%%!!%%%?%%!?%%%%!!!!%?!?!%%%!!%!?!!%!%!%!!%?%%%?!!%%!!!?%?!%!!?%!%%??!!!%%%%%%?!!?%%%%%??%?!!?%!!%%%!?%!!%%!%%%%%!!%%%%%%%!%!?%!?!!%!?%!!%%%%%!?%?!?!!?%%!%!%%!%%!%%%!%%!!%%!%!!%%%!!!%%!!%%!!%!!%!!%?!%%%??%!??%!%%?%!%%%?%%??%?%%%!!?!!!?%%!?!?%%!%%%!!?!%%!?!%!?!!%%%%?%%?!%!%%%%%?%%!%%%%%!!%?!%!%%!!%!%!!?%%!%%%%?%?%?%%!!%%%!%!?%%%!!%!!!!%!!!%%%!%?%%%!?!%%!%%?%%%!!!%!!!?!%!!%%?!?!?!!!%!%!!!%!!?!%%!%?%?!!!!%%!%%!!%%!%%%?!?!%%%!%%%?%%!!%%?!%%!%!%%%%!%!!%%%%?%!%!%!???!?!!!!?!%!?%%%%??%%%!!!%%?%%!!!%!%?%%!%!?!%%!%??!%!%%!!!%!!%%%!%%?%%?!!!%%%%!%%?!%%%%%??%%%%??%??%!!?%%!%%!!!%%!!!%%!?%?%?%%%%?!%%!%!!?!?%%%%%?%%!%!%%!%?%%%!%!%?%??!%%!%%?%%!%!?%!%%%?%?%!!%?%!%!!%%%!%!!%?%!%!%!%!%%%%%%!!?%%%%%%!!%?%%%%%%!%!%%!!%!!?%?%%%!%%%!%??%!!%%?!?!?%!%??%?%%%%!?!%?!%%%!%?%%%?%!%?!%??!!??%%!%?%!%!%%?!!%!!?!?!?%!%%!%%%?!!!%%!!%%%%%%%!!%%%%%%!?!!!?!%%%!!%%!%?%!!%?!!%!?!%?!!??!%!!%%%%?%%!??%%!%??%!!%%%!!%%?%%!?%%?%%%%%%!!%%%%??%!?%!?%%?%%%!??!%%%??!%%%%%%!%%%%%%%!%?%?%!%%%%?%?%?%%%!%!?%%%?%%%!%?%%%!%?%%%%?!!!??%!?%!%??!!!%!%%%?!!?%%?%%%!%!%!%?%%!!%%?!%!!%%%%!!%!!%%?!!?%%!%!?%%!%!!%!?!?%!%%%%!!!%%%%?!?!%%!!?!%?%%!%!%%%?!%%?!!!%%%!%%%%!%?%%%%%!!!!%!%%%%?%%%!%!!%!%%%%!!%%%!%?!%%?%%%%?!%%%%%%%!!%!!!%%?!%%%!%?%??%?%!%?%%??!!%??%!?!%%%!%%%%%%!?%%%??!?%%?%?%%?%%%!!%!%!%!%%!%%%%!!%!!!%%??!?%!%%!!!!?!??%!?%!%%?%?%!?%%!%?%!%%?%?%%%!!%%!%%!!%!?%%%%?!!%!!?%%%%%!!?%!%?!?%!?%!!!?!%!%%%?%!%%!%%!%%?%%!!!?%!%%!%?%%?!%!%!%!?%%!!?!!%%!%%%%%%!!%!?%!%%%%%!%?%!%%%%%%?%!%%!%%?%?%!?%%%!%!%!%!!!%%!%%%%%%?%%!?%%?!?!%%%!%!%!!!%!%%?!%!!%%?%%%%%%%%%%%!!!!!%!%!!%!%?%!%%%%!%!?%%%!%!%!?!%!!?!%!%%!%%?%?!?%!%%%?%%!%!?%?!?%!!%!??%%%???%!!%%!%!?%%%%%!!%%!%?%!??%!%!%?%%%%%%%%%!%!!%%?!%%?!%%%%%!%%%?%%%%!!?!%%!?!!!??%%%!!!!!?%!%!!!!!??%!!%%!!%!%%!%%%!%!%?%%%%%?%%%!%?%%%%%?%%!!%%%!!?%%%%%!!%?%!?%%%%!???%%!?!%??%%!%?%!%?!%%!!!%!!!!!%?%!%%?%!!?%!%?%?%!%!!%!%%!%!?!%?%%%?%%!!!!%!%%!!%!??%!!%%%!?%!!%!!!%%%!%%%?!%%%?!??%%!%%%%%%!?%%!%!%?!%!?!?%%?!%!!%%!!%%!%?%%!%!%!%!!!%%!%%!%?!!!%!%%%!%!?%%%%!%!!??!!?%%%!!!%%%%%!!%%!%%%%!!!!%%%%?%%!!!?%?%%!!%%?%!%!!!!!%%%%%?%%%%%!!%%%%%%%%?%?%!%%!!?!!%!%?%?!%?!%%%%!%!!%!%??%?%%%!!%?!?%%%?!?!?%%?%?%??!%%!%%!%?%%%%!%?!%%!!!!%%%!!%%%%!%%%%!%%?!!!??!%!!!?%!?%!?%%%%??%%%%?!%!??%%%%?%%%%?%?%%?!%!%?%!%%!%!%%%???%%%%!%!%%%%!!%!%%%%!!%%!!!!?%%%!%%%%%?%%%%%%%%?%%%%%?%%!%%%!%?!!??!!%?!!??%!?%??!%%??%?%!%%?!%%%%%!??%!!!%!?%%!!%!%%!%%!%!%%!%!!%%!%!%%?%%%%%!%%%?%%%%!%!%!%%%%!!%%%%!%?%!%%%%!!!?%!%!%%?!!%?!!?%%%?%%%%!!%%%!%?%%!%!%%%%?!!?!!!%?%!%!?%%%%%%%%!%!!%!%%!?%%!%%!%!?%!!%!%!!%!!?!!?!!%!%%%%%?!!??%%%%!?%?%?!?%!%%%?%%%!%!?%%%%!%%?%!%%%%%%%%%%?%%%!%%%!%!?%%?%%%!%!!%%%!!%%?%%?!%%?%!!%%?!!%?!?%?!!%!?%%%!%?%?%!?%%??%!!%%%?%!%?!!%%%%????%%?%!?!!%!!%!%?!%%!%%%?%!%%%%??!!!%%%!%%%!!!?%?!!%!%!!%!!?!%%?%!%%!!%%!%?%%!%!!%!%%!?%%!%!%%%%?!%!?!%?%%!%!?%%%!!!!!%%!!%!%?%!!%!%%!%%%???%!%!%%%%!%!!%!%%!?!%!!%?%!?!%%!!!!%!!?!?%!%!%!%%?%!!!%%%%!%%!?!%!%?%!%!%%!?%%%%?%!%%%!?%%%%%%?!!?%!%!%!%!%?%!?!%!%%!?!%!%%%%?!!!%!!%%%!!!%%!%%?!!!%%!!%%%!%%%%%%?%!!?!?%!%%!!%!%!!?!%%!!!!%!!?%!%?%%%%???%!?%!!!!%!!!%%%%%%!!?!??!%%%??%?%?%%!%%%!%?%%%!%!?!!%?%%!??%?!%%%%?!%%%?%%%!!%%%????!?!%!%?!%?!!%%%%%!!%!%!!%%?%!!!%%%!!%!?%!!!%!!?%?%%%%%%!!%%!!??%%?!%%%!%!?!!%%??!%%!%?%%%!%!!%%%??%!%%!%%%%!!!%??%%?%!????%%!%!!%%%%?!!%%?%!!?%%%%%?%%!%%%%%%%%%?%%%!%%%!!!%%!%!!%!!%!%?%?!!%!!!!?!!!!%%%%!?%%??!%!%%%!?!%%!!!!%%%%%!%!!!?!!!?%?!?%%%!!!!%%!!%%%%!%!?!%%%?!!%%!!!!%%!!%%%%!!!?!%!!%%!%%?%%%%%%?%!%!%%!%!%?!!!!?%%!!!%?%?%!%%?%!???%?%%?!?%%%%%%%?%%%!%%!%%%%%!%%?%?!!?!??%%!!%%%%%%!!%?!!?!%%!%!!%%!?%%!%%?%%%?!?!%?%%?%%!%%!!!!?%!!!%%??%!!!%%!%!%!%!!?!!%%%!!!%!%%??%%%%!%!%?%%%!%!!!%%!!%%?%!%%?!!%!%!?%??!%%!?%!!!!?%!!!?!%%?!%?%%?!%!?%!!%!!?%%%!%%!%?!!%?%%?%%!%%%?!%!!%%%%%%!!%%!%%%!%!%%!%%!??!?!?!!!%?!!%%?%%?!!%!?!??%%%%%!!%??%!!!!!%?%%%%%!!!!?!%?%!!?%%!!%!%!?!%!%%?!!!%%%%?%?%??%!?!!!%%%%!?%%%???!!?!!!%%%!!%%!?%%%?%%%!!?%?%%%%%??%%%%!%%!!!?%?%!!!!?%?!!%%%!%!??%?%?!!??%?%!!!?%!%!%%!!!%!%!!!!%!%!%%%?!%%?%!!%!!!%%!!!!%?%%%%?%!%%!%%?!?!%%!%?!%!%%!!%%%%!%!!%!%%%!!!%?%%%?%%?%!%%?!%!%??%!%?%!!!%!%%%!!!??!!?!!!??!!??%%!%%%!%%%%%!!%!!!%%%%%%!%??%!%?!%%!%%!!%%?%%%%%%!%%%!%%!!%%????!!%!!?%%!!%!%%!!!??%%%?!%??!!%?!%%!%!%%?%%!!%%%%??%!%!%!%%%%!?!%??!!!%%!?!%!%%!%??%!?%!?!?%%%%?!!%%!%%?!%!!%!%!!%!%%%?%!!%??!!!%%??%%!!!!%%%%%?%!%?!!%!!%%?!%%?%%!!?%?%!??!!!%?!%%?!%?%?%?%%!!!?%?!??%!%?!!%!!!%%!!%%!%???%%!%%?!%%??!%???!%?%!%%!!%%%!%!%%%?%?!!!!%!!!!%%!%!%%%%!%!%!!%%%!!%%!%%?%%!%%!!!%%%?!%!!!%%%%%??%?%%?!!!!!!%!%!?!%?%?%!?!%%?%!%%!%?!%!%%?%!%%?%!%%%%!!%%!%!%?!%!!!%?%%%?%%!?%!%!!%!%!!!?%%?%%!!?!%%!%%%?%%%%%%?%!%%!!?%?!%!!%%!?!!%%%%%!%%%%??!%!%%%!%!!??%??%%!?!%?!%%!!?!%%!??!%%!!?%?%!?%%!%!?!%%%?!%!!%!??!%%%!%%!%%%%!!%%%%%%!?%!%!%!!%!%%%%%??%?!%!%%%?!%%%%!%%?%?%!!%%?%%!?!%%!%?%!%%%?%???%!%%%?%?!?!%%!%?!!%%%?!!%%%!?!!%%%!?%%!%!?%%!%!??%!%%%%%%%!%?!%!!!%%%%%?!!%%?%%%%??!%%!!%%%%%%!!%%!?!%!!%??%??!%%!?%!%%!!%??%?!%%!%%%?!%%?%!??!!!%%?%!?!%%%%!%?!?!%!%%!%!!%%%!!%!!%%%!%%?%%%!%%%%%?!%!!%!!!?%%%%%%??%%%!!%?!%%!!?%%%%%!%!!%%?%%!%%?%%%?%!%!%?!%?%!%!%%!%!%!%%%%%%%?%!%!?%%?!?%%!%?!!%%!!%%%%!%!%!%%%??%%!%?%%%%%!!!%%?%%!?%%%!?%!%%%?%?%%%??!!%!%%!!!%??%??%%??!!%%%!%%?%?%?!?%?!%!?%%%!!%%!?%!%!!?%!%%%%?%%!%%!!%%%%%!%%%%!?%%%!%%?!%!!??!!%%%!??!%!!%?%%!!%!%!%%%!%?%%%?%!!%!%%?!%%!!%?%%!!%%%?%?%%%%%!!?%!!?!?%?%!!!?!%%!?%!%?%%!%!!?!?%%%%!%??%?%??%%?%?!%!%!!%!!%%%%???!%!?%!%?%%!%?%%?!!%!%!!%%%!%!%%!!!%%!!!%!%%%!!?!!%?%?%%!%!%!%!?%%%?%!%%?!%?%%%%!!?%%%!!%%!!!%%!?%!%!%?!?%%%%%!%%!%!!%!%%!%%%%%!!!%!!%%??%%%?!%!??%!%%?!!%%!!!%?%%??%%???!?%!!!%%%%!%?%?!%%!%?!!%%%!%?!%%%%%%!!%%!!!!!%%%!%%%!%!?%?%!??!!%?%%%%%%?!%%%%!?!!%?!%?%%%??%!%!%%%!!!%%!%%%!%%?!!!?%?%!?%%%%%!!%?%!%!%?%%!!?%!%%!???%?!%%%!?!!???%?!!%!%!%%%%%!!?!%??!%!!!%%%!%%!%?!%%%%%?%%?%%?%%!%%%%%!%!!!%!!%!?!%%!!%%%%!%%!?!!?%!%%%%?!%!%!%!!%!%!%%!%%?%!%?%%!!%?%!??%%%%%!!%%%?!%%!?%!%%%!%!?%%%%%!!!%?%!?%!!%!?%?%%!%!!!?!%!%!%%%!%%%?%%?%!!%%%%!%?!%%!%%?%!!%%%%%!??!%%!%!?!!!!%%!%!!!!%!!%%%?%%%!%%%%?!!%%?%?!!!%%%!%!%!?%!%%%%%%!?!%%?%?%%%%??????!!%?!%%%%%%!!%!%%%!?!%?!%%%%%%%!%!%!!??%%%?!??!%%?!%%?%!?%%!%%%%!%%%%%%%?%!?%?%??!%%%!%?%%%%!%%%%%!%%%%?!!?!?%%%%!%%?%%!!!%%%%%%%%!!!?%%?%!%!%%!?!!!!%%!!%%%!!?!%%%%!?%!%%!%!!%!!%%?!!!!!??!%%??%%%%%?%!?!%!%?!%%%%?%!!%!!%?%%%%%?!?%%?%!%??!!??%%%!?%!?%!%!?!%%%%!!!%%!%%%!?%%!%?!%!!%%%!%!%!!%!!!%!%!%?%!%!??%%%!%!!%%%!!!?%%%%?%?%!!%!%%%!!?!!%%%%%!!?!!?%%%!%?%%!%!%%!%%%%%!%?%%%!?!%%!%?!%!?%%!%%!?!!!%%%%?%??!!!%%!!!!%%!??%%%%%%%%!%!%%?!?%!?%?%??!%%?!%%%??%!%%%!%%%?!!?%!!%%%!!%%!?!%!?%!!%!??%!!?%%?%%?!%%%%!%?!%%!%%!%%!!!!?!!%!!%%%!%!%%!%?%!!!!%%%%%%!%!%%!%%%%%%!!?%?%?%%%%!%%%!?!?%!%!%!!%%!!%!%%!!!!%%!%%!!%?!?%!%%%!%%!!!?%%%%!%!%!%!%%!??%%!%?%?%%!%%%!%%%%?!%!!%?%%?!!?%!%%%%!!!%!!%%!!%?!??%?!%!%%!?!%%?%%%?!%%!?!!%%!%%!%!!%%%%%!%!!%!?%!%!%?!?!?%!%%%!%?%!?!%??%%!?!%%%%%%!!%!%!!!?%%%%?%%!%%?%!??!%??!??%!!%%%%!%%!%?%%%?%!!%!%!??!!!%%?%!%%!!!%!!!!%!%!%%%?!%?!%%%!!%!%!%%%?!?%%!%!!%%%%%%?%%%%!!?!!?%%%%??%%%%%!%%%!%?!!%?%%!!%?%%???%%%%%?%!%!%!%%??%%?!!%!!!%%%%%%%%%??!%?!?!%??%%%??!!?!%?!%?!%%!??%??!!%?!%%!!!!%%!%!%%?!%%%%!%%??%%!!%!%%!?%%?!!%?!!%%%!!!!?!!%%??%%?%%%!?%!%?!%!!!!%%?!!%!%%%!%?%%!?%%!%%??!!!!!!%%%?!%!%%!%!%!%!!%%!%?!!!??%%%%!?%%!!!%?%!%%%%!!%??!%%%%?%%!!%?%?%!!!!!%%!!%!!%%!%!%%%!%?%!!!%!%%!%%?!!!??%%?!%%%%!%?%%%%%?!%%%?!!%%?%!%%!%?%%%%!?!%%!?!!%!!!!!!%!%!%%!!%%%%??%!!!%%!?!%???%!!!!!!%!%!?%%!!%%%%%%?%%!!!%%!%%!%!!?%?!%!?%%!!%%!!%!!%%!%!%?%!?%!!%?%?%%!?!%!%%%????%!%%%!!!?!%?%!%??!!!?%%!?%!!%%!%?!?!%?%!!!%%%%%%%%%%!!?%%%%%!%?%%?%%!%%!%%%!%!%%!?%%!%!!!%%?%%!%%!%%%%%%%%%%?!%%%%!!!?%!%%%!%!?%!%%!?!%!!%%%!%!%?!%!%!!%!%!?%%%%%?%!%%!!%%%%%?%%%%!%?%?!%!!%!!!%%%%%?%!!%%%!?!?%!?%!?????%!%%%!?!!%!%!!%%?!!!%%%!?%%%%%!%!!%%!??%%%?%?!?%?!!!%%%%!%?%%!?!%%%%%%!!%%!?%%%%%!?!%%?%%!%%%!!?!%????!!%!%%!%?%%!%?%%!%!!?!!!!%?!!!!?%%!?!??%!%!??%!???%?!%!%!!!%!%!%%%%%%%!%%?%%%%?%%!!?%!!%!!%?%!%?%%?%%!%??%!!%%?%%?%!%!?%%!!!%??%%!!?!%!!?!?%!!%%%%!%%%?%?%%%!%?!%%%%%%%%!%!%%%!%?!%%%!!%%!!?%%%?%%%%%%!?%!%%%%%%!!!%%%?!!!%!%!!%%!%!!!!?%!%%?!?%!%%%!!!%!!?!%%?%%!%!%!%!%!?!%!%!%!?%!!%%%%!?%?!!%%!!%???!%!%%%%%%%?!!!!%!%%!%%%!?%%!%?!%%%!%?%%!%%!%%%!%%%!!?!%!%?!%??!%!!%%!!%%!!!%!?!!%%??%!%!%%!!%%%%%!%%?!!?%!%%%%!%?%!%?%%!%?%%!!!!%%%?!!!!%!!%%!!%!!?????%!%!%!%%%%%?!!!%?%%%?%!%%%!!%!!%%%!!!%??!%!!!!!%!%%%%%?%!?%%!%%%%%%!!%%!%%%?%!?%%%?%%?%!!!%!%%%%%%?!%!%%!%%!%!?!%%%?%!!?%!!%%!?%%??%!!!?!?!!?%%!%%%!%?%!%%!%!!%!?%!!!%!%%!?%!%!?!%!!%!%!??%!!%%%%???%%%!?%!!!%%%!%%!!%%%%%%!?!%!%%!%%%!!%!%!%%??!?%!%%%!%%%%%%%!%!%%!%!%%%??!!%!!%!%?!?%?!!%%%!%!%!%!%%%?!%!!!%?!!?!%!!%%?!?%!%!%%%%%%%%!!%%%!!%%%%%!%!%?%%%%?!%!!%%%?%!%%?%%%%%!%?%%%!??%?%!%%%%%!%%%%%!%%%!!%%!?!!?%%!??%??!%!!%?!!%%?!%!!%%%!!%?%%!%?!?%?%?!?!%%!%!%!?%%%%%%%!!%?!%%%%%%%!%!%%%!?!%%!%?%??!!%!%%!!?%!%%!%%!!%%???!%%!?%%!%!!!!!!%?%?%%%%%%%%%?!!%%%%!%%!??!%%!%%%!!?!!!?%?%%%%%%!!?%%!!%%%%%%%?%??%%??%?%?!%?%!?!%%???!%!?!??%!?!!%!?!%%!!!?!%%!%%%??%%%%%%%??!!!%%%%!!??%%%%%!%%%%%?%!?%%%!%%%%!!%!!???!%!?!%!??!%!!%%%%%??%?!%!!?%?%%%%!%!!!!!%!%!?%%%!!!%%?!%?!!%!!%%%!!%%!?!%?%%%!%?%%%%%%?!!%%!%%%%%%%%%%!%%?!!!?!!%%!%!%!%?%?!%!!%!%?!!!!%!%%!?!%%?%%%%%%%!!%%?%%!%!%!%%!!!!%!%%!!%%%!!!!!%%%?!!!!%%!?%!%!%%%!%%!!%%%!%%?%!%%%%!%!?%%%%!%?%!!%!%%%?!%%%!%?!%%?!??!%%??%%%!?!!!!!%%%%!%%%?!?%%?!!!%!%!%!!!%!!!!!!?%%%%%%!%?%!!%!%!%%!!%!%!?%!%%%!%!!?!?%!!%?!!%%%%%?%%%?%!!%!%!!!!%!%?%%%?!%%%%%?!%!?%%%%%%?%!!!!%!%%!!!%%%?%?%??%!!%%!!%%%!!?%%!%%%!?!!?%%!%%?!%%%%%%%%%!%%%?!%!%!!%?%?!!%??%%%%?%!%!%%%!%!!%%%!!%!%!!%%%!!!!%%??%%%!%%?%!%?!!!!!!%!!?!!?????%!%%!?%!!%!?%!%?!!%!%?!%%%%?%?%!?%!???%!%%%!%%?!%!!%%?!%!!%!%%%%!%!!%%%!?!%%%%?%!!!!%!%%!%%%!%!%%!%%%!%%!!!%!!%%%%%%!%!%%%%%%%%%%%%%%%!!!%?!!%!%?%!!%??%?%!%?%!%%%!%%%%??!%!??%%%!%%%!!%%%?%%%%!%!!!%%%%!?!!%?%!%%?!!%!%?%%%?%!!?!?!?!%?%%%???%%!!%%!%??%???!?%%%%%!?!!!!%%%?%!%!%?!%%%!%%!%%!?!!%!%!%!!%%!?!?!%%!!!!!!!!%?%!!%%!!%!!!%%!!%!!?!%%%%!%%!%!!!%!%!%%%%!!!%%%%!!%%!?!!!%!??!%%!%%%!!%%?!%!%?%%!!!!%?%!%%?!!!!%!%%%??!%%%%!!%!%%%%??%!!%%%%%!%?%%?%%%!?%!!!!!%%%%?%?%%!%%!!%%!!!!!%%!!%%%%%%!!!%%?%?%!%!!%%!%%%%%%!%!%!%%%%?!%?%!%%!%!!%?%%!%??%!?!%!!!!%!!%!%%%%?!%%%%!??%!%%%%!%!!%!%!?%!??%%%!%%?%%!?%%?%!%?%!!!%%!%%!??!!!%?%%!!!!!!%!%?!!%%%%%!!!%???%!%%!%%%%%!%%!!!%!%%%%?%!%%%?%%%??!!%!?%%%!?%%?%%%!%%%%!%%!?!%!%%!%?%!!%!%%?%!!!%!%??!!?!!%?!%!%!%!%!%%%%!??%!!?%%%??%%%!%%!%%?%%?%%%!%%!%??%!%%!%%%!%?%%?%%%?%%%%%!%%%!%!!%??%%%!!%%!%!%?!!%%%%%!?!?!!%%!!%%?!!%%%??%!?%?%!!%?%?%%%%!?%!%%!%%?%?!!%%!?%!%%?!%%%!?!!%%%%?%!%%%%!?!!!?!?%%!!!%%!%?%%?%!!!?!!!%%%!%%?%?%%?!!!?!%%%!?%!!!%?!%%%%%%?%!%!%!?%%?%!%!%%%?!!%%%!!?!%%%!%%!%%?!%%%???%%%!%%!%!%!%%%%?!%%!?!?!!?!?%?%!%!%%%%?%%!!%%!!%?!!??%%%%%!!!%!%%%!%?%!?%%%??%%%!!!?%%%%!!?%??%!%%!?%?!!%!%%!%!%?!%%!%?!?%%?%%?!%!%!%%!%%%%%%!%%!%!%?!%???!!?!%%!%??%%!!%!%!??%!%!!%!?!!%%%%%?!%%!%?%%!%!!%%%%%%%%%!%%!%%%!%%%?%?%!!!!!!?!%!%!%!?%!!?%!%%!?%!!!%!%??%%%%%%%!%?%%%!?%!%!%!!%!%%!%%%?!!%%!!?%%%%%%!?%!?!?!?%%!%%!?!%!!??%%!%%!%?!%?!!!!%%%!%!!%?%%!?%%!!%%!!!?%%!!%!!!?!%%?%!%!??!%%%%?%%%%%!%?%!??%!%!%?%%%!%%!!!%%?%!?!!%!!?%!!!%?%?%!?%%%%!%%%!!%!!!!%!??%!%?!?%?%!%!%!%%!%?!!%?%%!%%!!%!????%??%!!!!!!!?%?%%?%?!!!%%%!%%!!??%%%!!%!%!!!?!!?%%%%%%%?!?%!!?%%%%!!!%%%?!!%!!%%!?%!%!%%%%!%!!!?%%%%!%!!%!!!%%%%%!!!%???%%!%!!%%?%%?%!%%??%%%%%!%?!?!%%%!%%?%?%%?%%%!%?!?!!!?%%%!!%!!%%!??%%%!?%%!%%!!%!?%%!??!%!%!%%!%!!!?%%%!%%??!%%%?!!!%%%!%?%!!!!%!%%%%%!?!%%%!%!!!?%!?%%!%%%!%?!!%?!!!!%%%!?!%%?!%?!%%!%!%%%%%%%!!%?%%!?%!%!%%%%!!%%!%%!%%%%%%%%%%%!%%?!!!!?%%?%%!%%%!??!!!%!!%!!!?%%%?%??%!!%??%%%???%!!%%!?!!%%%%?%!!%%?!%!?%%%?!!%%%!%%!?!%%%%?%!%!!!%!%%%?!!!%%%%!?!%!%!%%%%?%%%!%?%%??%%!!%%!!?!?%!?%%%!!%!!!!?%?%?%?!%%%!!??!%??%?%!?%!%!!??%%%%!%!%%!%%!?%%!??!?!!%%%!?%??%!!!!%?%?%!%%!%%%?%%!!?%!?%%!!%?%!%!!!%%!%?!!?%%%%?!?!?%!!?!!??!%!%?!!%%?%!%!%%%%%%!!!!%!%!%%%!??%?!%!!%%??!%%!%%??!%?%%%%%!%%!%!!?%?%!%!!!%?!??!%!??!%%??%%!!!!%%%%!?!%!!%%%!%%%?!%!%!!%%!!!!%%%??!%!!?%%?%%%?!%%%%%??!%%%%%%?%%%%!%%%?!%!?%%%%%!%!!!!?%?%%%%?%!%!%%?!%!!%!%%%%!%%%%!!%!!%!!!!!?%!?%%!?%%%?%%!%!%!%%!%%%!%?%!%%!%%!!%!?%%%!??!%%%%!?%%!%!%!%!%%!?!!%%!%??!%%!%??%%%?%!!!%???%%%%!%!%?%!%!%!%%%%!%??!!?%!%!%?!%%?!%%!?!!!!??%%!!?%%!!?%%%!!?%%!%%%%%%%!!!!%%?%%%%%!%?!!%?%%%%?!?!?!%!!!%%?!%%%%?!%%!!?!?!%%!%%%?%%%%!!?%%%!!%!%!%%%%?!%!?!%%!%%%%%!!%??!!%?%?%?%?%?%!?%?%%?%%%!%?%%?%%!%%%!!%%!!?!?%%%%!!%%!!%!%%?%?!%%?%%!%%!!%%%%!!%!%%%???%!%%%?%!%!%%%?!%?!%?!%%%%!!%%?!%?%%!%%?%!%%?%!%%!?%!?%%%!!!??%%?%%%%%!%%?%?!%%!!%%%%??!%%!!?%%%!%?!!%!!?!!!%?%%%!%%%!%!%!!%%?%%!!!%!%%%?!%%%?%?%%!%!!%!%!?%%%%!%%!%!%%?%!%!%!%%?%%!%!%?%!%%!%!%?%%?%%!?!%%!%!!%!!%?%%?%?%?%%??!%?%!%?!%%!%!!!%!!!%%!%%%!%?!?%!!%%?%%!%?!!%%!%%%%!%%!??%!!!!%!!%%%%%%!?%%!%?!??!!!!!%%%%?%!!%%%%?%!%%%%%!%?%?%!%?%%?%?%%!%%!!?!?%?%%%%%!!!!%!%%!!!%??!!!?%!!!!%%?!%!%!%!!%%!%!%%?!%?!%?!%%%%%%!%!%!%?!!?%!%%?%%!%%!?%%%%?%!%!%!%%!%!%!?!%?%%%!!?!%%!!!?%?%?%%%%%%%!%%%!%!%%?!!%!%?%%%!!%%%!!%%!!??%!!!?%!%%!?!?%?%%?!!%%?%?%?!%!!??%?%%??%%%%%%!!!%%!%!%!%!%%%%%!!%%!!?!?%!??!%!!?%!%?%%!!!%%%?!%!%?%!%!%!%%!!!?!%?%!??%%?%%??!?%%%???!!%%!!%%!!!%?%!?!!!%!!?%%!%%!!%%%%%%!?!%!%!?%?%%!!?!%%%%!%?%?!!?%%%!%%%%!%?%%%?%?%%%%%?!!%%%!!%%!%%%%!!!%%%%%%%!!%!!?%?!%%!%?!!%?!!!!!%!!%%?%?!!%!%!!%!%%!%%??%%?!%!!%%%%!!!%?%%?!!!%!%%%%%!%%!!%%%!!%!%!%%!!%%!%?%%%!%?!?%%!!%%?%!%%!!?!%!%%%%%%!%%%%?!%%%%??%!!%%?!%%?%!?!%!!%%%!%??!?!!%%!!?!!?%%%%%?!!%!%%%%%%!!!%%%%!%%%?%!?!%??%!%!!%%!%?!!%%%%!%!%%%!!%%?%?%!!?%%!%?!%%%%%%?%%?%%%%%%!%%%?%!%!%%!%!%!?!%%%%!!!!%%%%!!!%!%%!%!%?%!!%%%??%%%??!%!!%%%%%%%?%!!%%?!%%?%%?%?%%%??%!!%!%!%!%!?%%%%?%!%?%%%%%!??!%%?%%!?%%%?%!%!!%%!???!!%!!%?%%%!!?!%%!%%%!%!%!%?%%?!%%%?%!!%!!!?!!!!%%%!?!%??%%%!%!!%%%%%!?%%!%%%%?%%?!%%!?%!%%%!%%%!?%!!%!?!?%%?!%%!%%!%!%?%!?!???%!?%%%%%!!%?%%%!!%%%!%!!%%?%%!!!%!%!%!%?!%%%?%%?%%%?!?%!%%%!?!?!!!%?!%!!???%%!!?%?!%!%%!%?!%%?%!%%%?!!%!?!%!%%?%%?!%%?%!!%%%!%!!!??%%%!!%?%!!%!%%%%!?%?%!%?%%!!!%!%%!!%%%!%!%!%%!%%!%?!%%%?!%%%%!!%!!%%!%%!%%!!!%%!%%%!%?!%!%%??%%?%%!?!%%%%%%!!?!!%%!%%%!%??%%%%?!%%%?!%%!!%!?%?%!!!!%!%?!?%%%!%!%%%%!%!%!%!%%%!%!?%!!!%?!!!!%!!%?%!!%%?!%%%%%!%?%!!%!%!!??!%!%!%!?!%!?!%?%!%!!%%%%?!?!!%%%%!??!%%%%%!!%?%!?!%!??!%%?%%%%%%!%!?!%%!%%%%%%%%%??!%!%%%%%%%?%??%%?!%!%%%%%%?!!?%%!!%!%??%%%%!?!%!?%%%%%?%!%%!%!!!!%!%%%%%%%?!%!%!%!%%!!%!!!?%!?!!!%!!?%%?%%%%%!%!%!?!!?%%?%%%%?%%%%!!??!%%?%%!%!!%?%!!%%!!!!%%%?!!!%%??%!%!%!?!%?%!%!?!%?%%!%!%!%%%%%??%%?%%%!%!%%!%%!!!!%%%!!%!?%?!%%!?%%%!!%%%?%?%%%%?!!?!!%!?!!%!!%!?%!?!%!%!!!%?%%%%!%%%!%%!%!%?!%%!!!?!%!!%?%!%%!??%?%%?!!%!??!%%!%!%!?%%%%%%%%%!!%%?!!!!%!!!!?%?%!%%%%!%!?%%!!?!!??%!%%%!%!?%%!%!?%!%???!%!!%%%!!?%%!!%!%!%%!%!%%?!!?!%%?%%!!!%?!?%!!!!%?!%!%?!%%%?!?!?!%%?!!!??%%%?%%%%%%%!%!%%?!%!!!!%%%!%!%!%%??%!!??%!%?%!!?%%%%?!%%%%!%%%?%%!%!%!!??!%?!?%?!??%%!!!%%%!!!!%!??!%%??%%?%%%%%?%???%!%!%!%!%?%%?!!%!%%%%%%!!%%%%%!!!!%?%%?!!%!%%%%%!%!%!!!%!%?!%%?%!%%!?%%??%%!?!%!%!%!!?!%!?!%!%%%%%!!%%%%%!!!%!!%!%!??%!!%%%!??%%!!%!%%%?%?!?!%!%!!%!?%?!!%%!%%!%!%?!%?%%%%??%%!%!%!?%!%!%?!%!%!%?%%%??!!!!%!%%%%%?!%%%?!%?%%%!%%!!%!%%%!%??%?!!%%?!%%%?%%%!!%!%%%%!!!!%%?%!%!!%?%!?%?%%!!%?!%?!!%!%!%??%?%!%!%!%%!%%%!!%%!%?%%!%!%%%%!!%%!%%!!??!%!%!%%?%%%!%%%!%%%%%%?!%%!%%%!!?%%%!!?%%?%!%?!?!%%%%%!!%?%!%!!!%?%%%%!%!!!%%%%?!!?%?%?%!%%!!%!!!%?!%!!%!?!%%!?!%%%%?%!%?!?!%%?%%!%%!%!%!%%%????%%?!%%%%?!?%?%%!!%%%!!!%%%%%!%???%%%%!!%%!!%%%%!??%?!%%!!%!%?%%%%%%%!!%!!%%%??%%!%!%%!!?%%%!!??%%%!!!%%?%%%!%%%%!!%!%!!!!?!!%!%%%?!%!!%?%%!!%%!!?%!??!!!%?!%%!%%%%!%%%?%%%!%!%!%%%%%%!!?!!%%!%?!%?!!?%!%?%%%!%?%%!%%%!?!?%!??%%?!?!%%!%!!%%!%??%!%%!!?!!%%!%!!?%!!%!?%!!!!!!%!?%%?%??!!!%?%!%%%!%%?%%%%%%?%??%%!?!!!%%!%?%%%%%!!%!?%%!!??!!%%%?%%%%!%%?%%?!%%!???%%%!%%?%%?%%??!%!!!%%%%!%%%%?%%!%%%??%!%!%%%?%?%!?%%%%%%%%%!%!%%%!%!%!?%%%%!!%%%!!!!%%?!%!!%?%?%!!?%?%!!%%%!!!!!%%%%%%%?%%?!%%%%??%%?!%%%%?%!?!%%%%%%%%!%!!!!!!%!%?!%%%%%!%!%%%%%??!!!?%?!!%%%!%%%!%!???!%?%!%!!%?%!!?%%%%%%%?%!??%%%%%?!!!%%!?!!%!%%!%!%?!%%?%?%%%%%!!%%?%%?%!!!%!!%!%?%!%!%!%!%!!!!?%%%%!%%%!%%%!%%%?!!%!!!%%!%!%?%!!%%!!%%%%%%%%%!!%%%%%%!%%%%%!?%?%%%?!!%%!!%%%%%!%%!!%!%!!!%%%!%%!!!??%!%%!?%!!!%?%!%%%??%!?!%%%!%%%%!!!?!%%!?!!%!%!%%%?%%%%!!%?%%%!%%!?%%!!???!%%%!%!%????!!%%%%%!!??%!%%%%!%%%%%%%?%%%!%%?%%!??%%!!!%%!?%%!!%!%%%%%?!%%%?%%?%%!!%%!%%%!!!!!??%??%??!!%%!!%%%!%%!%%!!!%?%!!!?!??!!!%%%!%!%!%%?!%%%%?%!?!?%!!?%?!%%%?%%?%%!??%?%?%%!%?!!!%!%%%%?!!?%%!%!!%%???%%!?%!!!%%!!!%%!%!!??!!!!!%%?%!??%%%!%?%??%%!!%%%%%?%%!!???!%%%!!%%%!%!%%%%?%%!!%%!%!!%%?!%!?%%!%%%%?!%%!%%!%!!%%??%%!%!%%%!%!%?!%!%%%%!?!!%%!%%!?%%%%!%??!%%%%!!%%?%%%%!?%?%%%!%!?!%!!%%%?!%%%%!%!!!??%%%?!%%!%%%%%%%%%!?%%%%%%!?%!%%!%%!%%!%!%%%?%?%?!%%!%%?%!%%!?!!?!!!%?!%%%%?!%%?%?!?%!%%!!%?%%%!%!?%%%!?%!%%%!%%%%%%!!!%%%%%!%%%%%!%%%%!!%%!%%%!%?!!!%%!%!%%!?%%%%%?%%%??%!%%%%%?%!%!?%!%??%%%!!!%!%%%%%%!%!!?%!%%?%%!!!?%!%!??!!!!?!%%?%!!%!!!%%???%!%?%%?!!%!%%?%%!%%?%!!%%%?!!%%!%??!?%%%!%?!%!!%!%%%!?!!%%?!%?%%??%%%%?%!?!%%!?%%%!!%%%%%??!?%!%?!!?%%%?%?%%!%%?%%%?%!!!%!!%!!%%??!!%!!!!%?%!%%%%!%!%%!%%%?%?%%!%!?!!%!!!?!%%%%?%!%%%%%?!!%%!%%%%%%%%%%%%?%!!%!!?!?%%%%%%%%%%!%?%?%?%!?%%%%!%%??!!?%?%!%%!%!?!?!!%!%!!!%%%%?!%%%!%%!!%!!%?%!%!!?%%%%!%!!??%%%!!??!%!?!!%%?%!%!%!!!?!%%%!%%!?%%???%!!!%!?%%!%?%!%%%!!%%!%%%?????%!%?!?%!?%!%!?%!%%!!!%?!?%!%?!%%?!%%%?%!?%!!!%%%!!!?!!%%!%%%%!%?!%!%%!%?%%%%!?%%%%%!!%!!%?%?%%%%!%?!%%!%%%!!!%%%%%%!%%!???%!??%!%!!!!?%!%!%!%!?%?%!!%!!%!%%!%%!%!%%%!!%%!!%%%%!?%%?!%%?%%%%?%?!%!%%!%%%!%%%?%!!?%!%%%%%!!%%!%!%%!%!%!%%%%%!!!%%%%!?%!%!!?%%%!!!?%%!!!!?%!!!!?%%%!%%?%%%%%!?%?!%?%!!?%%?%%?%%%%?!%!%!%%%!?!!%!!%%%?%%%%!?%%%%!??%%%%%%%%%%%?!!%%%!%?%!%%!%%%%%%%?!??%!!%!!!!%!!?%%%%!%%!!%!!!%?%%%%%!%?!!!!%%!%%%%!!!%%%!!%!!?%?%!%%%%%%?%?%%%!%?%!%!?!%!?!%%%!%%!!%%%%!%??!?!%!%%%?!!!%%%%%!?!%!?%!%%?!%%?!!!?!?%?!%%!?%!%%!%?!?%??%%?%%%?!%%!!!!%!!%!!%%%%%!%%!???!%%%!?%%!!!!%!%%!%%?!%!%?%??%!%!%!%!?%%%!!%!!!%!?!%!%%%%%%!!!!%%??!!!!%%!%%!%?%!!!???%%?%!%%%!?%!%%?!%%?%!!%%%%!!!%!%!%%!!?%%%%%!!%!%?!%%%!!%!%!%!!%%!!%%%%%?%!!?!!?%!!%!%!%!%!%!!%%!!%%?!%?!%!%%%?%!%?!%%!%%??!%%!%!%!!??%%!?%!%!!!%?!!%%%!%?!%%%!!%%%%%!?!!%!%!?!%%%!!%?%?!%!!!%?%!%?!%??%%%%!!%!!%?!%%%%%%%%??%%%%%%!%%?!!?%!%!%%??%!%%!!%!%??%!?%!?%%!%%%%?!%%!?%?%!!%!!???%?!%!!!!!%??%!%!%?!%!?!%!!%%?!?!%!!!%??!!!!%%?%?%%%?%!?%%%!%%?%%?!%%!%%!%!?!%%!!?!!!%%%%%!%%!%?%%%!!!%!!%%%!!!!%?%%%%%!?!!%?%!!!!%%?!%?!!!!%?%?!?!%%%!?%!%?%!%%!!%%%!!%%!!?!?!??!%?%??!%%%%!!!%!??%!%!%!%%?%!?%!%%%%%%%??%%%!!%%!?!%?%%%%%???!%%??!%%!?%%?!%%!?%%???%!%!%%%?!%%%!%!%!%!%%?!?!%%!!%%?%!%%!?!%!!%!%%?%!%!!%!!%%?%%!%!%?!?%!?%%%%!!!!!!!%%!%!!!!?%!!!%%!?!%!!%%!%%%%!%%%%!!%%!!!!%%%%%%%?%?%!%!%!%%!%?!?!!?%!??%%?!?%%%?%!%!!!%%!!%!%!?!%!%%%%!%%%?%!%?%!%!!%?%%??%%%??%%%%?%??!%%!%!!!!%!%?!!!?!!!%?!?!%%%?!!%!!!%%!???!%%%%!!?%%!%!%%!?%???!!!?%?%?%??%%!%%?%?!??%!%!%%%!!%%?%?%?!!%!?%%%?%%%!!?!!!%!%???%?!!??!%!!!%!!?%%!%!%%!!??!??%%?%!!%?%%!%!%%%!!!%%%%!!!!?!%%!%%!!!?!!%%%%!??%%%?!%%%%%%%%%%%?!?%?%?%!!!?%!!%!!%%?%%%?%!!%%%?!%%!!%!%?%!%%%?!%!!!!%!!%%%!%%%?!%%%%!!!%?!%%?!!?%%!!!?!!!!?%?!%!%!%!!!?%!!!%%%!%!?%??%%%?!%?!%%%!%!?!%?!!!%!%%!?!!!%!!%!%!!?!??%%!!%%!%%%?!%%%??!!%!%%%%!%!??!%?!%%!?%%%%?%!!?%!%%!?%%!%!%%!!?%?!!!%%?%!%%!%!%%%?!!%!!?%%!%?%%%!%!!!%!%???!%!%!%%%?!%%?!!%%%%?%%%%%!%%!%!!%%!%?!!!%?%%!!%%!?%??!%!%!!%!%%%??%!?%%%!%!!%%!?!%!%%?%%!%?%?%!%!!%%!!?!%!%!?!%!%%??!!!%?%!?!?%?%!!?!%!%???%!!%%%%!!%?!!%%%%?%!!!!%!?!!%???%?%!!!!?!!?!?!%?!?%??!%%%!%%%%%?%!!!%!%!%!!%!%%%%!?!!?%%%?!%%%%!??%%%%?!?%!%%!!%!%??!%%%%?%%!?!!!%%%%!?!!?%!!!%?%???!%!!!%!?%%%?%!%??%%!%!!%%%%%%?%!!!%!!?%%%!!%?!?%%%%!!!!%%!%%!%!!%!%%%?%?%%%!%%%?%?!!?!?%%%!%%%!!%!!??!!%!%?%%%!%%!!!?!%?%%!!!!?!%%!??%%!!%%!%!%%!%%!%!%%!??%%%!!%!?%?%!%%%!!!%??!!%%!!!!!%!%?%!?%!!!%%%%?%%%?!?!!!%%%%!!!!!%%!!%%%%!?%!%%!!!?!?!!??%!%%?%!?%%%!!?%!!%?%!%!%!?%!%!%%%?!%!%%%!%%?%!!!%%?!!%!!%%%%?!%%%!?%%%?!%%%%?%?!?%%?%??%%?%!!?%%??%%?%!!%!%%!!%%%!!%!%!??!!!%%!%!?!%%%%%!!%%%!!!!%%!!!%?%%%%%%%%%!!!%%?!%%%!!%?%!%%%!??!?%%%!%?%%%!%%%!%?%?%!!%!!%!%%%%!%!%%!!%%%?%%?%!!!%%!!?!%!?%%!!?!%!!%!%%%?!%!%!%%?%%!!%%!%!%?!!%%%%!%%%%%%!%!??%?%!%!?%?%%!!?%!!!?%%%%%!?!!%%%!!!!%%%%!%?%!%%!%??%%%%%%%?!%%!!%%%%%%%?!%%%!??%?!!!%!%?%?!%%?%%%%!%%%?%?%!!%?%!%%%!%!?!!%%%!%%%!!%!%!!!%%%%%!??!!!%%?%!!!?!!%%%%%%%!!!%!?%?%!!!!%!!%%%!!!!?!%!%%?%?%%%?!!?!%%?%%%%??%!%!!%%?%%?%%%!!!%%!!!!%!%%%?%!%!%%??%?%?!!!%!%%%!%!!%?!%!!!!%!!!!!?%!%?%!!%!%%!!%?!%?%%%??%%%%!??%!!%%!%!!!!%%%!!!?%!?!!!%!%?%!%!%!%?%%%?!%?!%%!!!%!!?!!!%!?!%!?!!!?!%!%%?%%?%!%%?%%%?!!!%!%!%%!%%!!!?%%!%?!!%!!!!?%!%%%%%%!!!%%%!!!!%%%?!!!?%%%?%?%?%!%!%!%!%?%!%%%!%%%%!%%%%??%%?!%%%%?%%%!!!%!%%!?%?%!%%%%%%%!%?%!%!%%%%%%!%?!?%!!%%?%%?%%!%%%?%??%%??????%!!%%!%%%!!!%%%?%%!%%!%%%!%%%%!!%?%%%%%%!%?%%%%%%%%!!?!!!!!?%!!%?!!!?%%!%!??!!%%?%!?%!?%!%%?!!%%%!%%%%!%%?%%%%!?%%!%!%%!%!!!!%??%!%%!!?%%!!%!!%%?!%!%???%%!%!%???%%?%?%%%!?%?%%!%%!?%%!?%!!!!%?!!%!!%%?%%!%!???!%!%%?!?%%%!?%%!!%?%%%%%!!?%?%%?%%%?!%%%%%%!%!!%!!?%%!%%%%!%?%%%%!!?%%!%%%%!%!%%!%%%%%%?!!%%%?!%!%?%%!!?%!!!!%%%%%?!%%?!?%!%!!%%!!!%%%!%%?!!?!%!!%??%!?!%?%%!?!?%%?%%?%?!%!??%?%%!%%%%!%%%%!!!?!%%!!!%%%?%!!!!%!%%%?%%%!!%%%%?!!%%?%!%%%!!%%!%?%?!%%%?!%!!%!?!!!%!!!?!%%%?%!?!%%%%%%?%%%?%%??%!%!!%!%%!%!!!!%%!!%%%!%?%%!%!%!%!!!?%!?%!%!!!?!%%!%?!!?!%?!!%%%!%%%!%%%!!!%%%!%%%%%%?!???%%!!%!?!!%?!%%%%!!%?%%%!%!!!%%!%?%!!?!!!!%!!%%%!!!%%%!!%!!!%%%%!%%%!?%%%%!?%!!?!!!%%%%%?%!%!%%%%%%%%%%%?!%%!?!%??%!%%%!!?%%?%?%!?!?%%%%!?!%!??!%!??!!%%!?%!!!!%!!?%!!!%%!?!%!%!?!%!!!!%%%%%%%%!!%?!%??!!??!%!!%!%%%%!%%?%!!%?%!%%%%!!%?%!%%!?!%%!!!%%!%!%?%%!%!?%%%!?%!?%%%%!!!?%!!!!!%%%?!?%%%%!!!!%!!%%%!%!%%%?!%!!?!%%!?!%%%%!%%%%!?%!!?!%%!%?!%%!??!!!%%!%%%%!%!!?!?%?%?!%?%!!%%!!!%%%%!%!!%%%?%!%!%!?%!?!%%!%!?!%!?!!?!%!%%?!!!%!%%%!%!!!?%?%%!!%%%!%%!!!?%??%%%%!%%%!%%!%!%!%%!!???%!?!%%%??!?%!!%%%%%?!%!%%!?!%!!!%%%!!%!%?%!!%?%%?!%!!?%!!!%!%!!%!%!%?%!!!%!?!??%?%%%%%%!%%%?!%!%!?%%????!!%%%!%!!%?!%%!!!!%?!%%%!!%%!!%?%!!%%%%!!%%!!!?%%!%!%!%!%%?%?%!!%?%!!%%?%?!%!%!%!?!%%%?%%!!!%!%!?!%!?!%?!%!%!%???%%?%?%%?%?%?!%%%!%!%%%%%!%%??%??!%!!?%%%!%!%%!?%%!!%!?%%%%%%%%%%?%%?%!?%%!%%%?!%!%!?!?!%%%?%!!%%%??!!%?%?%%??%?%%%!%%%?%%??%?%%%%%%%%?!?%!%!%??%%!%?!%!%%%!!%%%!!!%%%%%!%%?%%!%!%%!!!%%!???!!%!?%!%!!!!%?%%!?!%!%!!?!!!%!%!%?!!?!!%!!%???%?!%%%?%%?%!!!%%?%!!%%?%%!?!?%!!?!!%!?%%%%%%??!!%?%!?!%!%%!?%!%!%%!?!%%?%%!%?%?!!%%%%??!%%%!!!!?!%!%!!?!%%!%%%%!!%!?%%%!%%!%%%%?%%%%!!?!?!?%!%%%!%!%%??!%?!%!?%%%%%%?!!!%?%%%!%!%%%%!?%%??%%!%%!?%!%?!!%%!!%!%%!!?%%%%!!!%%%?!?!%%%%%%%?!!?!!%!%%!%%%%!%!?!%%%?!%!%!!%!%%%!%%%!%%%%%%?%%%%%!?%??!%%?!!%%%%%%%%%%%?!!!!!%%!!?%%%%!!!!%%%?%%%!!!!!%!!%%%%%!!%%%!!%%%%%%%?%%%!%?%??%%%%%%!!!?%%!!%%!!!%%%%???%!!%%!%!%!%!???%%!??!%%%!!?!!?%??%%%%!%%!%!%%%!%%?!!!!%%?!!?%?%%%?%!%%!%??%!!%%!!%%%%!%%!!!!!%%!!!%!%!!%?%%?%%?!%?%%%%??!%%!%!?%!%!?!!%?%%!!??!%!%!%!%!%%%!%%!%!%?%!%?!!!%%%%%%%%!?%%!%?%!%!%!!%%!?!!!%!%%!!?!%!%%!!%!%!%??%!%?!%%?%%%%%!%%!!%!!%%%!?%%!%%!!%%!!%!!%%!!%%%%%!?%!%!%?%%!%!%%!%!%%%%%%%!%!!!%%??%%%%%!!%?%!!%%?%%%%!%!??%!%!%%%????%?!%?%%%%!%%?!!%%%!!%!!%!%%%%%%%?!%!?%%!%!!!%?%%%%!%?!?!!%%!%!%%%!?%%%?%%!%%!%%%!???%?!%%!%!?!%!!!%?%!!!%?!?%!!!%?!!!!!!?!?%%!%%%%%?%!%!?%%%!!??%!%%!%%%!%%%!?!%%%%%%!%%!?%!%!?%!!%!%!%!%%!%!!%!%!%!!%%%%!?%?!!%%?%%!%%%?%!%%!!?!!%%!%!!%!??%?!!!!%!%!%!!%!%!!!%!!%%%%%!%%?%!?!!%%%!%!%%!%!%%%%%%!%%?%!%!%%!%%%%!!%%!??%!%!?%%!%!%!%%%?!??!%!%?!!%%!?!%%!!%!%!!!%!!!!!!%?!%!!%%%!!%%!!%%!%%%!!%%%?!%!?!%%?!?%%%%%%%!!%%%!%%!!?%%??!%?%!%%%%?%!%??%%%!%%!!%%!?!!!%!?%??%?%%%%!%??%!!%%%!%%?!!%!%!!!%!%?%%??%?!!%!%!??!%%%!%%!%!!!%%%%!%%%!%?!?!!%%!%%!!%%%%%%!??%?%!%!?!%?%!!%%?%%%%%?!%!!%%%!!%%?!!%%??%%%%!?!%?%%%?%%!%!%?!%%?%%!%%%%%%!!%?????!%!%%!%!!!%!%!!?%%%%!%?%?%!!%!!?!!!!%%%?%??!%%%!!?%!!?%%!%!!!!!?!!%%%!%!!%%!%?%%?!%!!%?%%%%%%?%%??%%%??!%%?%!!%!%!??%%%%%%?!!!%!%?%%!%!!%%%?!%%%!%?!!%%%%%%!%%!?%?%%%!%%?%!!!%%!%?!%?%!?%%%%%%!?%%??%!?%%!%!%%%%!%????!!!%%%!%?%?%%!??!?!%?!%%??%!!!%!!?%?!%%%??!?!!%%%??%!!%%%?%!%!!%%%!%!!?%%%!%%%%%%%%!!%%!?%!%%!%!%%!!!??!%!??%%%!%!%!%%%%!%%%!%!?!%!!%%%%%!%!?%!?%%%%%%%%!?!?%%!%!!?!!!%?!%!%%!?!%!?!%%%!%%!??%!!?!%!!!%%%!?%?!!!%!%%?!%%!%%!!%?!%%!%!?%?%%%!!?!!%%%%%%%!%%%!%!%%!!?%!!!?!!!%!!%!?!?%%%%%?%%?%%!%%%%!?%?%%?%%%!!%!?%%!%?%??!%!?!!!!!!%!%%%%!!%%!!!!!%%!!%!%!%%????%%?!!!!!%?%%%%!%?!%!?%%%??!!?!%?!!%%%%??!%%?%%?!!?%%%%!%%%!!%%?%%!!!%!%!!%%%?%!%%!%%%%%!%!!!%!!%%%%%?%!!?%!!!?!!!%?%%!%?!!%%%%%!!!%?%%%?!?!!%!?!%!%%?%!%!%%??%%%!!!%%?%!!%%!%!%?%%!%%%!%%%!!%%!%!%?%???!!%??%?!!?%%%%%%!%??%!??!!?!!!!!?%%%!?%?%!%!%%!%%%!!%%!%!?%%%!!!%!%%!!%!%%!?%%%!%??!!%%%%%!%?%%??%?!%?%!!!??%!!%!%!%!%%%%%%%%%%%?!%!!%%%%?%%%?!%%%%%!!%%!%%?%%?!??%?!%??%!%?!!!!!?%!!%!!?!?!%!!??!%!!?%%?%!%!!%!?%!%?%!%%!%%%!%%%%%!%%!!%!!%!%%!%!%!!!%%%%%%?%!?%??%%%!!%!%%%!%%!%%?%%%!%%%!!%%%??%%!%!!%!%%!%!?!%%!%%?%%?!!%%!%%?!%%%!!%!!!!?!%?%%?%?%!%%?!!!%%%!!%%%!!%%!%%?!!%!?!?!!?%?!%!%!!?%%!%%%%%??!!%!!%?%%?!%%?%%?%%!%!%?%?!!%%%%%%!%?!!?%%%?!%!!???%%!!!%%%%???!!?!!!%%%?%%!!%!%!!%!!%%!?!!!!!!?%!%%%%!!%%!!%?%!!%%?%??%!?%!!%%%!%%%%%?!%?%%!%!%%!!%!!%!!!%%%%!?!%?%%!!!?!?%%?%?!%%!%%%?!?%%%%!?!%%%%%%?!?!!?%%%%???%%!%%%%%%!!!!?%!!!%%!!!%?%%??!%??%%!%!!!%?!?!%?%!%!!%!%%?%!%%%%!!%?%!!%!!!%?%!%!?%%?%!!%%!%?%!%!??%?!%?%?%%!%!!%%%%!%!%!%%!%%%%%?%%!%%?%!!!?%!!%?%%!%%%!?!%%!%%%?%!%%!%%??%!%%!%%!!%%%?!%?!%%%%?%?%%%%!%%??%%!%!%!%%%!%%?!??%%?!!?!!!%%%!!!?!!%%%%?%%?%%!%!!%%%%%!?%?%%%!!%%%!?!%!%%!%?!%%!%?%%!?!?%!%%?!%%???!%%%?%!%!!!%%%!!%!?!!%%%%%!%?%%%%?%%!!!%%%%!!%!%?%?%%!%%!%?%?%!!%!!%!!%%!%%?!%?!%!%?!%!%??%??%!!!!%?%!!%%!!%%??!?%%?!?!!%!!%!%!!!!%!%!!!!%?%?%?%%!%%!?!%%%!??!!%%%?!%!%!!?!%%%%%%!!%%%?%%!%%%%!%?%!?%!!%!?!%%!%!!%??%%!%%?!!!!%%!%%%!%!!?%?!%!?!!!!?!%%%!%%!%!%?%?%?!%!!!!%!%!%%%?%!%??!!%!!%!?%!%%%%!%%%!%!%!%%!!!?%?%!!!%%%?!%%?%%%%%%!!%!%%%!??%?!!%!!!?%!!?%?%%%!!?!%%%%!%%?%%?%%%?%%%!%?!!!!%%%%?!%??%%%!?!%%%??%%!!%%%!!!%%%%%%%%!!?%%!!!!!!!%!%%%?!!%!%%!%!%!%!%!!!!!!?%!!%?%?%%%?%%!%?%%?%%!?%!?!%!%?%%??%!!%%?%!!%%!!%%!%!%%%!%!%!!%!%!%!%?!%!%%%!?%%%?!%%%%%%??!!%%%%%?%!?%%%%?%!%!%%%!!!%!!???!?%!%%%%%%%?%???%!%%!%!%%!!%%!!!!%??!%?!%%?!!?!%!%!!??%!!??!%%%%%%!!!%!?!!?%%%%%%!!%%!%%%!!?!!!?%%!??%?%?%%%!%%!!!??%!%!%%!!??!%!?!%%!!%!!!%%!!?%!?!%!!%!%!??!!%%!%!!!!%%!!!%!!!!!%!%!!?%!!!?!%!!?!?%!?!%!!%%%!?%%%?%%%%%%%!!%!!??%%%?%%!?!!?!!%!??!%%!!?%!%%%%%!!??!?!%!%!%!!!%?!%?!?!!%%%%?!!!!%%?%%!%%!%%%!%%%%%!?!!!?!!%%!%%!%%%!!!%%!??%%??%!%!!%?%!%%%!%%%%?%%?%%?!%%%!!%!!!??%?!%%?!%%%%!%!%!!%??%!!!?%!!!!%?%%!%!?%%%%?%!%?!!!%!%!!%%?%%%!%!%%?%%?!!%%?!%!!%!!??%!%%!!%?!%?%%%%!%%%!%?!%%%!!%!?%!?!!!%%!%%!%!%!%%!%%!%??!%!%%%!!%?%%%!%%!%!%??!%%%%%%%%%%?!%!!%!%%!%%!!%!?!!%%%%?%!?%?%!!!%?!%?%%!!%%!!%?%%%%!%%%%%%%!%%?%!?!?%?%!%%?%!%!?%!%%%%%%!?%%%%%%%%%%%%%%%%!!!%!%!??%!!?%%!%%!%!!!!%%!?%!%%!%!%??!?%%%%%%%?%!!%%!?%%%%%??%?%??%!%%%!%!!%!!!%%%!%%%?%%%!%%!!%?%!!!%%%?%%%%!!%%!%%!!?%%!%!%!%!!!!!%%%%%?!!?%%%!%!%%!%%!!%%%%!%?%!%%!?%?%%%%!%?!!?%%%!%%%%?%??!?%%!!%??%%!%%%%%%%!?!%%%%??!!!%%%!?%!%%%!?!%%%%%!!%%%??%%!%%!%%!!!!%?!%!!%!%?%%!%!!%%%%%%%!!%%?!?%%!%!!%!?%%!%?%%!%!!%!%%%!??%%%%!?!%!%?!?!%?%??!%?!!!%!!%?!!%%%%?!%%!!!%!%?!%!%%!???%!%?%!%?%!!!%!%%%!%!%%%%%%!!!?!%!%?%%%%!?%!%!?%%!?!?!!%%!!!!!%%!!%%%!?%!??!!%!%%%%%%!%%?!!%%%!%%%!?%%%!?%!!%%!%%?!%%!?%%!%!%%%?!%%!%??!!?!!%?%%?%!!%%%!%?!%!?!!!%%?!????%!!?%%%!%%?!?%%%%%!!!%!?%%!?!?%%!!!?!!?%%%%%%!%%%?%!?!!!%!%%%!!?%!?%!%??%%?!!%!?%!!?!%%%%!!!%?!%!!!?%?%%!%%!%?!?%!%!??!%%!%!%%!?%!?%%%!?!!??!!!%%%%%!%!!%?!?%!!%%%%??!%%!!?!%%!%!!%%%%??!!%!%%%!%!!??!?%%!!%!%!%!?%?!%%%%%??%%!%?%%!?!%!!?%%%%?!%!!%!!!%%%%?%!!%%%?%!%%!%%?!%!%!%?%!%%%!!!!%?%!%!%!%!%?%!%%??%?!%%?!%%%%%?!?!?%%!?%???!!%%!?!%%%!!%%!%!%!%%%!%%!%%!?%%%?!!%!%%?!!%!%?!%%%%%%%%%%!%!%!%%!%%%!%%?!%%?%!%%%%%%%%%%%%!!!%!!?!!%!!?%?%%%?!?%!?%%%%%%%%%%%?!?%?%%?!!!!!%%!!%%%%%?%%%%?%%?!!!%%%!??%!%!%!%!!?!!!!%?!!!%?%?%!?%!%%!%%!%!%!!%%%?%%%!%%%!!%%%%!%%?%!%%?%%!%!%%!%%!!%??%%%!??%??%%!!!!!!%%%%%!%???%!%!%%!%%!?%??%%?!!%!?!?%%%!!!%%%%!!!%%!?%?!!%%!%%?!!??!%%!!%!%!!%%%%!!!!%%!?%!!%?%?!!!%!%%!%%%%!!!!?!%!!%!!%%?%!%%%!!!!??!%%%?%?%%%?%%!%?!?%?%?%!!?!!?%%!%%!?!%!?%%?!%?%%!!%!!!%%%!%!%%%!!%%?%!%!%%%%%!%%!%!%%!%?!?!%!!%%%?%%!!!%%?!%!%?%%%!?!!%%!!%%%%%%%%!%!?%%%!%!%!?!%!?%?!!!!?%%%%%%%!!%?%%%%??!%%%?%%?!%%%%?%!?!!%%%?%?!?%!?%!!!!%%!%!%!%%%%%%%?%!%%%!!!!%!%?!%%?%%?!!%%%?%%!%%%%%!%%%?%%?%%?%%%%%%%%%!?%?!%%?%!%!!%?%%???%!!?%!!?%%!%%%%?!%%%%%%%%%!?%%%%%%?%%%%%!??%%!%?!!!?%?!%%%!!!!!?%!!%!??%%??%%!%%!!!!%!!%!%%!!!%%%!!%!%%?!!%%%%!!%?%?%!!!%?!!%????!!!!%%%%%!%!%%%!%%??%%%?!??!!%!%!!%%%%!!!?%%%!?%!%!%!!!!%%%!%!!!?%%!!%!%%%%!%!??%!%%%!?%!%%%!?%?%!%%%%%%%!!%!%%%%!!!%!%!!%%%%%!%%!??!%?%!??%!%?%!??!%%%?!%?!???%%!!?!?%%%!%%%%%%%%%!%!%!?%%%%!%%!%?%?%%??!%!!%???!%%%?!%?%%%%%!!!???%?%?%!!!??!%%?!?%!%!??!!%%??%?%!%%%%%%%!%%?!%%%%!%%%%!%%!!?!%%!%?%%??!%!%%!%!!?%!%%%%%!%!%?%?%!%%%%%!%%%!%!%%%!!%%%%!%!%%%%!%!?%%%??%%!%%?%!%%!?%!!!%%?%%%??!%!%%!!!%?%??%%%??!%!!?%%?!?!!%%?%%!%!?%%%%%!!!%!!%!!%!!!%%%%!!??%!??%??%%!!%!!!?!%!%!%%%%!%%%!%%%!!%%%!!%?%%%%!%%%%%%?%%%!?%%?%%?%%%!%?%?!!%%!%!%%!%%!?!%%?!%!!!%%!%?%?%!!?%!?%!?!!!%%!?%?%!%!!?!!%!%%!!%!?!%!%!?!!!%!!%!%!?%?!!!!!%!%%!%%??!?%%!!%%%?%?%%!%%!%!!%%?%%?!%%!%%%%?!!%!%%%%?!%!!%?%%%!%!!%%%!!%%%?%!%!?%%!?!!%!!!?%??!%%%!%%!!%%!!!%%%?%%?%%!%!?%%!?!??%%%%!??%!%!!?!!!%%%%%%!%%%%%?!%!%%??!!%%!!%!%!%%!!!?%%!?!%%!%%?%%%%%%!?!%%!!?%!%%%%%?!%!%?!%!?%!%?!%!%%?!!%!%!%?!%%%!%%%!!%%%!%%?%!!?%%!!%!%!%%!?%%%%?%!?%!!%?!!!%%%!%%!%!%%%!%!!%%!%!!%!%%%%!!%%!%!!??%??%!%%!!%%%%!%!%%%%%!!?%%!!%%%!!!!%%?!!?%!%%!%!?%%?%!?%%%%?!!%%%?!%%!%%!!?%!!%%%%%%!%?%%!%?!%%%!!%?!?%%%!?%?!!%%!!??!%?%!!?%?%!%%%%?%!%%%?!%??%!!!?!!!?%?!%!%%!?!%%!!%%!%%%%%?%!!!!!%!?!%!??%???!%%%%%%%%!!!%%!!%!?%!%%%%!%!%!?%%%!??%%?%!!%?!%!!%%%%!!?%%%!!??%!?%%%?%%%%!?!%%!?%!%%%%?%%%%%%!!?%%%!%!!%!%%!%%%!!%??%%%!?%%!!%%!%?!?%!!!!!%%%%!!%%!%%%%%%!%!!%??!%!%?!%?%??%!%%!!!%?!%%!%%!!%!%%%%!!?!?%!?%!%%??%%?!%%!%%%%%%%%%!%%%?%%!!!%?!%%%%?%%%%!!%!%%!!?%%%%%%??%!%%%%%!?%%!%?%%!%%%%!%?%!?!!!!%%%!!%%!%!%%!%!%%%%%%!!%%%?!%%%!%!?%%%%!?%?%%?!??!!!!!!%!%?!%!?%!%!?%%%!!!!!!%!%%!%%%!!?%%!%%!!%%%%%%%!!!?%%%%%?%%%??!!%%%%!%!%!%%%%%!%!%%%?%%!%?%!!!%%!!!!!!%?%%!?%%!??!%!!?%%%!%!!%?%!?!%?!%%%%%!?!!!%!%%%!!!!?%!!%!!!%!%!%%%%%!%%!%?%%%%!?%?%?!?%%%%?%?%!%%!%!!%%%!?%%!%?%%?!!!?%!?!%%%%!%?%!?!!?%%%!%%%!?!????!%!!%%%%!?%%!!!%!%!%%%!!%%%%!%?%%!%!%%!%%!%%!?!!!%%%%%%!%!%%%!??!%%%%%!!!!?!%%??!%!%!%!!?%%!%!!!%%%?!!%?%!%%!?!!?!%%!%%%%!?%%%%!%!%!%!!%%!?!!!%%!!%!!%%!?!?%%??!%%??!%%%%!%!!%?!%?%%%%%%%?!!%?!!%?%!%!%%%%%???!%%%%?!!!%%?%!?%%%!!%%!%!%%%!?%!%%?!%?!%%%!%??!!?%%%?!%%!!?%%%%%!%%!!%??!%!%??!!!!!!%%%%%%%%%?%??%%?%%!!%!!?!!%??!%?%%%?!%%%%?%???%%%%!!?%%%?%%!?%!%%%%%!!!%!%%?%%?%%%!?%%%?!%%??!%%??%%%%%%%%%!%%!%!??%!!%%%!?%%%!%%!%%?%%!?%%!%!%%!%%!%!%%!!%?!%%??!?%%!??%!?!%?!%!!!!%%%%!!!%!%!%!%!%?!%%!!%%%!%?%?%!!??!!!!%!%?!%%%%?!?%%!%!%!%!!%%!!%!!?%%%%%!?!!%?%%?!%%%%?!!%%%%%%?!?%%%!!%%%%%%!!!%!%!!%%!?%!!%%?%!%%!%%%?!?%!?%!%!%?%%%!%!?%?!%!!%%?%%!%?%?%%%?%!!!%!!%?%%%!%!!!%%!%%%?%%?%?!%%%%%!!%%%%%%%%!%!%%%!%%%?%%%%!?%%!%?!!%%%%!%!%!%%%!%%%?!!!%!!!?%%!?%!%!%!!!%!?!?%%%!%?%%%???!!%%%%%%%%%!%?!%!?%!%%%!!!%%?%%%!!%%!%!%%%%!%!%!%%!%!!%%%%%%%%?!!%!%!%!%%%!!!!?%%%%%%?%!?%?!!!!!!%!?%%%!!%%%%!%%?!%%?!?%%!%!!%%!%%?!%!??!?!?%!!%!?!%%!%%%!%?!%%?%%!!!?%%%?%%%%%!?%%%?%%%?!%!!%%%%?%?%!%!%%%?%!!%%!!?%%!%%%%%%!!%!%!!%!!!%!?%%%%%!%!%!%%!?!!?!%?%!!%!!!?!%%!!?!%%%%%?%%%?!!!%!?%!!?!??%%%!!!%?%%%%%%?%!%%!%%%%!%!?!%%!!%!?%%%%!!?%!!?!%%!%!!%?%%?%%%%!!%%%?%%%!%%%%!!?%%!%%!?%!!?%%!%!%%?%!%%%!%%%%!?%???!!?!%%!?%?%!!?%!!%%%%%%%%%?%!??!%%!?%?!%?!??!%%!%%?!?!%!%!%%%?!!%?%!?!%%!%%!!!%!?%%!%?%!!%%%!%%!%%?!!?%%%%%%%%%%%!%%!%%%?%%!!%!%!!!%%%?!%?!!%%%%%!%!%!%?%%%%!%%!!!%%%%%%!!%%%?%%?%!!%%!%%!%%%!%!!%!!%%!!?%!!%%???%%?!%!%%%!!!%%!%!%!%%!!%!!%!?!!%?!%%!%!!!%?!%%!%!%%!%!!??%%%!!%%%%?%?%%%%%%!?%!?%%!!?%?!!%%%%?%?%???!!?%%%%%?%!%?%!!??%!%?!%!%%!%!?%%!%%%%%%!!%%!%!%%%!%%!!%!!!%!!!!%?%%%?%%%?%!!?%%%!%!?%%%!!%%%%!%%%!%%%?!?%%%%%%%!!!%%!!!%%!!!?%???%!%?!?!!!!?%??%?%%?!%%%!?!%??%%%%%%!??!%%%?%%%%%%!%%?%?%!%!%%%?!%%%!?!!%%!?%!%%%?%!!!%!%%%%!%!!!%%%%%%?!!%!?!%%!%%!%!!%?!%?%%!!%%%%?!!%!%!%!!%%%%%%%%!!%!!!?%!?%!%!!!%%%?!%!!%%!%%%%%%?%!?%%%!%?!%%%!%%%%!?%%%%!!%?!%%?!!??!!!%%!!!%!!%!%!!%?%!%!!%%?!!%!?%%!!?!%!?!%!%%???!!?!%?%%!!%%?%!?%%%%!!%?%!%%!??%!%?!%?!%%%%%!??!?!?!!%%%%%?!!%%!%?!?%!%?%?%%!!?%?%!??%%!!!?%%%%??%%?%?!?%%?%%??%%!%!%?%%%%!!%%%!%%!%%!!%!!%?%!%!%%%%%!%%!%%!!!%?%%%%!%%%!%%!%%%%%%???%!!%!%%!%!%%%?%%%%!%!!%!!%%%%!%!%!%!!!%%%%?!%%%!%!%%!%?!%!!!!%%!?%?%?!%!%%%%%%%%%!!%?%!%%%%!!%%???!!%%%!?%!!!%!?!!!!%%?!?%%!!%!%%?!!?%%%%!%!!%!%!%%%%!?%?%?%%!%%%!?!?%!%!!!%!%%?%%%%%!%?%!!%%??%!!!??!%!??%%?%!%??%??%!!%!%!!%%%%!%?!?%%%%!!!!%!%%%%?%!%%%%%!!%?!!!!!%%?%!!!%!!%!?%!%%%!%!%%!!!%%%%!%%?%??%%%%%%%%%%!?!?%?%???!%%!%%?%%!?%!?!%!!%!%!%!?%?%%!%!%%%%%%%?!!!?!!%%%!!!%!!?%!%%!!!?%%%?!%%!%!!!!%?!?%!!!%%%%!!!%%!%!%!!%!%!%!%?%?!%%%%%%?%%!%!%%%%!!%!?%%?%%%%%?%!%%!?!!!?%??!!!%%!%%!!%!!!!!?%!%!%%?!%!%!%!%%!!%?!%!%!%%%?%%!?%!%?%%%%!!!%!!%!!%%%!%%!%%%??%%?%%%%?!!%!%%%%!!%%%%%%!!!%%!!!%%!!%%!??%%?%?%%!!?!%!%%%!%!%%?!%%%!!!%%!%%%?%%?%%?%%!!!?!!%%%%!%?%!?!%!!!!%!%!?%?!%!%%!%?%?!%!!!%%?%%%%%%!%!?!%?!%%!?!!%%?!!%!!!!%%%??%%%?%?%!%?%%%%%!?!%%!?%%%!!!?%%?%!??%%%%%!!%%%%%%%?%%%%!!%%??%???%!%!!%%!%?%?%!%%%?!!%?!?%%%!%!!!!%%%%%?!%%%%?!!!!%%%%%%!!%%%%!%%!%%%%%!%%%!?!%%?!!%%%?%%%!!!%!?!%!?!%%%%%%?%%!?%!%!!?!%%%%%?%!?%!%%%!?%!%!%!?!%%??%!%!?%%%!!????%%!%?%%%%?%??!%!%%!%?!?%%?%?!%!%?%%!%!%%?%!?%!%%?%!!!?!%?%%!%!%%?%%%!%?%!!!?%%?%%!%!%%%%!%%?%?%%%%!??!!!?!%?%?%?%?!!%!%!%??!!!%%%?!??!!%!%!!%!%%!%%!%%!?%%%%!!!!?!%%%%%%?%%?%?%%%%%!%%?%!%%%%%??%%!!?%%!!%%%%?%!?%%%!!!%?%!%%!!!%?%!???%!%%!!?!?!%%%%!%%%%%%!?%!?!%%!%%%%%%%%?!%!%!!?%?!!%!%%%!!%%%?!%%%%%!%!?%!%!%%?!!%%!!!%%?!!???%%%?%?!%!%!???%?%%?%%!%%%%?%!!?%?%%%?%!%%%%?!!!??%%!!?!!!!%!!%!!!!?%%!%%%!%%%!!!!%!!!%!!%%%!%!%!%%%!%!%!%%!%%%%%%!!%!!?!%%%!?%!%!!%?%%%!!%%?%%?%!!!%?%??!%!!%%!%!!%%!!%???!%%!?????%%!?%%!%!%!!?%%%%!?%%!%!!?%!%%!%%%%!%!?!%%!!%%!%!!?!%!%?%%%%%%?%%?!%!%%%%!%%%!%%%%%?%%?!%%!%%%%%!%%?%%%!!!%%%?%%!?!?%?%%?!%%?%?%?%%%??%%%??%%%!!??%!%%%%%%?%??!!%!%%%!%?!%%%%%?%!!%!%%!!%%%%!%%!?%!%%!%!???%!!!%!%%!!??%?%%!?%%%!%%?!%%?%?%%%%!%%?%%%%%!%%!%%%!!!%%!!%%%%!!%%%!!?!%%?%!%%%!%%%?!%%?!%%!%%%%!%!%?!?%!!?!!!!!%%!?%!%%?%%%!%%%%%%!%!!!%!!!!%%%!?%%!!!!!!%!?%!?!%!%%%!!%!%%??!%!!%%%%!!%%!!%!%%!%%!%%!%%?!!%%%%%%%!%!?%!!!%%!!%?%!!!%!?%%!?%?%!%%%!%%%%?%!%%?!!%?!!!%%%!!?%!%!%%!%%%!?!?!!?%%!??!%??!%%%%!?!!%?%!%%?%!%!%%%!!%%?!%%%%%?!!!%!!%%%!!?!%%?%%?!!?%%?!!!?!%??!!??!!%?%%!?%!!!!%%%%%%!%!!%!%%!%?%!?!%!????%%?%%!?%???!%%%!%%%%!?%!%%%%?%!!?!%%!!%!%!%!?%?%?!%%%%!?!%?!?%%%!!%!%!?!??!?!%%%%!!%?%!!%%%%!%!?!%%?%!!!!?!!%%%?!%!!!!!!??!%!??%%!??%?%?!!%!?!%%!%%%?!!%%!%?%%%%%%?%?!%%!!%%!!??!!!!%%!%%%%!??!!!???%!%%%%%?!!?%!!%?%%!?%!%!??%%!%%%!!?%!!%%!!?%?%%!!!%%%%??%%%%?%%%!%%!%!?!?%%!!%%!!?%?!!!%!%!%%%%%?!??!?%!%%!!%%%!%%%%!%%%%%!!!!!%?%?%?%%%!%%!!%!%%!!!%?%%!%!%??%!?%!?%!!%%!%%%?%!!%?%%!?!%%!!!!%%?%%%!%!?%!!%!!!?!%%%%%%!%%%!%!%%!!!!%!%%!!!%?!!?!%!!%???!?%!%?!%!!!%?!%%%%?!%!!!%!!%?!%?!!!!!!%%!!!%%%%%%%!%%%?%%%??%!!!%!%!!%!?%%!!!?!!?%!???!!%%!%%%%%%%!!%%%?%!%!%?!%!!%?!%%%%%%!%!!!%%%%%%?!%!%%?!%%%%!!?%!%%%%%?%!?%!%%!??%!%%!!%?%!%%!%!%!%%%!%?%%!?%%%%%!%%%%%%!?%!!%%!!%%%%%%%%?%?%!%%!%%!!%%?%!!!%%!!%%%!%%%%%?!?%%!??!?%!%%%?%%!%%?!?%%!%!!%%!%%!!?!%%%!!!!!%%%%!%%?%%?!!!%!%!%%?!%!?%!??!??!%!?!%%%?!%%?%!%%!!%%%!%?!!!?!%%?%??!!!%%!!%%!%!?%!%!%%!%%!%!%!!%!?%%%!%%!?%?%%%%%%?%!%%%!?%!%%!?%%?%!%%!?!!???%%%%!?%!!?%%%??!%%!!%%?%%?!%?!%%!%!%?%!%%%%%%!?!%%%%?%%%??%%?!%?!!?!!?!?%?!!%!?%!!%%!!%%%%%%%!!%!%%%%%%!%!!%??%%%%%!!%%%!%%%%%%%!?!??!%%!?!!%!!%!!%%%%!%!!!%%%!%%!?%%?!?%%!!%?!%!!?!!%%%?%!?!?!!?%%!%%%!!%%?!!%!%%?%%%%%%?!%!!!!%!?%!%%%!%%?!???!!%!!!!!!%?%!?%!!!%%%%??!%!%%%%%%%!!??%%!!!%%!?!%%%%%!%%%!%%%?%!!%%!!!?!%%!%%!%%%%%%%%%%??!!%%%!%%!?%!%!!%!??%%%%%?!%%!!!%%?%%?%%%!%!%!!%%!%??!%!%?%%%!??!!%%!%?%%?!!!%!?!!%?!!!%%!!%%%?!!?%%?%%%!%%%%!?%!!%!%??%%%%!%!!!%!%%!%?%%?!?!!!!?%?%!?%%!%?!%!%%?%%!!%%!?!??!%%!%?%%%!?!%?%?%!%!%%?!?%%!?%%%%!%!%?%?%?%%%!%%%%!%!%%?%!%!%??%!%%!?!!?%!!!!??%%?!!%?%?%%%!?%!%?!!!%!!!!%?!%%?%%%%!%?%?%!?!?%%?!%%!%!%!%%!?!!!?%%%%%!%%%%%??!%%?!!!!!%?%!%%%%%%%!!!%%%!?%!%%!%?%!%%%%%%%%!?%!??!?%?%!!%%%%%%%!!%%%%!%?%%!%!?%?%%?%%%!?%%%%?%%%!%??%!%%%%%?!!%!!!%?!!?%%!?%!%%!!!%%%!%!%?%!%%?%%!%%?%%%??%?%!%%%%%%%!%???!!%%!!%!%%%%?!%%%%!!%%!%?%!?!??!?!%%!%!!!!!%?%%?!%!?!!%%?!%?!!%!?!%%?!!??%%%!%?%?!!%%%!!%!%!??%%??%?!%!%%%%%%?!%%%!?%??!?%%!%!%%?!!%%%!!?!?%%%%!%?!%%%%?%?!!%!!%!!!%%%!%%!%!!?%?!?%!%!!%!!!?%!%??!!!!%%!%%!%%!%??%!?%%?!!%!%!%%%!%!%??%?%%!?%!!!%!%?%%%!%!%%!%!%%%?!!%!!!%?%%%%%%!%!%%%%%%!%%!!?%%?%%!%!%%%%!%!!%?!%??%%%!%%%!!!!!!%%%%?%%%!%%%!%%??%!%%%??%!%!!%%?!!%%?%%?%!!%%!%%!%%%!%!%%!!!%?%!%%!!%!?!%%%%??%%%%%%%%!?!!%!%%%?%%!!%!?!%!%%!!!%!%%%!%%?!%%%!%!%!!!!!!%%%%?%!%!!!!%??%?%?!!%?!!?%!%?%?!%%?%%%%%!?%!?!%%??%%?%!?!%%%%%%?%%??%!%?!!?!!%%%!%%%%%%%%!!%%%!!%!!%%!%!!?%!%!?%!%%!%??!%%%!%%%!!%!%%?!?!!!%%%%!??%%%%%%%%%?%?%%%??%%?%!!!%?%%?!%!??%%?%!%!%!?%%!?%%%!%%%%%!?%%!?%%%%?!?%%!%!%%?!!%%!%?!!%%!?%!!!%%!!%!!!%!?%!%%!%%%!!%%?!?%%%!%%?%%%%??!%%%%%%!?%?%!!?%%%!%%?!%%%%!?%%!%?!%%!%!?%!%%!%!?%%%%!%!%!?!%%?%%!??%??%?!%!%%?!%!%%!%%%%%!%!%%%%?!!%!%!!%!%%%?%%%!%!%?!?!%%?!?!?%%%!!!%!%!%%%%%%%%!?!?%!%!!!!?%%?%%!%!%%!%%!?%%!%!!!%%!%%%!!%%%???%!!!!!%!!%?!%!%%%!%%??%%??%%!!%?!%%?%!%??%!%!!!!!!??%%!%%!%?%%?!!%?%%?!%%%!!?!%!??%%%%%%!%!!%!?!?%%!%%!%!?%%?%%%?!%???%!%%?%%!%?%!!!!?%%!%??%%??!!%%%?!%%%!??!%???%%?%!!%%?%!!%%%??!?%%%!?%%%%?%?!%!!%%!?!%%!?!%!?!%!!!!%%?%!%!?%?!%!!!!%!!!%!%%%%%%%!!!?!%%!!%%%%%%%%%?%%?%?%!!%!%%%%%!?%%!!%%%%%?%%%%!!?%!?%%%!%%%%%!%%%%?%%!%%!!?!!%!!!%%!?%%!!!!!!!!!!%!!%%!!??!%%%!%!?%!!%!%%!%%!%!%%!?!!%!%%!!!!?%%%!??!%??!%?%!!?%%!%%%!%!%??!?%?%?!%%%%!%!%?!!!!%?!?!!%??!!%%%!%?%%??!?%!!%%!%%!%?%%%!?%!?%?%%%%%!?!%?%???%%%%%??!?%%?%%%!!!%!%!%%%%%!%!%%!%?%%%!%%?%!%%%?%%%%%%!!%!%%%%%???!?!%!%%???%%%!%?!%?%!%%%%%%%%?!?%!!?%%!!!!%!%%%%%%!%%!%%%?%!%%%%!?!!!%%?%%!!?%%?%%%?!%%!%%?!!%?%%!!!%?%?%%%!%%%%%%%!%%%%%?%???%!%%%%%?%!%??!%?%!?!%%%!%%%?%!%%%%!!%%?%%%!%%%?!!!%%%?!%!?%%!!??%!%%%%!%?%%!%!!?%!!%?!!!??%%?%?!?!%%!%!%%%%%%%%!!??!%%!%??%%%%%?!%?!?%!!%%%!%%?%!!%!!!!!%!!!%!%%!%!%!%%!!!%!?%%%!%?%?%?!%%%?!%%%!%?!%%?%%?!%%?%%??%%%?%!!%!!!?%%!%%!!!%%??!%%%!!!?!%%!%%%!!!%%!%!!%!!!!!%?%%%!?!%%%%%?%%%%%?%!!%%%%%%%!?!?%!%!%!%!!!%%!!?%%%%%!%?!??!!%!%!%%%?%%!%%?%!%!!??!%%!%?%!%!?%!%%!!!%!!?!%%%%?%%?!%!!?%%%%%%?!?%%%%!!%%!?%!?!%%?!?%!!%%%%%%%%%%!%%!!%%%%%%%!!%!%!%%?!?!!!?%%%!!!!!%!?!%%!%%!%%%%?!!!%%%!%%%?%%%%%%%%%!!%%!?!%!%!%%!!!%??%%%%%!%!?!%%%%!%?%!%!!!%??!%%!%?!%!!!!%%!%%!!!!%%%%!%%%%%%%?!!%%!!?%!?!%%!!%%%%%%!!!!!!!??%???!%%%%!!!%%!?%%%!%%%!%???%%?!!%%%!%%%%!?!%%!!?!%!%!%?!?%!?!%%??%%?!!%?!%!%%???!%!!%!!??!?%!!!%!%?%??%!%!?%%%%%%?%%%%?%%!?!!%%??!!??!!%?!!!!!?%!!!!%!!%%!%%%%%!%!%%??!!!!!%?%!%%%%%%%%%%!!!%!%!%%%?!%%%!??!%!!!!!!!!%%%%%%%%!%%!????!%%%%%%!%%%?%%?%%%!%!?%%%!%?!?%%%%%?%!%%!%?!?%!%%%%%%?!%%%%?!!%!%%%?%%!%!%?%%%%%%!%%!%!%%?%!%%!!%%!%!%%!%?%!?%%!%!%%?!%%!!?!%?%!%!!?%!!%?!!%!%%!%!!%!%%!!?%%!%%!!%?%%!%%??!!!?!!?%%!%!!!%!%%!!!%?%!?!%%!!?%?%!!!!!????%%!%%!%%%%!%??%!?!?!!%%%%%!!%%%!%%%?%?!%!%??%%%!!%??%%?%%?%%!%!%!%?%%%%%%%%%!%%!!%%%%!%!!%!?%%%??%!%%%!!%!%%!!?%%%%%?%%?%%!%%%%!%!%?!%%!!%%%!!%%%%%!!!%%?!!%%%?%%%!?!%%%%?%%!!%%!?%!!!!%!!%%!%!!%!?!%%%%!%!%!%%%!?!!?!%!!%?%%%?%!!%%!%%%?%!!!%%%???!?!!%%?%!!?!!!!%%%%?!%%!!%!!!%%!?%%%%!%%%%%!%%%!!%%%%!!%?%%!%%!?!%?!%%!!%!!%%%?!!!!!%%%?!!?%!%!?%%%!%%%!?!?%%??%%!%!%%!%%!%%!!%%?!!%??%%%%!!?%?%?%?!%!%%!%!!%!!!%!%!!%%?%?%?%!%?%!!?%!?!%!%?!%%%%?%?!?%%!!%%%%%!%!%!!%?!%!%?%?!%%%!!%%!%??!%!!%%%%?%?!!!!!%%%%%!%%?%%%%%!?%%!%??!%%%%%%%?%?%!!%?!!!%!!!!%%%??!%%%!!!?!!%%!!%!?%%!%%!!!%%!!???!!?%%!%%?%%!%%!!!%%!!!%%!%!!!%?%%?%%!!%%!%%%!%%%%%%%%%%!!?%%!%!%%%?!%!%!??%%!?!??%%%%!%%!!!%%%!?!%%!%%%%!?%%%!%!%%%!!%%%?%%?!%??%%%?!!%%%?%!!%%?%!?%%??!!%?%%%!%???%?!?!?%?%%%!%%%!!!?!%%!!%%%!!?%%!%?%?!%%!!%%%%?%!?%?%%!%%!%?!%%?%%!%!?%?!%%!!%%!%%!%%!%%%%?%!?!!%%?%%?%?!!%%!%?%?!%%!!%!!%%!?!%%?%??!?!?%%!?%%!!!?%!%%%?%!?!%!%!!%%%?%%!?%%%!%%!?%!%?%%?%%%%!%%?!!?%%!%!!!?%%%?%!!%%!%!%!%%?%?%?%!%!%!%!?%%?!!!!%%?!?%%%%%%%!%!!!!!%!%!???%?!%%!%?%%%!%!!!%%%!!%%!%!?%!%%!!!%%?!!!%!%%%%%!%%%!??!%%%%%%%?%!%%%!%%?!%!?%!%?!%!%?%%%!%!%%!%?!%!!!%%%%?%%%!%%!?%!?%%%%%%%%%?%???!!??!%!%!%!??%%%!?%%%%!%!?%%!%!%%!!%?%%%?%?%!??%!!%%%%?%!?%!?%!%%%%%%!?%%!%!%%??!!%%%%%?%%%%%!%!!???%%!%!?%%%!%%!%!%%%!%!?!!%%%%!!!!%%%!!!%!%%%!?!%%!%%!%!!%!?%!%?%%%!%!?%!%!%?%??%!!%%!%?!%%!%!!%?%%!%%!%!%!%!%!%%?%!!?!!!!?%!!!%%%!!%%%%%!%%%!%!%!%!%!?!%?!!%%!!!%?!%%%%!%?%%%%!%!%%?%%!!!!!%!!!%%%?%%%%%!?!%!?%%%!!!!?!%%%%??%!!%!???!%%%!!%%%!%%!!%?%%%%?%%%%!%%!!%!!!!?!?%%%??%%?%!!%%?%!!%%%?!%%%!!!?%?%%!%%?!??%?%!!?%%!%%%%%!%!!%%%!%!!!%!%??%!%%%?%%%%%!%!%%%!!?%%?%!%?%!!?%%%?%!%%%?%%!%!%?%?!%%!!%!!%!%!%!!!%%%!?!%!%%!%%!%%%%?!%%%!!%!??%!%%%?%?%%%%!!!%!%?%?!%!?!%%!!!!%!%%!%%%%%%!%%??%!%?!%??%??!%%%%!!%!%%!%%!?%%%!%%%%%%!???!!!?%%%!%??%!!!!!!%%??%!!%!%%?!%%%!%%??%!?%%!%?%?%%%%!!!!%!?%%!?%%%%!???%%%%!%%%?%%%?!!%?%%%?!?%%??!!%%!!!%%!?!!?%%%!!%%%!%!?%!%!!%??%%!%%!%!%%?%%%?!?%%%?%!?%%%%?!%%!%%%%%!??!%%!!%!!%%?!%!!!%!%!%?!??!%?!?%!%%%?!%%%?!%%%?%!%%??%%!!!!!%!%%!%%%!?%%%%%%%!%%!%%%?%%%%%!?%%%??!%%?%%!%%%!?%%%!?!%?%!!%!?!%%!?%%%%?%!!!!%%%!?!%?%!%?!%!%%%%!!%?%%!!!!%%!%%%%?!!!!!%%??%!%!%!!!!%%%!!?%!?%!!!?%??%%%%%!%%%?!%!%%%%%!%%%%%%!??%%%%!!!%%?!%!%!%?%%!%%?!!!!%%!!%%%%%%!%?!!!!%%%!!%%%%!%%%%!%%%!?!!!%%%%%%!??!%%%!!%%!%!%%?!?%%!%??%!%?%%%!%%%??%!?!?%%?%%!??!%%%%%!%!!!!!%%!??%%%%!%%%%?!%??%?%!%%%!!%%%?%!%?%%%!!%!%!%%%?%!%%!!%%%%?%%%%%?%!%!%!%%%!%%%%!?%?!%?%%%!%%%%!!!??%!!%!?%!!%%%!%!%%!!%!%%%!!!!?%!?%?!%%%?%%%?%%%!?%?%%!%!?%!%!%%%!%%!!%?!%%!%%!%%%?%!!%%%?!%%?!%%%!%!??%!%?%!%%%??%%%?!!!!!%%!!!%?!%%!?!%?!%!!%!%%!!?!%!!%!%%!!%?!%?%%%%%%!%%%%!!!!%?!?%??%!?!%%%!%%!?%!%!?!?%%%%!%%?%%%!%!%?!%!%%?%%!!%?!!%%!%?%%!?%%%!%%%!?%!%?!%%?%%%!%%%%!%%?%%%%%!%%%%%%!%%%%?!!%!%?%!!%?%?!?%!%?!?%%%!?%%%%!!%%%!?%!!%!%!%?%!!%%!%%%?%!%%%%??%?%??!%?%%?%??%%!%!%!!%%%!%!!!%%!!%%%!%!!%!?%?!%!%?%!%%!%?!%%!!%!%%!%!%%!?!%?!%?%!%!%?%%%%%!!%!%%%%!%!!%%%%!!%%?%!%%%!%%%%?%%!%%?%!%?%%!!%%?!!!!%%%%%!%%%%%%%?%!!!%?%%%!%%%%%?!%?%%%%!%%!%%?!!?%%!?%%%!%!!!!!%%?%%%%!!%%%!%!%%%!!??%!?%!!!!!?!!%%!!!?!%!%!%!!%%?%!%%%%%!%?%!%!?!%%?!!%!%%?!%!!?%%%%%?%%!?%%%%!!!%?%?%!%%?!?!!!%%!?%%%??!?!%%?!%%!%%%%%%%%%!%%??%%!%%%!!??!!!%!%%!%?%??%?%%!%!%!!%%?%%%?%!!%?%?!%%%?!%!??!!!%?%!%%?%!!!%%%%%!!!!!%!%!%!%%%%%?%!?!%%%%?%!?%!%%!%%%%!!%!?%!%%%%!%%?%%?%%!%??%%!!!!?!!????!?%!?%%!?%%%!!%%%!!!!%%!%!%!!??%%!%!%!%%!!%!?%?%%?%!%%!?%%%?!%!%%!%%?!%!!?%%%%!!!%%%!%%%!%?%%%%%%!%%%%!%??%?%!%?!%%%!!%%%!%%!%%!%%%?%%%%%?%%!%?%%!!!%!?%%?%%%%%!!!!!!!%%%!%!%!%%?!%%!!!%%%?%%%?%%!?!%?%!%!?%!!?!!??%?%!?%%%!%!%?%%!%!%%%?%%!?!%%%!!!!??!!%%!?!?%%%%%%%%%!%??%!?%%%!!%%%!?!?!%%!?%%!%%!!%%!%%%!%!!%%%?!%%%%%%?%%!!%%!!?%?%%!!?%??!%!%%?%?!??%!!!%%%%%%%%?%%!%!%!!%?%!%%%!%!???%?%!!?!!%%%!?%%!%%!!!!?%%?%%%%%!!?%%!%%?%%!!!??!!%!!%!%%!!%!%!!%?%!!%!?%!%!%%%?%!%%??!!?!?!!!%%?%??%!!!?!%%!!%%!!!!%!%!?!!!%%!!?%%%!%!%?%?!%?!?%!!!?%!%%%??!?%%!?%!!!?!%!%%%%!!!?!!%!%%!?!%??%%!%%!%%%%%!!%!%%?!!%%%!!%%%%!!!!!%%!!%%?%%?%%%!?%%!!!%!%??%!???!!%!%%%?%!!??%!%%%!!%??!!?!%%?%!!?!!%?!?%?!?%%?!!%??%%%?!%%!!%%?%?%%!!%%!%!!!%??!!%%%!!%%!%!?%??%?%!!%%%%?!%???%%!%!%%?%%%!%%%%%!!?%%?%%?%%%%?%%%??%%!!!%!!!%!%%?%!?!%!?%%!%?%!!?%???!!!!?%%%!?%%!%%%%%!%!%%?!?!%%?!%%!!%%!%?!!%%!!!!!%!%?%!%?!!!%%!!?!!?!??%!!%?!!!%!%%%%%%?%!?%!%??!!%%%!!%?%?%!!%%%%%?%!!!!%?%?%%!%!!%%??%?%%%!%%??!%?!%%?%%%!!%%%!%?%?%%!%?!%%!!!%%%%?!!???%!?!%%!%%!!%!??%???%%%!%%%%%%!!%%?!???!!%%!%!%?!!?%%%!%!%!%%%?%!!!%%!%%%!%%?%??!%%?%?%!%!?%!%!!%???%%!%?!%%%%%!%!%%!%!!!%%%!!?%!%%??%%%%%!!?%%!?!?!!%%!!%!%%%%%!%!%!%%?!%!!!%!!%!%!!%?!%%%!%%%!?%!%?!%%??!!?%?%!%%%!%?%!%%%!!?%%!!%%!%!!?%%!%!%?!?!?%%%%%?!?%%?%!%%!!%!!%!%%!!%%%!%?%%%!%!%?%%!%!!!!?%%?%!%%%?!%!%%%?%%??%!!%!%%!???!%!%!%?!%%%!!%?%%%%!%!?!!?%!%%%!!%!!?%%!%%%!%%!?!%!%%%%!%!%?!%!%?%%!%?%%%%%!%!!?%%?!?%%!%%%%%%!!?!?!%!!?%%!?%?%%%%%!!%%%?!?!%%!%!%?%?%%%?!!%%%!%%!%!%%!%%%%!%!%%%?!!!!!%%!%%!%%%%!%%!%!%%!%%?%%%%!!?!?%!%%%%!%%?%?!%%%%?%%%!%%%!!?!?!!!!!!!!%!??%!%?%!%!!??%%%!%%!!%%!%%!!%!!!!%%!!!%?!!!%?%?%?!!!%!%%%!%?!!?%%!!!%?%?%%!%%!?%%!!%?!%??!%!%%%?!!?%%%%!%!!%!%?!?%!?%!!%!?!?%!?%%!!%%%%%%%??%%!!%!%%%%%%%%?!!%%?%%%%%%?%!%%!%!?%%?%?%%?!%!?!?%!!!!!%%%%!%!%%!%%!!%!%%?%?!!?%!?!%!%?%!%%%%%%?%%%!%!%!%%!?!!!%%!%!%%%!!%%??!!%?!??%!%%!!!!%!%%!%!!%?%%%%!!?%!!%%%!!%!%%?!%%!%%%!!%!!%%!%%%%!%%%!%%?!%%%!%??%!%%!!?%?%?%%%%?!%!%%!%?!?%!%?!%%%?%%!%!!!?%%%%%!??%%!?!%!%%%%?%%?%%%%!%%?!!%!!!!!!%%%!%%?%%%%!%!%?!%?!!?!%%%?%!%%!?!!%%!%%!%%!%?%!!%%?!%%%%%??!%%%!!!?%!%%%%%!?%?%?%%%!!!%!!!%%!%?%%?%%%?!?%%!%%!%%!%!%!?%%?%!%!!!%%%%?!?!!?!%%??%%%%??%%%!%!?!%%%%?%%%%??%%!%%%!%%!!%!%!%%%%%!%!%%?%!!!%?%%%?!!??!?%!%?%%!%?!?!!%%%%!!!!%%%%!!!?!!%?!%!%!%%!!%%%%!!!!%%%%!%???!%%%!!!%%%!%?%!!!!%!%%!!%%?%!!!%!%?!!%%?!%%!!%%%!%?%!?!!!!?!%!%!?%!?!!?%!%%?%%!%%!!!%?%!!!!%!!%%%!?%!???%%%%?!?!%?!?%%?%!%%%!%%%!!?%?!?%%?!%%!!%!?%%%!%???!%%%!??%!?!%%!%%%!!%?!%%%%%!!%?!?!!!!!%!%%%?%?%%%%%!!%%!%%%%%!?!%%?!%%?%?%%?%!%!!!%?!%%!%%?%!%?%!!!!%%!!%%?!%%%%%!%?%!?!%%?!%!%%%!%?%%!%!%!%!%!!???!%%%!%!%%!%!?!%%!%%%!%!!!!%%??!?!??!%??!%?%%!%%%%!%??%%%%%%!!??!%!!!!%%?!%!?!!%!!!%!%??%!%%?!%%%%%!%?!%%%%%!!?%%%%%?!!!%!%?%!%%!!!!!!%%%!%%%%%%%%%%!!!!%?!%?%!%%%%!%!!!!%%!!%??%%%!?!%!%!%%%%%%%!%!!?%!%!%!%%%%!%?!?!!%!!!!!!%!!!%%!%%%%%?!!%%%!%!%%%?%!?%%!?!%%?%%%??!%%%?%%%!?!?%%%??%!%??%%!?%!%?%!?!?!%%%%%%%?%??!%!%!%!!!%!?!%?!!?%%?%?!!!%%?%?%%%???!%%!%%!%!%?!!%%!%!!!!!!!!%%??!%%%%%%%???%?%%?%?!!%%?!%!%%%%%%%!!%%!%?%%!!%!%!?!!!?!!!!?%%%!?%%!%%%%?!%!%!!!!%!%??%!!%?!!!?!%!!%%?!!!%%%%%%%%!?%%%!%%?%%%?%%!!?%!%%%%%%?!??!!%!%!!?!%!%%!%!%%!%!?%??!?!%!%!%!%%%?%!%!%!?!%%%%%%%!%%!%!!!?%!!!%%%%!?%????%?%%%%!!%??%%!!%%%%!?%%!!?!!%??%%?%?!!?%!??%%%!!?%%%?!!?!%%%%%?%!!%!%%!%!%%!!?%%%?%%!%%!!!%!%%?!%????%!%%%!!%?%%!%%%%!%%!%%%!%!%%%!%!!!?%%%%!%%!!%!!%!%%?%%%!%%?%%!!!?%%!!%%!!??!%%%?!%%?%?!!%%!%!!!%%%%!!%!?!!!%%!%!??!!%%%?!?!%%??!%%%?%?%?%???%!!%?%%%%%%%%?!%!%%%!!?%%%%%%%!%%!%%%%!!%!%%?%?!!?%%%?!%%?%?!%??%!%??%%?!%%%%%%!%!%%%%%!%%!?!%!!!%?!!%%??!!%!%%!!?%%%%?!%%%%!%!?!%!?%!!%!?!%%%?%%%!!!%!!?!%!%%?%%!%%!%!?%!%!%!%%%%%%%%!%!!!%!%%%?%%!%%%???!!!%!?!%!%%!%!?%%!!!%!!!!%%%!%!%%%!?%!!%!?%?!%?!!%%!?%%%%%%??%%!%?%%%!%%!%%!%!%%%!!?!!?!??!%!%%%?!!??%?%%%%%?%%!%?%!!%%%%%?!?%?%%?%%?%!%!%%%%%%!%!!?%%!!%?%??%!?%%%!!?%%%?%%?%!%%%??!?!%%!%%%!?!%?%%?!!%%%%!!%!!%%?%%%!?%%?%!!???!%!?%!!!!%!%%!!!%%%%??!%!%%%%!%?!??%!%!%!!%!%%%!?%?%!!!%%!?!%%!!?!%%!%???!?!%?%?!?%%%!%%?%%!%!!!!%%%?!%%!%?%%%%!!?%!%%!!%!%!??%!?%!%%!!!%%!%%%?!!%%!%%%?!!??!!%!!!%%%%!%%%%!%%%!%%?!%!%!!%!?%!%%!!!%!%!%?%!%!%%!%%%%!%!?%!??!?%%?%!%!?!%%??!%!!!%%!%%%!!!!?!!%%!%!%!?%%%%?%!!%%%!!!?!!%%%?!?%!%%%%!!?%!!%%%%!%%%%?!%%!!%%?!%!?%?%%%!?%!%!!?!!%!%%?%%?!%%%%?%%%!%?%!!%%!!!%!%!!!!?!%?!%%%!%!%%%%%!%%??!??%%!!%?!!%!!%%%!!!!!!!%%%%?%%!%%%%%%!!!%?%%!!!??%!%!?!!%!!!%%!!!%%!?%!%!%?%%!?%!!%%!%%!%!%?!!!%%%%!?%%%%??!!%%%??%%?%%%!%%%!%??%!%%!?!!!?!!!%%%?%%%!!??!??!!%%%!%!%%!%!%%!!%?%!!%%%!%%%%!??!%%%%%!!!%%%%%?!%%%%%%!!!%%%%!%%!%%?%!!%%??!?!%?!%%?%?%%%??%??%%!%!%!%!!?%!?%%?!%%%%!!?%%?%!?%?%%!!!%%%!!!!!?%%!?%%?%!%%%%%%%%%!?%%!!!?!??%%!%??!??%%?%%%%?%!%%%%??%%!%%%!!??%%%%%%?!%!%?!%%%!%!%!%?%%%%%%%%%%!%?!%%?!%?%?%%!!%!!!%%?%!!%!%%!%%%!%!%!?%%%!!%??!!?%!%??%%%%?%%%!!%?%%%%!!%%!%%%%!?%!%%%?%?%!%?%%%%?!%?%%%%??!%!?%!%%%!!!%%%%?%!%%?%%!??!!!!%?!%%%!!!!!%!%!!%%%%%?%%%?!?%!!!!%%!!%!%!!%!%%!%%?!%?%!!%%!!%%?%!!%!!%%!%!!?%!%%%%%%?%%%!%!?!!%!!!%!%%%%!%%!%%!!%%?%%!%%%?!!!?!%%!!%%%!!!!!!%!?!%%!%?%!!!%?!%!%%!!!?%%%!%%!!??%?%%?!%?%?!!!!?!%%!!%?!!!!%%!%!%!%?%%%%!!%%%%!%???%%!%%!%%%%%!%%%?!?%%!%%?%%?!%%%%%?%!%!%%!!%%%!!%!%?!?%!%%%%%%%!!!!!?!%%!!%?!%!%!%!%?%%?!%!!!%!!!%?%%%?%%%!%!?%!???!!%?!%!%%!%%%%?%%!%!?%%!%!!!%%!%!!%%%!?%!%%%%!!%?%?%%%%!%%%%%%!%%!%%?!%%!%!!%%%!%%?%??%!%%%%?!?%!%!!!%%%%!!!%!%!%%%?%%!!%?%%%!!%!%%%%%%!%!!!%%!%?!???!!?%!!?!!%?%!!%%%%%%!%!!!%!%%!%!%%%%%%??%%!%?!%!%?%!?!%%%%??%%??%?%!%%%!!%?!%!%!%%%??!?%%%%%%!!?!!%%!%!!!%!%%%!%%%!%?%!%%%!!%%%!%?%?%%!%%%%%?!%!!!!?!?%!%!%%%%???%?%%?!%!%%%%!%%!%?%!%%!!!%%%!!%!%?%%%!?%!%%%?%!%%%%%!%!%?!%%%%!%!?!!%!?%%!?%?!!?%!?!!%!?!%%%!!!!%??%%!%!%%?!!%%!!%%%%%?%%%%%?%%%%!!!%%!%!%%%!!!%!%%!%!%%%%??%?!!%%%%!!!%%%??%!!!?!%!!!!!%%%%%%?!%%!%??%%%%%!%?%!!%!!!!%%!!%!?!%?%%!!!!%%%%%%?%%!%?%%?%?!%??!%%%%!!%?!!?%!%!%!??!!!%!%%%%%%?!!%%%%!%!?%%%%??%%!!%!!%!%%??%%%%!!%!!%!???!%!!%!%%!?%%!%%%!%%%%%%!%%!?%?!!!!%!?!%%%!?%%%%!?%!!!%%%!!!%%!%!?%??%?%!%%%!!!!%%!%%!!!%!%%%!%%??%%%!!?!!!!!!%%!%%!?!%!!??%%%!%!?!%!!%!%%?%?%!%%?!?!!%!!%%?!!!!!%%?!!?%%?%%%%%%%!%?%%%?!%%?%?%%!%!!%?%%!%?%%%!%%%%?%%!%%%%%%%!!%%!%?%%%?%?%!!%!?%!%%%!!%!!%!!!%?%!%%%!%%%%!?%%??!!%?%?%%!%%%%%!%%?%%%%%?%?!%%%!%!?!%!!?%!!%!?!%%%%%!!?!!%%%%?%%!%%!%?%%!%!!%%%%!!!%!%?%%!!%!%??!!?!%%%??%%%!%!%%!!?%!?%!%?%%!%%!%!%%?!!!??%%?%%!%!!%%!!!!%!%!%%?!!%!%%!!!%%%?%!%?%!%??%%%?!%!?!%%%!!%?%!%%%%%%%%%%!!%?%%%%%!!%%?!!%????%!?%!!!!!%!!%%?!!!!%??%!?!!!?%%%%?%%!%!%!?%?%!%%%?%%!%%!?%%!%!!!!!%?%%!!%!??!%%!%%!!!!%%!!%!!%%!!!%%%?%%%?%%?%?%%%!!%%%!%!?%%!!?%!?%?!%?!!%!!%%!%??%!%!%!%!!%!?%?%!%?!?!!%%!%?!%%?!!%!%%%!!?!%!%%%%%%!%%%!%!!!%?!%!%%!!!!%!%!!%%?!%!%%%%%%!!?!!?!!%%%!%!!%%%!??%%!%%!!!?!%%%%%!!%%!?%!%%!%%!%%?!%!?%!%%!!!%?%%?!!%%%%%!%??!!%%?%!%%%!%?!%!!%!!%!!!!!%%%%?!?%?!!%%!!%%%?%%%!!!%%%%!%%!!!%!%?%%%%%%%!!!%?%!??!!%%%%%%%%!!%%%%%?%!!%!%%!%%%%%!%!!%!%%%!%!%%%?!%%!!!!%!?%!!%%!%%?%!?!!!%!!%%!%%!!%!%?%!!%%!%%!%!?%%%%!%!!!!%%!%?%%%!!%%!%!!?%%!%!!?!!!%!!!?!%%%%%%!%%?%%%!!%!%%%?%%?!!%%%!!?!%!??!?%%%?!?!!!!%!!%%!%?%!%%!%%!%?%%%%?%!!%?%?%?%!!%%%%%%!!!!!!%!???!!%?%%%%!%%!%%!!!!?%!?%%!!!%%!?%?%%%!%%!%%!!%%!!?%%%%%%!%?!%%?%%%%?%%!%!!!!%%%%?%!!%%%??%?!%%!?%%!%%?%?%!?!!!%!!!!!%!%!%%!!%!?%!!%!!%!?%%!?%!%!?!!!%%%!%???!%?%%%!%%%%!?%%%%??%%!%?%!%!%?%?%%%?%%%%!?!!%!?!!%!%%%%!%%?%%!%?!!?!?!%%%?%!?%!!!%%?%%?%!%!?!%!!%%!!%%%%!%!?!??%%%!%!?%%%!%%%!%%!?%%%%%%%%??!!?!!?!!%%!!?%%!%%%%?%!!%!!%!!%%%!!!!?%%%%!%%?%?%?!%%!!%%?%%%!%%!!?!%%?%%%%!?%%%%%%%%%%%!!%%%%%%!%!%%%%%!!%!%!%!%%!%%%!%%%%%?%%!!%%%%%?%!%%?????%?%!%!!%%%?!%%%!!?%!!!!%!!!%!!%%%%?%!!?!%%%%%!!?%!%!!??%!!%?%%%%%!!%%?!!?%!%!!%%!%!%%!%%%%%%%%%%%%?!%%%!?%%?%!!%%!%%%?%???%%!%%%?!!%!!!%?%%%!%%%!?!%!?!%!%%?!%%%!%%%%%!!!!???!!??%?%!!%%%?%!%%!!!%!%%%!%!%!%?%!!%?%!!!%!!!??!??%?%??%!%%??%!!%%%!%%!%%!%%?%%!!!%%%%?%%%!!!???%??%%%!??!%!%!?!!%??!%%!%%!!%%%!!%%!%!?!%?!!%?%%!?%?%%%%?%%??%!?!%%!%!%!!?%%%%?%%!%%?%%!%%?%%%%!!%%%!!%%!%%!!!%%%!%??%%%%%?%!!%%?!??!??!%!%%%%%!!%%%?%?!!%%!%!%%?%!!!%?%?%!%!%%?!%%%%!%??%%%%!%!?!%%%?%%!!?%%%%%%%%%!!!%!?!%!%!?%?!!%!?%%%%%%%!?%!!%!??%?%%%!!!?%%%%!%?!%%!!%!%%%!%!%%!%!%!%%?%!%%%!??%%!%?!!!%%%%%%!%?!!%%%%%%?%%%%%!%%%!!!%%!%%%?!!%??!%!!!!%!%%%%%?%!%!!!%!%%%%?%%!!!%%%!??!%%!?%!!%?!!%%!%%!%%%!?!?%%!%%%?!!!%?%?!!%!!!%%!%%%!%??%%%?%?%!!%!%!%!!?%%%!%%%!%!?!%%!%%!!%!%?!!%%?%%?%?!!%%!%%%%%!?!!!!!%%?!!%%?%%%%%!%???%!%%?!%%%%!%%!!!%%!%%?%!%%%!%%%!%%%%%!!??%!%%!%!%!!!?%!?%%!%%%?%%!!!%%%!%%%%%%?%%?%!?%!!%!!?%%!%!!%%%%!%%!!!%%!???!!%!%!!??%?%!%?%!!!%%%%!%%!!?%!%%%%%?%?%!!!!%??!!%!!!!%%%%%?%%%!%%%%!?!%!%%?!%?!??%%?%%!%!%%%!!%!!!%?!!%?%%%%!!%%%?%%%%!?%%%%%%??!%%%%!!%?%%%?!!%%%%%%!!%%%?%!!!?%?!%???!%%%?%!%!!%%%!!%!%!%%!%%%?!%!%%%?!?!?!%%%??%!%%?%?%%?%%!%?!?!!!%%!%!%??%!!%%!%%%!%%%%%!%!?%?%!%!%%%!!?!?!%%!%%!!%!?!%!!!%%!%%%%%!%!??!!%??%%%!!!?%!!!??!%?!%%%?%%%%%!?!!!%%!!%%%%%!?%%!%%??%%%%%!%!%!%!%!%?!%%%%%%?%%?%%%%!?!%!!!%!%!?!?!%%%%!%%!!%??!!%%!%%%!?%%%!?%%??%%%%%%!%%!??!%??%??%%%%???%%?%!?%!%%?!?!??!%%!%%%!%?!%%!%%%!%?%%%!!!%?%?%?%%%?%!%!!!??%%%?%!?!!?%%?%!?!%%!?%%?%%!%!!!!%!%%%!!%%%%%!%!%!!?%?%%%%%%%!!%%%!!!%!%!%%%%!!!?!%%%%%!!%!%%%%!%?%!!%%!%!%%%?%%!!?%%!%%%%%?%%%!%%!%%!!!%!!?%%!%%!%?!?!%!%%%!!%!%%?%%!%%%%%%%!!!!?%!!??!%?!!%?!%?!%%%%%%?%%%%%%??!%!?!%!%!%!!!%!%!!%??%!%!!!!!%?%%%?%%!?!!?!%!!!%!%%%%?%?%%!%!!%!!!???!!%%%!?!%%!?%%%%??%?%?%!!!%%!%!!!%!%%%%%%%?!????%!%%!?%!%!%?%%?!%%%%%!!!%%%%%!?%%!%?!%!%??%!%!%%%%%%%!%%!%%%!??!!%%!?%?%?%!%%%%!%!??!%??%%%!%%%%?!!!%%%?%!!%%?%%?%!%%%!?!!%!?%!?!!!?%!!%?!!?%!!%?%%%%%%?%!!??%!%%!%%??!!%%!!%%?%!%?!??%%%!%%?%%!%%?!!?%!?%!%%%%?%!!%%%%?%!!!!?!!!%!%!%%%%!%%%!%!%%%%%%%%?%%!?!%?!!%!?!?%%!!%%!%%%!%%%%%%?!%!?%!%%!%%%!!%%?!!?%%%!%%%?%!%?!?!%?!%%%%%%!%!!%%%%%!%%%%!%%!?!%%%?%!%%!!!%%?%?%!?%%?%%!!!!%!?%%%%%%%?%%?!%%?!?!%?%?%!??%!%%%%%!!!%??!%%?%%%?!%%?%???!%!%%%%%%!!%%!%!%!!%%%%%?%?%?!%%!%%??!%!??%%%%!%%%?%%?!!?!!%!!?!?!!?!!%%%?!!?!%?%!!%!!?%%!!?!?!?!!%%%%!%%?!!%%%%!%%!%?!?%%!%!!??%?%!!!%%%?!%%!%?%%!?%?%%?%%%?%%%?%?%%%%!!%%%%!!%!!%!%%%%%!%%%?!%!%%%%!%%%%!!!%%?%%%?%%%%%%%????%!!%!%%!%%%?%%!!%!?!!%??!%!!??!%%%?!%%!!!%!!%%!!%%!!!???!?%?!%%%!!%%!?!!!!%!%!!?!!%%!%%?!!%%%?%!?!%!!%%!%%?!?%%%!%!!%??%?!%%!%%!%%%!%%?%%?%%%%%!!?%%!!%%%?%!?%%%%!!!?!?%!!%!!?%?!!?!%%%%!%%%!?%!%%%!%?%!%!%%%?!%%%!%!!!?!?!%%%%!!!??!?%%%!!!?%%%!?%%!?%%%%!!%%!%%%?!%?%%?%%???%!%??!!%%!%%%%%%!%!!!?!%%!!!%!%%%!%?!%%?!%%!%?%%%%!%%%!!!%%!%%?%?%!!!!%%?%%!!!!!%%!%!!%%%%%%%%%!%%!!!%%!!!%%??%%!%!%!%%!!!!!%?%?!%%%%%??!!%%!!!%!!%!!?%?%?!!!%!!?!%?%!%%?%%?%!%!!!%%%%!%%%!%!%%!!%%!%!%!%%%%%?%%%??!%%!%!??%?%?!!%%?!%%!%%%!?%!%!!!%!%%?%?%!!!!%%%!!%%%%%%!%%!?!%??%%%%!!?%%%?!!!!?%%!!%!%%%?%%!%!%!??%!%!%%!!%%%!%!%?%!%??%?%%!??%?%!%!%!%%%!%%!%!%%%!%%!%%?%%?!%!?%%!%!%!!%%!%%%!%%??!%!?%?!?%!!%%?!!!!%%!%?%!!%!%!%%?%%%?%%%%%?%?%%!!?%!?!%%!?!%%!?!!!!%%%%!!%%!?%%!!%%%%??!!%!?%!?!%?%!%%%%??%!!%%%%!!!!?%%%?%%!%!?%!!%!%!%!%?!%%%!!%%??%%!%%%%!?%!%%!!%!%%%!?!%??!%!!!!!!%?%%%?!%!!!?%%!%?!%!!?!%%%??%!!%?!%%!!!%!%%!%!%%!%!%??!!?!%%%!!%?%%!%%!%%!%!!%!%?%!%!?!%%%!%%!%!!%?%%!?%!!%!%%%%!%%%!%%!%%%?%%%%!!?!%?%!%%!?%!%?%?%!?!%%?!%?!?%%!%%%!!?%!!?!%!!!%%%%%%!%?%%!%??%!!?%!%%%!?%!%%%!%%%!%%%%!%%%%!!%%!!!%!%%?%%???%?!%!%!?%%!%%%??!%%%?%!%%!%!%%%%%?%!!%!!!!%%%!!%!%?!!?%!!%%%%!%%%%?!%%%??%%%!%%!???!??%%%%%%%!!%!!%%%%!!%%%!!?!!%?%%!!!!?%%!%%%%!?%%%%!!%%%!!%%?%!!!?%%!%%?!%!!!!!%%?!!!%??%?!?%%!!!?!?!%??%%%!%%!%%?%!!%?%?!%%!!!!!%%!!?%%%%%?%%!%%%?%??!!!%!!!%?%%%%!%???!!%%!%!%%%%!%%%!!?!%%%%%%!!%%!%%?%!!!%%?%!%!!?!!!!%!%!%%%%%!!??!%?%%!?%!!!%!%%%?!%%!%%%!%!%?!%%%?%%?!!!%%%!%%!?%%!!?!?%!!!%%%?%%%%!!%?%?!!%!!%%%?!!!!%%%%%%%%!?%%!%%?!%?!?!!%!%!?%!!?%%%!%%%!%%%!?%???!???%?%!%!%!%%?%!?%!?%%!%%!%%!%%?!%%!!!%%%%%%?%?%%%!!??%%?!%?%%%!%!%!!%%???%%%%%%!!%!%%!%%%!%!%!!%%%!%!?!%%!%!?%?!%%%%!%??!?%%%%!?%%%%%%?%?!%%!!%%!%%!!!%%!!!!?%?%%?%!%%%%!!%!!%!!%%!%!!!%?!!%%%?!!??%!%%?%!!%%!?%!%%%!%!?!?%%%%?!%%%!%%!%?!?!%%?%!%%!?%%!?!%%???%!%%!%%%!%!!!%!!?%?!?!!!%%%%%%!!%%!%!!%!%%%!%%!!!%??%%?%!!%%%!%%%%?%%!??!%!!!%%%!%?%!%%%%!!!%%!!%%!%!?!!?%%%%!%%!%%%%%%%%?%!?%%%%%!!!%?%%%!%!!?%?%%%%%%%%?!!!%!%!%!%!!%%?%%%%!!%%%!%%!%%%%!%?!%?!!!%%%%%%!??%%!%%?%%%!?%%?%?!?%%!!!!%%?!!%%%!!!?!?!!!%!%%%!%!%!%!%!%%?%?%%%%?%!!!!!!?%!%%!%?%!%%?%!?%!%?!!!!%%!?%%!%%%!?%%%%%!!!!??%!!?!!!!%?%%!!!%%%%%%?!!%%!%%%%%?%%?!%%%!!%%!?!!!%%%%%%%!?%???!!%%%%%%?%%!%!%!%%%%%!!%!??%!%%?%!!%!%?!%?%%?!?!%%?!%!!%!!%%%%??!!%%!?%?%%!%%%%%?!%%?!%%?%??%!%%%%%!%?%%!%%%%!%?%!?%%!?!!?!?%%%%%?%!!!!%!%%!%%?%!?!%%!!%!?%?%%%%%!!%%%%!%%%!%%%%%!!%?%?!!!!!!%%%%?%!!!?%%%%%%!%%!%!!%!%%!%%%?!%%??!!%%%%!!%!?!!!%%!!!%!!%!%%!%!%%%!!%?!?!!%?%!!%!!%%%!%%!%%%%!%%!%!%%%??%??!?!%%%!%!!%!%%%!?!%!%!%%%%%??!!%%%%%!%!!%!%?!!?!%%!??!%%%?%!%!!?!?%%%?%?%%%%!!!!%%%%%!%?%%??%?%!%%%?%!%%!?%!!%??%%!%%%!!!%?!!%%!%%?!%%?%%??!!!!%!%!!%%??%!%%%?!?%%!?!?%??!%%%!%%%%%%!%!%%!%?%!!%!%?%%!?!%!%!!!%%%?%%!!%?!?%?%%%%!!!!?%%??!%!?!!!%%%%%%!?%%!?!%%%?!!%!%%%%%?!%%%%%%!%!%%!%!%!%%%!%%%!%%%%%???!!!%%%?!?!%%!%?%!%%%%!%!%?%%!!!?%!%!!????%?!%!%%%%%%?!%!%%!?!!!%%%?%%!!%!!%!!!!%%%%!%%%!%%!%!%!%!!%!!!?%%%?%%%%%?!!!?!!%%%%%%!%%!%%%!!%%?%!!?%%%?%!%%%?!!%?%!!%%!!!!%!??!%?!?!%!%!?%?%%!!!%!??!?%!%%%!!!!!!?%!!%!%!%!!%??!!!!%!!%%%?!?%%%!!%!%%%!%!?!%%%%%%%%%%!%%!?%%%%??%%%%??!%%?%%%%%%!%!!!%!!%?!??!%%!%%%??!%!!!%%%%%?!%?%!?%?%!!%?%?!!??!%?!%%%%%%%%%?!?!!%!!?!%?%%%%??%!?%!!?%%?!%!!!%!%?%%???%%%%?!?!%%!!%!%!%%%!%?!!!??%%!%?!%!?%%!??%!%%?!%%%!!%%?!%%%%%!!%!!%%%%%!!!!%%%%!?%!!?!!?%??!!%!?%!!%%%%%%!%?%!%?!!%!?%??%!?%!%!?%!!?!!%%%%%!!%!!!%!%%%%%%%!!%%%!!!%!%%%!%%%%!%%??!%!?%%!!%!%!!!%!!?%!??!?!?!%?!??%!!!%%%%%!%!?!?!%!?!%%?%%%!!%!%!?%%%!!!!!!%!??%?%!%%!!?!!%!%%%%!!%!%?%%!!%%??!!%%%!%%!!%%%%!%!%!!%%!!%%!%!!!!!%?%?%%!%?%%%!!!%%%!%!?%%!!%%?%!%%%%!%!%%%??!?!%!?!?!%!!!%!?%!!!!?!?%%!%!!%%%?!?%%%!!%?%?!!%?%%%?%%%%?%!%%%!?%!%?%!!%!!%?%!%%!%%!%??!!%!%%%!!%!?!?%%%!!%!%!%!???!%%??!!%%%%%!!??!!!!!%!%!%%%??!%!!?!%%!!!%!!%%%?%??%%?%%%%!%%%!%?%%%!%%%%%!%%%!?%!%!?%%%???%%?!!!%!!?!!!!%!%%?!!!%!?%%%%!!!!%%!!?!%!?!%!!!!%%!!%%!!!!%!%?!?!%?%%?!%!!!%%?!%?%%%?!%?!%!!%!??%%%%!?!??%%?%%%%!%%!%?%!!%%%%!%!!!!%%?%%%%?!%!?%?!?%!%%%%!!?!!!!%!%?!%?%!%%%%!!!!!%?%%?%!%!!%!?%%%!%%?%?%%!%%%%%%%!?%%%?%%%??!%%!!%%??%%%%%?%%%%%%!!!?!%%%?!?%%?%!!%%%??!%%!%!!!%??!!?%%!%%!?!!!!%!!%%!%%%!!%%???%!%?%%%?!%!%%!?%%%?%?!!%%?!%?!??%?%!%!%%!!!!%%%!%%%!?!!%?!%%%!%!!%??%!!?!?!%%!!?%?!%%%%?!!!%%%!!%!%%%!!!%?%!%!?%!!!?%%??%%%!!?%%?%%!!%!!%!%!!%!%?!!!%?!!%%%!!!!%!!!!%?%!??%%%%%!??%%%%!%!%!%?%%!!%%!!??!%%??%!%!%%!%!%!%%!%?%!%!!%??!%%%!%%%%!%!!?!!%!!!%!%!%%%?%%!%%!%%%!%!!%!%?%?!%%!!%%%%!!!%%!%!%?!%%%?%%%!!!%??%!%!%%%!!!%%?%%?!!%%?%%%%%%%%%!!%%!%!?!?!!!%%?%!!?!!%%%%%!%%%%!!%?%%%%%%!%%?%%!%?!!%%?%%?%!%!?!%%%%!!%!%!%%!!?%%%%%%!?!%!%%!%%!%%%!%!%!!%?%!?%!!?!!!%%%!!!%%%%%!?%%%!%%%%%!%?%!%%%!%%%!%%!!%!%%???!?!%%%!%%%!%%%!!%?!!%!%%!%!%!!!%%%%?!%!?!%?!!%!!!!?!%?!!%%!?%%?%!%?!%!!%!!!%!!?%%!!%%!!!!%!?%%%!?!%%%%%%!%%!!!!%!!%!?%%!!!%%%%%%!%!!!?!!!!%?!?%%??!%%!!!%!!?%%%!?%%?%%%%%%%%!%%%%?%%?%!?%!?%%%?%%?%!?!!?%?%%%?%%%!!%%%!?%??%%%%%%!%??%!?%%%!%%!%%%%%!%!%%%%!!%!!%!?!%!!!%%?%?%!!%%!?!%???%%%?!%%%%%?!!%!!%%%%%!!!!%%!!!!??%%%!!!%!%!%!!?!!%%!?!%%%?%!!!%!??%!!%?!%%!%%!%?%%%!%%%??!%%?%%!%%!%?%%%%%%%!!!?!??!?%%%%%%?!!%%%?%%%%%%!?%%%?%!%?!%!%?!?!???%!?%!%%?%?%%%!%!!!?!!%?%%!%?%%!%%%!%?%%%!%%%%!%%??%%%%%?!!%!%%?!%?%!%?%?%%?!%!%%!!%%!!?!%!%?!%%%%%!?%%!?%%!?!?%??%!!!?%%%!!?!%%%!!!!????%!%?%??!%%%%%%%%?%!%?!%!%??%%!!%!!%!!!!%%!!%??!!%!%%!%%%!?%?!!!%!?!%!!%??%!!%!?!%%!%%?!%!!%%!%!%?%%!!!%%%%%%!%!%%!%!!%%!?%!!!!%!%%%%%!!!?!?%!?%%%%%%%?!!%%%!%%%%%%!!!%!?%!%?%%!?%!%???%!%?%??%%?%%?%%%%!%!%?!!!%???%?!%%!?%!%?%!%%?!??!!!%%??!!%%!%%%?!!%?!!!!%%%%?!!?%%%!%!!%?!!?!?!%!%!%!!%%%!%%%%%%!%%%!!??%!?%%%%?!%!%?!!%!!!%?%%!!!!?!%%!%!%?!%%%!?!%%!!%??%?%!!?%%%?%%!!%?%!%%%!!!!?!%?!?!!!?%!%%%!!%!!%%%%!%!!!%??%%?%%!%%%??!?%?!%%!%%!%?!%%%!%%%!!?%%!!%%%!%!%%!%%%%%%%%%%??%??%?%?!%!!!%%!?%%%?%%!!!??!!%?!!%?%??%%%%!%%!!%%%!!%%%!%?!!!!%%%?!%%!!%%%%%!!?%!%!%!?%%%!%%!?!%%%%%!%%%%%%!?!%%?%%%?!%!!?%?!%!!%!!!%%%%!%%!!?%!%!!%!%!?%!%?%??!%%!!!!%?!%!??%!%%!?!!%?!!!!!!%!?%%!?%??%?!%??%!!!!!!%%??!!!?!?%!%%%%!%%!????%!?%!%%!%%?!%%!?%!!%%?%??%!%%!?%??!%?!%%%?%!!!%%%?%%%%!!%??%?!%%%%%!%?!%%!%!!!?!%%%!!%%%%%%%!!%!%%%%!?%!%!!?!!%%%%?%!%!?%??%%%%%???%!%!!%?!%?!%%!?%?%??!??%?%!!%%!%%!%!%??%%%?%!%!%!!!!%%%%%%%!%!%?%?%%%??!!!!%!%%%%!%?%?%?%%%!!?!%%?!%?%%?%%%%!%%?%%!!?%?%!%%%!%%!!!%%%!!%%%?%!??!?%?%%%%%%!?!%%!?%%!?!%%!!!?!%%????!!!%%%!%?%!!?%!?!%!%!%%!%%%!!!%%!%?%%!%%!%!!!%%!!%?%!!%%%?!!%%%%%!?!?!?!%?!%%!%%%?%?%!!!!%!%!%?%!%!%%%%!!!!!!!?%!%%!%%?!%!%%!!%!?!%!!%%%%%%%!%?!%%!%?%%?%!?%%!!%?%???%!!!?!!%!?%!!??!%!%%%%!?%%?%!??!!!%?%%?%%?!!%%%?!!?%?%%%%!!%%!!!%?!!!%!%%%%!!!!!%%?%%%%!%!%!%!%!%!%?!%??%!!%%%?!!??!%%%?%%%%%?!!?%%%%!%%?!!%?%??%%?!!%%!?!%%%%?%%!%%?%!?!%%!?%!!?!%!%?%%%%%?!?%!!!%%!%?%%?%%%%?!!!!!%!%?%!%%%?%?%%%!%!?%??!!!%%!!%!?!%!!%%%!%!!!!!%!??!?%?%!%!%%!??!%%%%!?%?!%!%%%%!?%%%%!%%%???%%%%%!%%%%%%!!%%%%%!?%?%?!%%%%%%!%%!%!!%%!%%%%!%%??%!?!%%%%!!?%%??%%%?%%%?!%!!%%!?%%%?%%!?%%?%%%?!!%?%!!!%%??%%?!!%!!%%?!%%!!!%?%%!?%%%?%?%!%%%%!!%!!!!!%%%?%!!%!!%%%%%%!%%?%?%?%????!??!%?%%?!!?%!%%?!!!%!%!%?%%!%!%%%%!!%??!%?%!?!!!!!%%?%%!!!%?%%%!%%%!?!!!%%%%!%?!!%%%%%!!%%%%%???!!%!%%%!!%!%%%?%%%%!!%%!?!!!%%%!!%%%%?%%?%!%?%%%?!%?%%!%?%!!%%!%!!?!%!!%!%!!%%?!?%%%!!%%%?%%!%%%%%!!!%%%!%%?!!%!!%%!!%!!??%?%%%%?!?%%%%%%%%!%?!!?%?!!!?%!!%!%%%?!%%!%!%?%%%!?%%?%?%%%%%%%?!%%!!%%!%%!!??%%%%%!%?!??%?%?%%%!%%%%?%!?%%%%!!?%?%%%%%%%?%%%!%!??!!%!!!%%!!%%%%%%?!%?%%!%!?!?%!!%??!%???%!?%?!?%!%?%!!%%%%?%?!%%%%%?!%%%%%?!%!%%?!?%%%%%!?%%!!!?!!%%!!%%%!!!%%%%!%!!!!!!!!!?%%!%?%!!%%??%?!!!!%%%%%%%%!%%!!?%!%!!?%!!!!%%!%!?!!%%!???!%%%%%%?!!??!?!%%!%!%!!!!!?%%?%%%%%!%%!%?%!%?%?%%!!%!?!!%%!!%!%%%?%%?!%!??!!%%%%%%!%?%%?%!!!%!%!!%%!!!!!!?%!%!%%%%!%%%!%%?%%?%!%%%%!%!!!!%!!%!%%?%%!!%?!%!?%%%%%!!%%%!?!!%%?%!?%%!%?!%%%?!%?%%!%?!!%!%%?!%%%%%%%%!!!!!%%%!%%%%!%!!??!?%%??!%?%%%%%!??%?%%??%??%%%!%?!%!!%%%?%%!?!%%%!??!!!?%%!%?!?%?%%!!%%%!%%%!!%!!!?%!!%?%%!!%!%?!?%%%%%%!%!!!!%!%%?%!!!!%%!%!!%!!%%%%%%?%!!%%%%%!%!!??%!%%%%!?%%%%%%%?%?!??!!?%!?%?!!??!?!!%?%%%%%%%%%%%%%!%!%%?%%!?%!%%%%!!%!%%!%%%%!?%%%?!??%?!%%???%!%!?%%?%!?!%%!!!!!!?%%%!%%%!%%?!%%%?%!%%%!?%?%%?!%%!%!%??!!%!?%%!!!!!%!???!%%%%%!!!??%%%!?!?%%!??%%%!!%!?%%!%?%%%?%%%%!!?%%!!!%%!%%?%%%!%!!!%%%%%%%??%%!%!??%!!%%%%?!?!%!!!%?%?%%%!!!?%%?!%!!%%!%!?!%?%?!!%%!%?%%!?%??%%%%%!%!%!%%%!!!%!?%%%%!%%!%%?%!%%%%%!%%!%%??%!??%!!%%!%%%!!!%!!!!!!%!%%?!%%!%%?!!%!??!!%%!%%!!!?%%%%!%%!!!%!%!%%?%%?%!!%%%%%?!%!%%%%?%%%%%%%!?!!%%?!%%!%%%%!%!!!%!%%!%%%!!%?%%%!!%!!%!!!%%%%%%%%?%%%%!!%%!%%%%?!?%%%!%%?!??%%???!!%%%?!!%!%%%?%!%%?!??%%!?!%%%??%!%!%!!!!%%%%?%!!?%%?%%%!?!%?!%!%!%%%%%!!%?%%?!%%!%%%!?%%%!%%%!%%?!!!!?%%%?!%%%!%%!!!!%%%%%%!%!!!%%!!!!%!%!!!%!%!%%%%%%??%%!!%%!%!!%!%?%!%%%%%?!!!%!?%%!!%%%??%!%%%%!%%!%%!?!%%!?!!?!%%%%%%%%!!%%%%!%!!?%?!%%?%?%?!%%!??!!%??%!%??!%!!!%%%%!!??!%%!%!%!%%%%%%%!!?%!%%%!%%%%%!%!!?%!?!%%%!%!?!?%%%%!!%%%%%!!!?%!%!?%!!%%!!?%%!?%??%???!??%%?%%%!%%!%!%!%%%%%%%!!%%!!!?!%%%!?!%%%!!?!%!!%%!!%!?%?!%%%?!%%%?%%!!%!%%%!%?!%!%?%%?!!!%%!%%%!!!%?%!%%%%?%!%!!?%%?%?%!!%%%!%??!!%%%?!!%!%!!!?!!??%%?!!%!%%!%%!%%%%%%!%%%!%%%%%%!?%%!!%%%%!!%%%%%!!%%!?%%%%!%?%!%%%?!%%?%%%%!!!??%%!!??%?%%%%%%%!!?%??%!%!%?%%!%!%?%!%!!!%!%!!!%%?%%%?%%%?!%!?%!!!%!%!%%%!%%!?!%!%%!?%%%%!!%!??%!!?%!!%%%!?!!!%?!%%%%%!%!!%%??!!%%?!!!!%%%!%!%!!%!!%?%!!%!!!%?!%%%%%%!!!!%!!?%%%%%!%%!?%%%?!%%%??%!%!!%%!?!?%%%%!!%!%?!?%!%%%%%%!%%%!%!%?!!?%%!!%!%?!%%!%%%!%!?%%!%%%??%!%!%%%%%%?%!!%!?%%?!!%%%%??%%%%%?%%??%%%!%%%!??!!%!%%%!%!%%%?!!%%%??%!!!!%!%!%?!%!%%%??%%?%!!%%%???!%!%%%?%!%%!!%%%!%%%%%!%%%%?%?!%%%%!%!!!%%%!%%?!!%%%!%!%!%!!!!?!??!!?%??%!%!%?!%!???%%%%!?!!%%%!%!%%!!!!%!!%%%%?!?!!%!%!!!!???!%%%%!?%%%%!%%!!%!!%%%%%%?%%!%!!%!%!!%!%%%%%!%?%%%%!!%!?%!%!?!%%!!?!%%%%%!%%%?!%!!?%%???%%%!!?%%?!!%!%?!%!!??%%?%%%??!!?%!%%%%%%!%%!!?!!%%%?!%%?%%%??%%!%%%!!%%!%??%%%!%?%!%%%!%?%!%%%%!?%?%%?!%%!?%%%?%%%%%%?%%%%%%!%%?%%?!!!!!%?!!?%!??!!%%!%%%%%%%!%%!!!%%%%%!??%!!%!!!!!!%%!%%!%!%?%%%%!!??%!%!%%?%??!%??%%%?%?!%%??!%%%!!%%?%?!%!%%!%!?!%%%%??%%%%!!!!!%!%!%%?!%?%%!%!!!??!!!%!%%%%%%%%?%%%%%%%!%%%!!%%!!??%%?!%!!!%!?%??%??!!%%!%?%!%?%%!!!%%!%%%!?%%%?%?!%%%!%%%%%?!!!?%%???!%%%!!%!%!!!!!%???%%??!!%?!%%%%!??%%%!?!!!%%?%!?%!?%%%!%!??!%%%%!?%!!!%%!?%%%%%%!???%!%%!!%%%%%!!%!!%!%?%%?!?%%??%%%!%!!??!%!?%%!%%!!!!????!??%!!!%!!!%!%%%%%!!%!%%%!!!%!?%%%%!%%%!%%%?!!%!?!!?%!%?!?%?%%?%?!!%!?%????%%!%!%%?!%%!!?%%!!%?!%%!!!!?%?%!!!%%%%%!%%%%!%%%%%%!!%!%!!!?%!%%%!%!?%?!%%!%!%%%!!!%!%!!%%%%%!%%%?%!!?%%%?%!%%%%!%???!%!%!!!%%!!%%!%?!!!%!%%?%?!!%!?!%%!%!!%%!%!%!!%?!?!%%%%?%!!!?!?%!%?%%%%%%%%%?!%!%?!!%%%?%%!!%%%%!?!!!?!!%%%%!!!?%%%!%%?%%%%%!%%%%!?%%?%?%??!%??!??!??%?%%!!%!%!!!%%%%!%%!??!!%!?%!?!?%%%!!!%!!%%?%!%!%!??%!!%%%?!%!!%!%%%!%%%!!?%%%%?!!%%?%%?!!!??!!!%%%!!!%%%%!?!!%%!%!!%%%!!%%?%%!!%!%%%%!!%!!%!%%!%%%!!%!!%?!%!%%??!%!%%?!?%!%!%!!%!%%?!%!!%%%??%%%%!%?%%!!%?%%%%?%?%?%%?%%%!!?%?!%%???%!!%%%%!?!%!?%!%?%%?!!!%%!!%!??%!?%%!!!%%%?%%%?!!%!?%%!!??!?%!%%%!!!%!%%!%?!?%%?%?%%!%%!!%%?!%%%?%%%?%%?!!?%%!%!??!%%%%%%!!!!!?%??%!!!?%%!????%%%?!%?!!%%?!%%?!?%%%!!!%%%?!%%%?%!%?!?%%??%%!%%%%!!%%%%%!?%%%%!%!!!%!!!?!%?%!%%%%%%!%%%!%!%%%%??%!!?%%%!!%%!%!%%!%%%%%!!%%!?%?%!%?!!?%?%!%!%%!%?%?%!!%%!?%!!!%!?%!?!!!!%%!!?!!?!%!%%%%%?!!??%%!?%?!?%!!%%%!%%%!!!%%!!%?%%??!%%!%!!%!%%!%%!!!!%!!?%?!?%%?%!?%!?!!!%%%%%%?%!!%%%%%?!%%%!!!?!%!%!!%!%%%%%!%!???%%?%!%!?%%%???!%%!!!!%%%?%%!!?!?!?%?!?%%%%?%!!!%%?!%!%!??%!%!%%!?!%%!!!?%!%!?%?!?!%%%%%%?!%%%!!%!!!%%!!!%?%%%%?!%?%!!?%!%%%!%%!!%%%%?%!!!%%!%%%!%%??%!!?%?%%%%%?%%%%%!%%!%%%!!%%%%%%!!%!%%!!%%!!!%?%%!%%%%?!%%??%!!?%!%%?!%!!%%%?!!?!%%%%?%%%!!!!%!%??%!%?%?%!!!%%!%%?%%!%!%%!%!!%%?!!%!%!?%%%!!%?!%%%%!?!?%%!?%%!?!!?!?!?!%?%!!%%?!!%!%%%%!!?%!%%!%%!!%%!!!%%%%!%!!!?%%!?!%%!%!!%%%%%!?%%!%!%??!%!!?%!%!!%%%%%%?!!!!%%%%%%%%%!!!!%?%%!?%?!?%!?%%!!!?!%!%!!!!!!!!!%%?%?%%!%%%???!!%%%!%%%%?!!!!!?!%%!%?%!!%?%??!%%!%?%%%!!!???%!%%%!%?%%!%%!%%!%%!%!%!??%!%%!%?!?%%?!?!!%???%%!!%!!!!!%%!?!%!%?!%!!!?!%%?!?!%!%%%%!!%%!!%%%?!!!%%%!%%!%%!%??!%!%%!%!!%%%%?%%!!%%!?%!%%!?!?%?%%?%%%%!%!%?%%%!%!!%!%%!%!%!%%%!%?%!??%!!!!%!!%!?!!%!%?!???!??%%!%!%!!!%!%%!?!!%!!!??!!!?!!?!?%?%?%!%%!!%!!?%%!?%%?%%!%%%%%!%!?!%!!%%!%%!%%%%%%!%%!?%!%%!%%!%%?!!?!%%!%%!!!%%!!%!?%%!!!?%%%%!%%%%%!%%%!%!%%!!!%!%!%%%%%%%%%%?!%!%%%??%%%%%?%%%%%!!!%?!%%%!%!!%%!%!%%%%!%%%%!?%!%%%%!%!?!%!?%?%%%!%%%%%%%!!%?!?%?!!%!!?%!!%??%???%%!%%??%%?%%!%!!?!!!!%!%%%?%%%%!%%!%%%??%%?!%!%?%%%%%%%%!%%%!%?!%?!!!?%%%%!%%%%%%%%%%!%%%%%%%!!%%!%!!%!!?%!%%?%%!%%?%?!!?!!!%%%!!?%%!%?!%%%%%?%?%!?%?%!!!?!%%!%?%?%!%!??%%!%%!%?%??%?!%!!!%%!%!%%!!%?%!!!?!!%%?%?!%%???!%?!!%%%!%!%!%%?%!%%?!%%!%!!%%%!%%%%!!%%%%%!%%%?%%?%!!%!?!%!%%?%%!%%!%!%%!?!%%?!!!%?!?%%%%!%!?!!!%%!!?!%%%!%!!!%!%!%!%?%%?%!%%!?%%%!%%!?!%%%!!%%!!%%!?!!%?!%!?!!!%?%?%%?!%%%%!%%?!!%!%!%%%%%?!%!%!%!?!?%%!%%!!%%%?!!%%?!!!%!%?%?!?!%%!%!!%%%%%%!%!!!?!%?!!!!%!?%%%!%!%!%??%%!!!!%%?!%!%%%%%%%?%?%%!?!%!!%%%%?%!%!%%%!!!?%?%!?%%%?%!!%%%%!!?!%%!?%%!!%%%!!%!%%%!!%%%%%%?!!%!!??!%???%!?!!%%!%!?!?!%!!?%!?%%%!%%?!!%%!!%%%!%??%!?%%!%%!!!??!!%%%?!%%!!%!?!!%%!??!?!%!%%%%%%%%%!!!?%%!!%!%?!?!!%%!%%%%%?!%!%%!%%!!%%%?!!!!%?!?!%!!?!!%%%%!!?%!%?!%%!%?%%%%%%%?%!%%%%!?%!%%!?!!%%!%%!!!%!%!%??%%!%%!%%!?%%!?%!?!%!?!%!!%%!!%%%?%%!%!%%%%%!%%%%?!%%!!%%%%?%%?%%%!!!%!%?%!%?%!!%!%?!?%%!!!%%!!?!!?%%?%!!%%%??%!!%!!%%!%%%!%%!%%?!%?!!%!!!!%!!%%!%!%%!%%!%%!?!%??%!?!%!%%%%?%!!!!!%%%%!?%%!%!%?!%%!%%%%%%%%%!%%?!?%??!!?!%%?%%?!%%%!?!%!!!%!!%!!%!%!!?!%!%!%!!%?!?!?%%%!%%%%%?!?!!!%!!?%!!!%!%!%%!%%%?!%%?!%!%!?!!?!?!?!%!%%%%??%%?%!%%?%!%%%?!!%?!!!%%!%%%!%%%%%?!?%!%%%!!!%%!!%%!%?!!!%%%!%?%%???%?%?%!!!!%!%%!%%!?%!!!%!?%%?!%!%%!%%!%!%!!!?%%%%%!%!%%%!?%%%%!%%%?%!%?!!!%!?!%%%%?!!%%%%%!?!?%%?%%!%!?%!!!?%?%%%!%%!!%?%?!!%!?!%!?%!!?%%%%%%?%%%!%!%%!!%!?!%%!!%%%!!%?%!?%%?%!%!%??!%%%!%!%!%%?%%?%!%!%?!%!%%%%%!!!!%?%?!!%?!%%%!%??!!%%!%!!%!!?%!%%%%!%%%!!???%%!!%%%%%?!%!%?%?!%%?%??%??%%!!!!%!%!??%%%%%%%%%!%!!?!?%%!!!%%%!??%!%!%%!%%!?!!%!%?%!!%%!%!!!!?%%%%?!!!!%%!!%%%!!%%%!!%!!?%%%%%%%%%!!%%%!?!%%%%!%??%?%!%%!%%%%!%!!!!!%!%%%%%%?!!%%%?!%%!!%!%??%%%!%??%%%%??%%%?%%%%!!%?!!?!!%!%%!?!%!%%%!%!%?%?%!!%%%!!%%%?!?%%%!!!?%%%!%%%%%%!!%?!%%%!!%!%!%%%%%??%%!%?%%??!%%%%%!%!%%?%%??%%!%!!%%?%%!???%%!??%??%?%%%%!!%!%??%!%%%?%%!%!?!%%%!%%%?!!%%%!%??%!??!!!?!%!%%!!%!?%!%!?!%%?????%?%%?%%!!!!%!%%??%!%%!%??%?!?%!%%!!%!%?%%%%%!%!?!!%%!%%%?!%!!%?%%%?%%??%%??%%!?%?%!%?%!%%!?!!%!!%!%%%?!%?!???%!!!??!?!%!%%!%?%%!!%%!?%?%!%!!!%%%?!?!?%%%!%%!%%%!!%%%!?%%!%%%%%%?%%!%%%%!!%%!%!%!?!%?%!%!!%!%%?%!%%!!%%!%!%%%!!%%!!?%!%%%%?!?%%!%%%!%%!%%%!!???!%!%%%!%%!!%%%%%%%%%%!%%?%%%?%%!%%%%?????%!%!!!%%?!%%%%!!!%?!%%%!%?!%%!!!!!?!%%!??%%!%%%%%%%%!!%?%!??!!%%%?%!%!%%%?!?!%%!?%%?!%%!%?!%!%%%!%%%%%%%%!%%%%?%!?%?!%%%?%%%!%%%%!!%%%%%!%%%?!%!%??!!!%%!%%!%%%%%?%%%%?%%!%%%%%%!!?!?!!%??!%?%!%??%?%!%%%%%%%?%%%!!!!%%%%%?%%!!%?!!%%%%!!%%?!!%?%!%?!!%%%%?%%%?%!!?%%!%!%%?%!!%!?%%!%%%?%%%!%?%?%!!!??%%%!%!!!!%?%%!%%%%%%?%??!%%%%!!!%!!%%?!!%%%%%%?%%!!%%?!!%?!%?%!?!%%!%??!%!%%?!!!%%!!!!%%%%?%%%%%!?!!!%%%!%!!%%%%%!!?!!%%%!%!!%%%%!%%!%!%%??%!??!?%%?%!%%%!!?!!%!%!!!!!%%!%%!%%%!??!%!%?%?!!%!?%%%%%%%%!%!%?%%!%%%%!!%?%!!!%!?!?%?%%%%!%%%!%%!?%%!?%!!%%!!%%!???%?%!%%!!!%!%%!?%!!!!%?%%%!%%?!!?!%%!%!!!!!?%%!%%%?!!%?%!%!%%%%!!%?!?%?%%!%!%%!?%??!!?!%!?%%!!%!%!?%%!??%%%!%%!%!%!!!%%!%!!!!?!%%?%%!%!!%%%?!%%%?!?!!%!%?!!!!?!!!%%?%%%!!%?!!!!!?%?%!%!%!?!%%%!%?%?%?!%%!?!%%!?%!!!?%!!%?!!%!!%!!!?!!%!??%%!!%!%!!%%!!%%!!!%!?%%%%%!%%%%%?%!!%?!!!?%!?%!!!%!?!%?!%!%!%!!%%??!%%%!%!%%?%!!%?%%%?%%%!?%%!?%!%!%!!%%!!%??%!!%!?!%%%?!%?!?%%%!!?%?%%%%?!!%!?%!?%%?!%!!!?%%%?%%!!!!!%%!%%%?%!!%??!!%!%?%!!%?%%!%%!!!!!!?%!%!%%?!%%%%%%!%%%%%%%?%%?!?!!%%%%%!!?%?%%!%???!%!?%%%??%%!!%%%!!%?%!!%!!%!%?!!?%%%%??%%!?%%%!%%%!!!!%%%!%%!%%%!!!%??%%?%%?!!%!%%%!?%!%%%!%%%%%%!%%%%%%?!!%!%!??%!!%%?!%%?%%%%%!!!!%%!%%%%!%?!!%!%!%%%%?%%%%%?!?!?!!!%!%%!%%!!!%?%!%%%?%!!%%%%?%!?%?%%!!%!!!!%?%%%%!!!%!%!%!!?%!%!!%%%%?%%%!!%!!!!!?!%!!!!%?%%!%!??%!!%!%%%%!%%%%%%%%!!%!%%?%!%%%!!?%!!%%?%!%%!%?!%!%?%!?%!?%%%!?%!%?%%%!%?%%!%!!!%%%!%%%!!%!%!%!!?%!!%!%!!!!?%%?!%%%!!!?%%%!%!?!%!!!%!?!%!%!%%%!%%!%%!%%!%!!%?%!%!%%!%?!!%!?%!?%%!%%!%!%%!!%!%!%!!!?%?%!!%??%!!%?%%%!!%!!!!%?%!%%!!!%%%%%??!?%%?!%%%??%%?!!%!%!?!%!!%%?!%?%??%!!!!%!%!!%%!%?!?%?%!!?%%%!!?%!!%%%!?!%!!?%%%%%?!!!%%%!%%%!!%!!?!%%%%%%%!!!%%?!%!%!!%?!%%!%!??%!!%!!!%?%!%%?%%%?%%%%%%?!!%?%%%%%%?!%!?!!!%%%?!!%%!%%!%?%%!%!%!!%%%?%%!%%!%%!%%!%!!??%%!??!%%?%%!?!!%!?%%%!%!?!%!!!!%%?%%%?!!!%%?!%!?!?%%%!%?%%!!%%%!%!%%!!!%%?%%!%%%%%?%%%%%!%%!%!%%!%!%!%!!%?%%%!%!??%?%!%%%!!!?%!%!!%?!!%%%?!!!%%%%!%!%?%%%%%?%%!!?%%%%!%!!?!%%!%%!!%!%%?%!%%!%%%%%??%%%!?%!!!%%!%%%!!%%%!%%!!??%%!%!!!%%!!!%?!!%!?%%!%?!%?%!!!%%%!?!??%%%%!!!%??!%!%!!?%?%!%!?!%%%%%!?!?!!!%%!!%?%%%!%%%%%%%!!!!!?%%%!?%%%%!!%%!?%%%!?!%??%??!!%%%?!!%%%%%%%%%%%%!!?%%?!!!!?!%%%%%??!%?%!%!!%%?%%%!!%%!?%%??%%!%%%!?%!!%!%%%%%%!%?%%!%%%!!!!!%!%!!?%?%%!%!%?!?%%%%%%%!%!%!!!!!!%!%%%!!%%%%%!??%%%?!%%%%%%!?%%%%!!??!!?%%!%%!%??!%!%?%%%%%?!%%!%?%%%!!%%!%!!%?%%%%%!?%%!%%?%%%%%%%%%%!%!%%%%!%!!?!!!%!!!%!!?!?%!!!!%%!%%?!%%!?!!%!%?!!%%%?%?!!%%??%%%?!?!!!?%?%??!%%!%%%!%%?%%!%!!?%!%%!?!?!%%!%!!!%%!!%!!!!!!!%!!!?%%%!!!!!?%!%%%!%%!!%%!%???%%!%%%%%?%%!!%?!?!!!%!?!?%?!%%!!??!%%%?%!%%%!%%!?%!!%%!!?!%!%?%???%!%%??!!?%%!%%!%%%??!%%%%%?!%??%!%%%!!!?%!!?!?%%?%!?%%%%!%%%!%?%%%!!?%%%%!%!!%%!%?!!%?%%!%%!%%%?%%%%!%??%%%!%%!%!?%!?%??%%?!%!%?!%%?%%%%%%%%%!%%?%!???%!?%?%!!!%%!%?!%%!%?!%%%%!??!!!%!%?!%%!%%!%%%?!%%%?!!%%%%!!%%?!!!!%%!%%%%?%!!?!!%%%%?%%?%!%?!?%%??%!??%!%%%%??%?%?!!%!!!%%%%!%%%?!%%%!!%%!!%!!!%??%%%?%%!?%!%%%%%?%%%%?%?%!%!!?%?%%%!!%!!!%!?!%%!%?!!%!%!%%%?%!%!!?%%!?%%!!!%!?%%%!%%%!%!!!!!!!!?!%%%!%%%%!?!%%%!?!%%!%%?!%%%%%%%%?%%%!!%%%%%%?!!%?%%!!%?%?%%?!%%%%?%%??%%%?%%%!%%%??%%%??%!%%%%?!%%?%!%!?!!!%!?%%?%%%%?%%!?!!!!%%%!!!!!%%%?%!!%%%!%%?%%%%!!%!!%!?%%?!%%%%%%%!!%%??%?%%%%!%?!???%?%%!!%!%?%%%!!%%!%%%%%%%!%!%?!%!%%%%!%%%?!!%?%%??%?%%!!!%%!%??!%!!%!%%!!%?!%!!%??%?%%%!%!!!!!!?!!%?%%%%!!??!%%!?!!?%?%!%!%%!!!%%%??!%%%%%%?%?%%?!!%!%%?%?!%%%??%%%%?%%?%!%%%%%!%%!?%%!%!%%?%!%%?%?!!%!%!%!%!!%!%%%?%%!%?!?%%!?%!%%%%%!%%%%?!%!%%!!!%!%!%!%%!!?%?!%%%?%?%!%!%%?!!%!%!%?%??%%%?%??%!?%%%%%%!!%?!%%%!%!!!!?%?%?%!%%%!!%%?%?%%?%%%%%%%!%%?%%!%%!%%??!!!%%%!%%%?%!?!%!%%%!?!?%%!!%!!%!!!%%%%%%%?%%%%%%?%%%!!%!%!!%%%%!!%??%!!%!?%!!!!%%!!%!?%%!%?%!%%%%?%%!!%!%%%?%%?%!%%%!?!%%%%%!?!%!!!?%%?!!%%!?%%!!%%%%!%%!!!%%%%%?%%?!%!%!%!%!%!%%%!!!%!?%%??%%%%?!%%!%!?!!%%!!!%?%!!%!%%!!%!!%%?%%!!%%%%?%%%!!!%%%!%!!?!%!!%%!?%%%!!%%%!%!%!%%!%!%?!?!!???%?%%%!%%!%%!%?!%!%!!%%%!?!%%%%%%%%!!!%%!!!?%%%%%!??!%?%%!?%!%!%%!!!!!%%!%!!!%??!!%!%!%%%%%%?%??!!%!!!%%%!%%%!%?%%!!%%!%%%%!!%?!!?!%!%?%!!%%!%%%%?%?!!%%%!%%??%%%%?!!%%!?%%%%!%!?!%!%!?!%%%!%%!!%%!%!%!%%!?!%%?%%%??%!??%%!%!%%?!!!?%%%%%!%!%%?%!!?!?%!%?%!!%!?!!%%%!?%%%??%?%!!%%%!%%!!%%%%!%!%%%%!%%%%!%!%%%!?!!!??%?!%?%!%!!%%%!%?!!%!%!%?%%?%!!%%%%%%%%%%%%!%?%%%%%%!?%%%?%%!%%%!!?%?%!%%!?%%%%%!!?%!!?%%%%!%!%!%%%%!!!?%%%?%!??!%??%!%?%!!!!%!!%%??!%%?!!?!%%%%%%!??%%?%!!?%%!%!?%%!%%%??!%%%!%%!!%%?%%!?!!%?%!%%%!?!??!!%!?!%%%%!%%%??%%!!!%!!!%!%%%!!??%%%?%!!!%%%?%%%%%!%?%!%%%%!?%%!!?%%%!?%!!%%%%%%!%!!%%%%%!%?%!!%%%%!!%%?%%!%?%?%!%!%%%!%%!%!???%%??%%!?%%%%%%%?%?%%%!!??%%!?!!?%!!!%%!%!%%%%%?%!!%%%%%%!!!%!%!%!%!%%?%?%%?%!?%%!?%?%%?%!!?%!%%!%!!!?!%%!%%!?!?%!!%%%!%%!!%%!%%??%!%%%!!%%?%!!!%!%%?%%?!!!!?%%?%%!%%!?%%%!!%?!!%%%%%!!?%%%%%!%!?!%%?%!%%?!!%!%%%%!%!?!!?%???!!!!%%!!?!?%!%?!%!??%%?%?!!%??!%%%%%%%%%%%!%!%%%?%%??!!%%!%%%%%%%!%%%!%!!!%%??%%!%!!!?%!%!??%!%?!%%?!!%!%!%%!!%!%!?!?!!%%!!?%?!%%%%!%!???!?%!%!?%?%%%!!!%!!?%%!%?!!!!!%%!%!%?%?%?!%!??!%?!??%!!?%%!%!%?!%%?!?!!%!!%!%!%!!?!!!%!%!%!!?%%!!!%!%%!!??%%!!!%??%!!!!%%!%%%%%?!%!?%!!%!!?%?%!?%%%%%%%!?%%%%!!!!!%!%???%%?%!%!%%%%%%%!%%%%!!!!?!%%?%%?%!!%%?%!%%?%!%!%%!!%?!!%!%!%%%!%?!%?!!%%%%!?!%%%!?!??%!%?%%%%!!!!%%!!!!!%!%%?%%%!%%%??%?!%%!!??!!!?%%%?!?%?%?%%!!!!!!!!%%%!%!%%%?%!%%!%!%!%%%!???%?!%%!%%!%%!?%?!%!%!?%%%%!!%?%!!%?%!?%??%%%???%!?%!%%%!!%%%%%%%%%!%%?!?!%!%%%%?!!?%%%??%%%%%!%%%!%!?!!%!%%!??%%%%%%!?%%?!!?%!?!%!%!%%%!%?!%%!%%%%%!%!?!%%%%!%?!%?%%%!!!!!%%!%!!%!%%%!!%%!%%%!%!!%%?%!!!%%!%!!%!%%%%!!%!?%%%??!?%!%%%!!%!!?!%!!%!!%!%?!!!!%%%%%!?!!??!??!%!%%%%?%?!!%%!?!?!!%!%?%!%!%!??%%%!?!?%%!%!!%!??!%?%?%%!%!!%!!!%%!!!!!%!%!!%%!%!?%%?!???%%!%!!??%%%!%?!!???!%%?!%%!%%??%%%!%!!%%%%!%!!%%?%??%%?%%!%?%?%%!%%%%!%!%%%!!%!%%?!%%!%!!%%?!%%!%%!%%!%!%!%!%%!%!?%%??%%%!%!%%?!%!%!?!?!!!%!%!!%%?!!!%%%%%%%%!%%%%!!%!%!%?!!!%%%%%?%!!%%%%%%%%!%%?%!!%!!%!%%!!%!%!?%%%%%!!?!?!%%%%?%%!%!!%!%!!!%!!?!!?%%!?!!??%%%%%?!!%%!!!!%?!!?%%!%?%%%%%!!!%!?!%%!!!!!%%%!!%!%%?!%%!%%%!!%%!?!%!%!!%%?!?%?%?%!?%%!%!!%%!%?%!?%!!%?!!%!%?%%%%!%%%?!!!%%!!!%%%!??%!%%!?%!%!%!!!!%???%!%?%!%%!%%%%%%%%?%!!%?%!%%!%!!!%%%?!%%%%%%%!%?!!!??!!!?%!!!%%%%%%%%%!%?!!%%?!!!!!%?%!!!%?!??%%??%!!%%%!%%%%!%%?%?%%%%%?!!!!!%!!!!%!!%!!?%%%%?!!!%?%%!!%%?%?!!!%!%%?!%%%%!???!%?%%%%%!!%!?%%%%%%%%%%?%??!%%?%%!%%!!!%%%?!%!?!%%%!%!%!?%%%!%!%%%!%%?%!!!%%!%%%!%!%%%%%!!!!%?%?%!%?%%%!%%%!!??%?!%%%!!!%%!%?%!%%%%!%?!%!?!%%%%!!%!%%%%!%%%%%%%?%?%%?%!%?!%%!!!!!%!!%%!?!!%!%?%!?%?!%?%??%!?%?%%%%%%??%?!??!%%!?%!!%!!!%%?!%!%?%%!?!!%!%%!!%%!?%!%!!!%?%%????!%!!?!%%?!!!?!%%%!%%?%!%???!%%%!%!%%%!!!%???!!!%%%!!%!%%%%%%?%%%!?%%?!%?%?%!%?!!!!%%%%!%%!!%%%%%!!%%%!%!%%%%!!%!?!%%!!%!?!%%%%%!!!%???%%!%%!%!!%%%%%%!%%%!!%%!!%%!%!!%!%!%?!!!!%?!!%!??%?%!!!!!!!%?!%!!!%%%%!??%?%%%!%%!%%?%??%?%??%%%!%?%!!%%?!?%%??!!!%?!%%!!%?!?!?%!%%%%!!%!%%%?!?%%%%%!!?!%??%!?%%%%!%%!!%%!%%%%%?%%%?!%%%%!!%%!%?%!%!!%%?%%!%%!!!%%%%%%%?%!%%%!%!%%?%?%%!%??%%!%!!%!!!?%?%%!!%!%%%?%%!%%!!%%?!!%!!?%!!%%%!%%%%%%%!%%?%%!%!%%?%%%%?%%!%%%!!%%!!?%%%%%!?%%!??!%%?%!%%!%%!!!%%%%!%%%%!!??!%!?!?!%%?%!!?!?%%!!%%%%?!?!!%?%!%?%%%%!?%%!!?!!!!%!%%%%?%!%%!%%%%??%!%%!!%!!!!!%!%!!!!!%?%%!!?!%%!%!%%!%%%!%%%?!!!?%%%!?%?!!%!!%%!?!%!%!!!!!%%?%%%%%%!%%?%%!%!%?!!%%!%%!%%%?%!%!%%%%!%!!??!!%%%?!!!!!%??%?%%!?%%?!%!?%%!!%%%%!?%%%%%?!%!!!%%!%%%??%%!%%%%%%%!!%!%%%%%!%!!!%%!%!!%%!!!?%?!!!%%%!?%%%!%!%%%%%!%%%%?!%!!!??%%%!%%%??%??%%?!%%!%%%%!%!!%!%%!%!%!%%!!?%%%%%!!%!!!%!!!%%%!%?%!?%%!%?%?%!!!!!%%%%%!!%??%!!!%!%%?%!%!%%%%!!%%?!%!!%%%???!%!%?%%%%%!%%%?!%%%!!!!!!%%?%!!!%%!?%%?%%%%%!%%%!?%!!!%!%%!!%%%%?%%%?%%?!?%%!!%?%%!%?%%%%%%!%%?%!?%%!!!%%%%%?%??%%%!!!!%!!?!%%%?%%!?%%%%%%%%%?!?%%?%%%!!!!!%?%%%?!%%%%%?%!%%??!?%?%!%!%%!%%!%!!%!!!%%!!?%?%?!%?%%????%%%?%!%!!!%%%?!%%??!%!?!%%%%?!!!%?%%%%%?%!!%%%%?%%?%%%!?%!!%?%%%%%%?!%!??!?%!!%%%%??%%%%!%??%%??!?%%%!%!%%%%!%%!!%%%!!%%%%!%?%%!%%%%?%%!?!%?%!!%?!%?%%?%?!???%!!%!?%%%?%?!?%!!%%%%%!%?%!%!?%%%%%%!%!%%!%%!?!?!%%%%%%?%?!!!%%%%!%?!%%?!%?!!!%%%%!?!%%!!!%!%%?%!!!!%%%?!%%%%?!%?!%?%%%!!%%%%%%%%%!!?%%%%!?%!!!!%%%!%%!!%%%????!!%%!%!!!!!!%!%%!!%%?!%%%?!!%%%%%?%%%%%%%%%??!!%!!%%?%?%%!%!!%%%%?%%%!%!!%%?%!?!%%%!!%%?!%%%!!%?!%!?!%!?%?%!!!!%!!?%%%%!?%%!!%??%!%%%%%!%%%!?!%%!!!%??%%!!%!!%!%!%?!!?%?%?!%%?!!%%%?!?!%!%%!!%!!%??%%?!%?!%?%%%%%%!?%!?%!%%%%%%%%!!?!??%%%%!%%!%%!%!%!!%%!%!!%%%!!%!%?%%%%%?%!%%!%!!%!%%?%%!?!%!!!!?!%%%%%%!!!!!?%??!%!%%?!!!?%?!%%!!?%%%%!!%!%!?%%%%!%!%!!%?!?!!?!%%%%%!%%%??%%?%%?!%!%%!%%%%?!!!%???%?%%%%%?!!%%%%!?%%!!%%%!%%%%%!!%?%%?!%??%%%!!?!%%%%?!%%%!%!?!%%%%!%%%%%%!%!!???%%?!?!%%%%?%!%!%!%?!%!!!!%!!!%%!!%%!%%%?%%!!??!%?%!!%?!%!?%!%!%%%%!!??!%!?!%%%!!!%!%%?!%%%%%%!!%%!%?!%%?!!?!!?!%!%%%!?!!!%!??%%%!?%!!?%%%%!%%!%%!!%!%!!?%%!?%?%%%?%%!%!!%!%%%%%!!%?!!??%%%?!%!%%!%%!%!?%?!%?!?%%?%%%!!%%!%%??%!%%??%!%!%!!?!%!%!!!?%%%!%%%!%%%%%%?%??%%%%!%%!!%!!%%!%%!%%%?%%!?%%?%?!%%%%!?%%??%!%%%%!%%%?%!%%??%%%%%!%%!%!%!!%!%!%!!%!%??!?!%!!!!!!%!!%%?%!%%!%%%%!!%!?%%!?%?!?%!%%%?!!%%!?!!%%%!?%!%%%%%%!!!%!%%!%%??%!!%!%%!%%!!!%!%?%%%!%%%??!?%!%!!%%!%%!%!!%%%!%%%%%%!%%%%!!%!%?!%???!%!%!%%!%!%%!!%%?%%!!%%?%%?%!?%%??%!!!%%!%!%%!%%!?!%!%?!!!%?%%%%%?%?!%!%%!%%%!%%!!!%!%%!!!%%??!!!?!!%%!%?%!%%%!%!%%?%%!%%?!%!!?%!?!!?%%!%%!?%%%%%!!%%%?%?!??%%!%!?!??%%!!!!!%!?%%%?%%%%%%%%%%??%%%!%%?!%!%!%%%?%!%%%??%!%!%!%%!%%!%%%!%?%?%%%!!%!!?%%?!?!%%!%%?!%%!?%!%!%%!!??!%%!%!!%%!!%!%?!!!%?!!%%!%!!%%!!%%!!!!!%!?%!%%!%!?!%%!%%%?!%!%!%%!!!!%!?%?%?!!%%%!!%%?!!%%%?%?%%!%?!!%?!?%?%%%%%%%%?%!!%%!?%%?%%!!?!%%%!%!%%%%?!!%%!%!%!!?!???%%%?%?!!!%!!%?%%%???!%!%%!!!?%%??!%%?%%!!?%%%%!!??%!%!!!%!!%%%%?%?!%%?%%?!!%%%%%%!%?%%!%%!?%!%%!!%?!??!!%%!?!?%%?%?%!!?!%%%!%!!!%%%%%?%%%!%%%!%?!!%?%%%%!!%%%!%%%%!!%!%%!?%!%!%!%%?%%!%?!!%!!%%%%!%%!%!!%?!%%%%!!!%!?!%?%!%!%!%%%%%!%?%?!%?%!!!?%?!!%?!%%!??%!??!%%%%?%%!?!%%!%%!%?%%%%%!%!?%%%%%%!?!?%!%%%??!%?%%%!%!?%%!!%%!!!!?!!!%%!%%!%?!!!?!!%!!!%%!!?%!%%%%%!!%!%?!?!%!!!%%%!%!!!?%!!%!%%%?%!%%%?%?!%!%%!%???%%?%%?%?%%?%%%%%?!?!%%!%?!%%%?%!?%%%%!%!???!%%%%!??%!!?%%%?%?%%??!%?%%?%?%!?%%%!!%%!%%?%%%!!?%%%!%!!%%%%?%?!!%%!?%%%!!%%?%?%!%!%%?!%%!?%!%%%!!?!!%!!?%%%%%!%??%!%%!%?%%!%%!%?%%%%!?%%%%!?!%!%%?%!%%%%!?%%!?!!!%!%!!%?%%!%!%%!%?!%%%!??%!??%%!!%?!%%!!%%%!%%!?%%%%!%!%%%!!?%%?!%%?!%?!%%%%!%!!!!%%%?!%!%%!!%%%!!%!%!%!!%!%!!!%%%%%??!%?%%%%%!!?%%%%??!%?%%%?!?%%!!%!!%?!%%!??%%!%%!!%??!!%??%???%!!%%%%%!!?%!?!!!%!!?!%%???%?%%!!!%!%%%?!%!%?%%!!!!!!%%%%!%!%%?!??%%!%%??%!?%%!!%?!?!%!?!?!?!%!%!%%%%?%?!!%?%%?!!!?!%%%!!%%%%%%%%??%%%%%%!%%!!%%%?%!!!?%?%!!!!!?!?%%%!%!%%?%%?!!%%%!!%!?!%%%%?!!%%!?!?%%!%%!?!!%!%%%%%!!!?!%%%!!!%?%?%!%%%%!%%!%%%!%?!!!%!!!%!?%??%!?!%%!%!!%?%!?!?%%!%%%%%%%%?!?%%%!%%%%%%?%%!!%%?%!%!%%%!%!%!%!!%?!!!!?%%%?%%%%!!%%!!%%%%%%%%!!%%%%%%?!%%?%!%!!?%!%%!!???!%!!!%%%%!!?%%!!!!!%%?%%%%%!%%!!!%%?!%!!%!%%!!!!%%%!!!!?%!!?!??%%?%!?!?%??%%!?!!!%%?%!!!!!?!%%%!%?%!!?!%%%%!!!!%!%!%!%%!!%%%!%%%!?%%!!%%%?%%%%!!%%!?!%?%%!!!??%?%%!%!%?!!%%!!%!%%%%%%%!%%!%!?%!!!%!!%%%?!%!%!!!%%%%?!%!%!%%%!??!!%%%!%!!!!?!%%?%%?%%%%!!!%?!!%%!!%!?%%%%%!%!?!%%!%?%%%%%!!!!%!%!!%!!%?!!%%!!%!!!!%!%!!!!!%???!%%!!?%%!!!!!??!?%%!%?!!%%%?!%%%%%%!%%%?!!!!!%%%!%!%%?%!%!?%?%%%!!!?%%!%%?%%%?!%%%%??%%!!%!??%%%?%%%%%!%%?%!%!?%%%!%?!%%?!%%%!%%!%%%?%%?%?%!%?!?!?%!!!!%!%!%%%!%?!%%?%%!%%%!!!?%%!%%%%%?%%!%%%?%!%?%?%?!%%!?!!%%%%?%%!!%%%?%??!!?!?%!%%?!?%%%!!%!%%?%%!%?%%%%%%?!%!!?%!!?!!%!%%%?!?!!!!!!%%!%%%?%!!!%%?!?!?%%!%!?%%!!?!!?%%%%%?%%%%%!%??!!!%?!!?%!%%%!?%%!%%!%!%!!%%%%%?%%%!??%%%%%%%%%%?!%!!%%%%%!?%!%%%!!%%%!!!?!!!%?!!%?%??%!%%??!!?%%%%%!!?%%?%?!%!%!!%%%%!!!!%%!!!!%%%!%%?!%!!!??%?!%!!%%!?%!%!??%!?%%%?%%!%%%!?%?%!!!!?!!!%%%!!!!%%!%?%%%!%?%%?!%%!%?%!%!?%%?!%!%%%!!%%%%%%%!%?%%!!%??!%%!?!???%??!!%%?%?%!%!!!%%%%%%%%%!?%%%?%!!%%%%%!!%???%!%%%!!??%!!%%%%%!!!!%?!!!?%%%!%%!!!???!!?%?%%%!?!?%!%%!?%!%!!!??!%%%%!%%%%%?%%%%%!!%%!?!!%%%!%%?%%!?!?%%%?%!%?!%%%?%%!%%!%!!%?%!%%!!?%%%???%%%%%!%%%!%?%?!?%??%!!!!%?!!?%?!%???!?%%!!!!%?%?%!%?!%??!%!!?%%%%%!!?%%!!!%%?%%%!!%?%?%??%%%%!%%??%%!%!%?%?%??%!!%?!???!%!%!%?%!!%??!!%%%%!%???%%%!!%!!!!%?!!!?%%%%!!%?%?!!%%%!?!%!%%!%%!!%!%%%%?%?!!%!!%?%!!!!!%%!!%!%!?!!!!%%%%%!!%%!%!%%%!!%!%%!!?%%%%%!%?%!%!%!!!%%!%%!%%!?!%?%%%%!?%%!%!!!!!%%%%!%!%%!%%%%%%%%?%%?%%!%%%!%!%!?!%?%%?%!%%!%?!%!!?!?%%!%%!?%%!!!?!!!%?!!%!?!%%%%%%!%?!!!!!%??%!!?%%%!%%%%!%%%%!!%%?!!%%!!!%!!%!!%%!!??%%%!!!!%?%%%!!!!!!%?!%%!%?%!%?%%!?%!%?%?%?%!!!!%?%%%!!!?%%!%!%?%%%?!!%!!%!%?%%!%%%%!!%%%!%?!%%%?!%!%%%?%%!?!%?%?%!%%%%!!%%!%%!?%%!!%%%!?%%%%%%????!!%!%?%!%!?%!!%%%%!%%%!%%%!?%?%%%%!??!?%!!%%%!%%%%?%!%%%?!!!%%?%%?%!!%!!!%%%!%%%?!?%%??!!!%?!!?%%%%!%?%!%!%%%!%?%%!?!?!!!%?%%??!!%%!?!%??%%!%%?%!%??%%%%%!%%%!!!%%%%%%%%!%%!!%!%!%!!%!!?!?%%%%!%?%!!!%%%!!???%%??%?%%!%%%?%%%!!!%!?%%%%%%!%%!%?!!!%%?!%!!!%!%%!!%!!!%!%%%%%!%%%!!%%%%%%%%?%?!%%?%%%%?%?%%!!?%?%!?%%!!%!%!%%?!?%?%!??!?%%%!!%!%!!!!!!!!%!!?%%%??%!!!??!!%%!%!%!%%!%%!%??%%!!%!%!%%%!!%%!!!!!%?%%!%%!%%%!%!%%%!%%!%%%!!?!%!%!!!%%%%!!!%!%?%?%!%?%!!!?%!!%%%!?%%%%%!%!%%%?!??%!%?%?!%!%%?!%!?!!%!?!%%!?%%??!%!%%!%!??%?%!%%%%!?%%%%%%?!!!%%!%%!!!%!!?!!%%?!%!%%!!%?!!?!!%%%%%?%%!%%?!%?!%?%!%%%!!!?!!%%?%!!%!?%%%%!!!!%%?!%?!%%??%%%%%?!!!!%?!%%!%!!%!%%!!!%%%!%%!??!!%!%!!??!?%!%%%!!?%%?!%%!%%%?%!%?!%!!%!%!!!%?!%%%!?%?%%%!%!%!%!!%%%%!!!!?%?!?!%%!?%!!%!%%%%%!%%%%%!%!%!%!?!?!%!%%%?%%!?!??%?%!!%%!!!!!!!%!%%!!!!?!?!!?%?!!!??!%%%!!!?%!!!%%!!!!%!?%!!!?!%!%?%!%!%?%%%%!%??%!%?!!%!!%!%%!%%%!%%%%%??!%??%!%!!%%%?%%!%?%!?%!%%!!?!%?!!!%!?%!%!%%%!%!%!%%%!%!%!%%%%!%!!%?!??!!?%%!?%!%?%!!%!%!!%!%%%%!%!%%!!!!?%!%%?!!!%%?%%!%!!%!!%%%%!%!?%%!?!!%%%!!?!%?!%%!!!%!%%!!%%!%!%%%!!?%!%%%%!%%%%%!??%%?%!?%%?%%!%%%%!%%??!!!%?%?%!%!??!!!!%%!!%!?%?!%%%?%!!!?%???!%%?%%%!!!%%%?!%%%!?!%%?!%%%!??%%%%!?%%?%??!?%!!%?%%%%%?%%?%%!!%!?!?!?!?%!%%?!!??%%%!%%?%%?%!!!%!%!?%%!%%%!%!!%!%%!!!%%!%%%%%??%!!%?!!!%%%!%%%%??!!?%%!%%%!!?%??!%!!%!!%%?%%??%!%!!?%!!?%??!?%!%!%%?!%?!%!!%?!!!?%%!%%!%%!?!!%?%!!?%!%%%?%%!!%!%%%!%%%!%%!!!%!%%%!%%%!%?!%!%%?%%?!%%%%%!%!%!?%!%%%%%?%!?!%%%%!%?%!!%%!!?!!?%%%%%%!!%!!!%?!%%!!!?%%!?%?!!!%%%?%%%!%%?!%%%!%%!?%%!?%%%!%%%%%%%%!!%%%%!!%%%!%?%!?%%?!%?!%%!!!!?%%??%!?!%%%!!%%%?!%%%??!%%%%?!%%%%!%%!%%!!%%!%%%%%%?%%%!?%%%%%!??%%%!%??!!%%!!%!%%?%%?%%%%!!%!%!%!%%!?%?!!%!!%?%%%!%!!%?!%!%%!%?!!!%%!?%!!%%!%%%%%%!%%%%?%%!%!?%%%!%%%%?%%?!?!%%%!%%!?!!?%?!!%!%%??%%%%!?%?!%?%%?%%%%%%%%!%!!%!!!%%%!!?!!?%%!!%!!!%!%%?%?!%%!!%?%!!!%%?!!?%!%!%%%%%%?%%%%%%%!?%%%%?%%%%?%!!?%%?%?!!!%!!!%%!?%!%%?%?!%%!%!!!??%%!%!%!%!%%!!?!%%%%!!%%%%?!!%!%%!!%%!?%!!%%%%!!!%%%!%!!!!!??%!%%!!!?!%?%?!!%%!!%!!%%%%?%!!%!%%%%%%%??%%!!?%!!%%%%%!!!!!%%%?!!!%%!%%%%!!?!?%%%%!%!%!?%%!!!!!%%!?!?!%%!?%?%??%!?!%!%!!%!!%%%!%%?!!%%!!!%??%!?!%!?!!!%%%!%?!%!!?!%?%!!?%%%%%!%!?%!!%%?%%%?!%?!!%!!?!%%%?%!%!%?%%%?%!!!%%%%%%!%!??!%%?%%%%!!!!?%!%%%!%?!%%%%%%!%?!!!%%?!%%!!?!%?%%%%%?!%??%!%%%%%!?!%!!!%%??%!?%%!%%!!?%%!?!%!%?%!!%!?%%!??!%?%!%%!%!%!%%%%!%%!!%%!!%?%!?%!%%%%!%!%%!%?%%?%?!!?%!%!?!%%!%!!?!%%?!%?!%%%%%%!%%!%!%!%%?%!%%%%%%!!%!%???%%!%!%%%?%!?!!!%%?%%!??!%%%!?%%?!%?!!%%!!?%%%%!??%!!!%!%%!%!%%!%%?!!%%%%!?%!?!%?%!!!%%%!%!!!!!!%!!!!%?%?%%%!%?%?!!%!%%%!!%!%%!!!%%!!%%%!??%%%!%!%!%!?%%%%?!%!%!%??%?%??%!%%%!?%?%!%%!!?!%%%%%!!%%%?%!%%%??%!?%!%%!%!!!!?!!%!%?%!%?!!%%!!?%%%%%%?%%??!!%?%?%!!%!!%?%%!!?!%?!?%%%!!!!%??!?%!%!%%%%??!?!%!!!%%%%%!%%!?%%!!!%!?%%!!!?%!!!?%!%??%!!%%%%??%?!!!%%%%?!%%?%%%%?%!%%!%?!!%%%%!%%?%?!%%%??%!!???%%?!!%!%!!?%%%%%%!!%!%%!%%%??%%%%%%?!%%%%%!!%%!!!!%!??%!!%?!%!%!%%!%%!?%%%%!?!%!!?!!!?%%%?%!%!%%%!!??%?%%%%!%%?%%!%!!!!%?!%%!%!?%%?!!?%!!?%%?%%!!%?!%%!?!%?!%!%%!?%%?%!!!?%%!!%!!%%%%%%%%%!%!!%!%!?!!%%!!!%%!%??%!?%%%%!!?%%%!%?%%!%!%!!%!!%!%!%!%%!%!%!%%%!!!?%%%%?!%!!!%!!%%%%%%!%%!%%%!!!%%!!!%%!!%%?%%!%!%!%%!%!!?%!!%%%%%!%?%!%!%!%!?!%!??!%?!?%%%?%%!!%!%%!%!?%%!!%!%%%%!%%%!!%%%?%!!%!?%!%??!%!!%!!!%!%!%%%%%!%?%%!%%!?!%!%?%??%%!?%?!%!%%?%%%!?%???%!??!%%%!%%%%%?!%%%%!!!?%??!!%%%%?%?!%%%!%%%%%%!!???%%!!??%!!!!%%?%%%%%%!%%%%%!?%%%%!%%!!%!%!%!!%!%!!?%?!%!?!!??!??%%!?%%%%%!!!!!%!%??%%!%%%%%!%!%??%%%%%%!%!%?!!%!!!!?%!?!??%!?%%%%%?%!!%!!%%!!??!%?!!!!%???%!!?%%%???%%%%!!!?!!%%%%!%%%%?????!%%!!%!!%!?%%!?%??%%%!%!%?%%%!!%?%%%%!!%!%%%!?%%!!%!??%%%!%%%%%!%%%%%?%!!!!%!?!?%!%??%?%%!!?!!!?!%!%%%%!%!!%?!%!%%??%!!%!%%%%!!!!%!?!???!%!%?%%?%?%!!%!%!!??%!!?%!%!!%%%%%%!%%!?!%%%?%!%??%%!%!!%!%%!%%!%%%%!%!??%%!?!%%!?%?!?!!!%%?%!%%%%?%%%!!%%%!!%!!!%!%%%!!?!%!!%!!%!?%%%%%%%%!%%%!?%!%!!!%?%?!%!!?%%!%%!%!%%!?%%%%!?!!!!!%!%%%!%?%%?%%%%?%?%%%!!!!?%%%?!!!??%?%%%%!?!%!%%?%%!%?%?!%%%!!??!%%!?!!?%!!?%%?!%!!%!%%%%%%!%%!%%%%!!%%%!%%?%%!%?!%!%%%%!%!!%?%%?%%?%%?%!%!!!%%!!!!!%%!%?%%!?%!?%%%%%!!%!?!%!%%%!%%%?%!!%!%%%%??%%%%%%?!%%?%%%!?!?%!!%%%!!!!%%!%!%?%?%%%!?!%%!?%!%!!%!%!!!%%%!!!?!%%?!?%%!?%%!!?%!!%!?%!%%?!!%!%!%!%%?!%%?%%%!!!!%!%%%!?%!%%?!!%%%%%!!!!!!%%%%%%!!%!%!%?%!%?!%!!!?%?!%?!!%?%%?%?!%%!!!%!%!%%!!?%%%%!!?%%!%!!??%%%%?!!!!%%?!??%!!%?!!%%%!%!?%%%%%%??%?!?!%%%%%!!%!%%%%!%%%%!?%!%!!!!%%!!!%%%!%%%%%%?%%%%%%%?%!%!!%!?%??!!?%%!!%?%%!%!%%%!%!%!%%%%%??!!%%%%!%!!?!????!!?%!!?!!%%?%%?!!!?%%%?%!?%%%!%!%%%%!!%%%%%%!%%%%!!?!%!%?!??!!!!%%%%?!!%!?%%%%!!!%%!?!%%?%!%!?%%%%%%!%?!%!!!%%?%?%%!!%%%?%!?!?%!?!?%%%%!!!%%%%%?!%%!%!%%%%!!!%!%%%!!?!%?%%??!%%%?!?!!%?%!?%?%%%!?%%%%!??%%!%%!!!?!!%%%!!%%!%%%%%%!%!!%%!?!%?!?%!%%%!!!%!!!?%?%%?%%!!!!%!%!%!!!%!%!%%?%%%???%%%%%!%%%!!!!?!%%!!%%%?%?!%%!!!%?%!%%!!%%?!%!!%???%!!%%%?!%%!!!?%%!%%%!%!??%%%%!!%%%!%!%%!!%?%!%!!?%%%?%??%%!%%%!!%!%!%!%?!!??%%!%%%%!!%%!?!!%%!%!%%!%?%!%%%!!!%?%!%!%%?%%!%!%?%!%%?!%!%!?!%%!%??%%%?%%%?!!%%%%!%%%?%%%!!!!%?%!?!%%%%%%%%%%%%%%%?%%%%%!!!?%?%!%!?!%%!?%?!?%?!%!??%%%%%!%!%!!%%??%!%%%?!!?%!!!!!!!%!!%%%%!?%!%!!!?!%!%%??!?%%?%?!?%!!!%%%%!%%?!?%!%%%!!!?!%%%!%!%?%%%%%!?!%!%?%???!!%!%%%!%%!!!!!!!%?!%%?!%%%???%!?%!%?!%!!!%!%!%%!%%%!!!!%%%%??%!%%%!%%?!%!%%%!?!%%!%%%!!%!!%%%?%??!!?%%%%!%%%?!%%%!%%%?!%?%!%!%%%%%%%?!!%?%!?!?%%%!%%%?%!%!?%?%?%%%%%!%%%!%!%!%!!!??%!?!%%%!%!%%%%%!?%!!?%!!!!?!%%?%%%%!!%!%%!%?%%!??%??%%!!?%%%?%%%!?!!?!!%%%%%!!?%!?%%%!%%%%!!%%%!%%!%??%??%%%%%%!??%??!%%%???!?%!?!%!%!%!%%!!%?!!!!%!!%%%!!!%!%!?!!%%!!!%%%%!%!%%%%!?!%%%%%?!%%!!%!%%?%?!!!!%%!%!%%%?!%%%%!!%!%?!?!!%!?!%!?%!%!!!!%%%?!!%!!!%!%%%%!%!%??%!%?!!?%%!%%%%!??!!%!!%!!!%%%%%?!!%?%%%???%!%%%?%%%?!?!?%%%!%!%!%!!%!!%!%%%!!??!!%!%?!!!!!!%!?%!%%!!?%%!!%!%!!?%%?!?%%%%%!%!%?%!%%%%?%!%!%!?%??!%%!%??%!!!!?%%!%!?!%%%%%?!%?%!?%!%!%!%%%!!%!%??%%!!?%%%!??!!%%%%?%%!!?%!!%%!%!%!!!%%?%?%%!!?!%!%%?%%!!%%%%!!%%%%%!%!%%!!%!!?%??%!?%%%!%%%?%%%!?!!%%!!%%%!!???!%?%!?%!%!!%!%%%%!%%!%%%%%%%%!!%%?!!%?%%%!%%!%!??%%??!%%%%%%%!!?%%%%%%!?%?!!?%%?%?!?%%%%!%?%?%%!!%!?%?%%!!%?%!%%%!%?%%!%?!!%!%%!?!!?%%?%%?%?%%!?%%%%!%%!!%%%!%?%%!%!!!%!?%!%!%!!!%!%%!%!%%%??%!%!%?!%%%%!?!%%!!%%!%%%%%%%%%%!!%?%%!??!%%%!%!!%%%%%%!%%%%%!!!%???!!!!!!%!!%%!%%%%?%!!%%!%?!?%%!?%?%%%%?%%!!!%%!%%!!!%!%%!%!%!!?!%!!!?%%!!%%%%?%!!!?%%%%%%?!%%%%%!%%%%%?%?%?%!%%%%!?%%?%%%!?!!%!!?!%%?%%%??!!!%!%!!%?%%!!%??!!!?%%?!!%%!%%!%%!%?%!%!????!!!%%%%???!!%??%%!%!!%%?%?%?!!!!!%!!%%!%?%?!%%!%!!!!%%?!!?!%!%%%%!%??%%!%%%!!!%??!!%%%!!%!%%%!%%!%!%%!%%!!%%%%???%%%!%!%!!%%%!!!!%!%!%%!?%!%%!??%%%??!?%!%%?!!%!%!%%!%%%%!%%%!%!%!????!?%%!%!%%%%%!?%%%%!%%%!%%!!%%!%!??!%!%!%%?%%!??!?!%!!?%%!%%!%?%%?%%!%%!%?!%!!%!!%??!%!!%%!!!!!!%%?%%!!%%%!!%!%!!!%??%!!?%%?%!%%!%?%!?%!!?!!%!!%?!!%?%!!%?%!!?!?%?!%!!%%??!%%%%%!%!?!!?%%!%%?!%??%%%%!!?%!!%%?%%%%%%!!%%%%%%%%%%%%%%%?%!!%!%??!!%%!%!!!%?!%%!%?!!?!%?!%%?%!%%%!%!?%%!?!!%?!%?!%?!!!%%!!%%!?%%%%%?!%!%%%%%!%%%!!!%?%%%%!%%!%%?%!?%??%%!%!%%!%!%?!%!!!?%!%!!%!%?%?%%!%!%%??%%!!?%%!%!!%!%%%%!!?%?%??!?%??!%?%!%!%?!%%?%?!?!%%!%?%!!!%?%%?%%!?%?%%%%%%??!?%%!!%%%!%%!%%%!?%!%%%%?!!%???%!%%!%%%%%!%!?!?!!!!!%%%%%%%%%!!%%?!%%%%%%%!%!%%%%?%%%%!!!%%!%?!!!%!%!??!?%?%%!?!!%%%!%?%%%%!!!?%%!%!%%!!%?!!?%!!%%!%!%?!%%!%%?!!%?%!%%%?!%!!%%?%!!%?!???%%?!%?%!!%%%%%%%!??%?!%!!%%%!%%%%!?!%?%!?%!%!%%!!?%%!!%%?!?!!!%%%%!%!%%?!%%%%?!!%%!!!!%%!?!%%%%%%!!%?!%%%?%%%%!??%%!?%%%%%%%%!%%!!%?!?%!%%!?!!!%%%!!!%%!??%?!%!!%?%!%!%!!%!!??!%%%?%%!?!!!?%%%??%%!%!%!!!?%?!!?%%?%%%?%!?%!%!%%??%?!!!%%!?%%%%%!!!!%%%!%%%!?%%!!!%%%!!%!%%!!%%%!%%??%??%!%%%!?%!%%%!!%%%%%??%%?%!!%!?!!%!%%!?%!!!%?%%?%%?%!!%%!!%!!!!!%!%%%%!%!!%%!%!!?%!!%?%%%?!%!!%%%!%%%%%??%!!%%%%%%%%%%!%!%%%!%!?%%?!%!%%%!%%%?%%??%%!?!%%%%%%%%!??%%?%!!?%%%?%%?%%%%!!%!!!%%?%?%!%!%%%!!!?!%!%?!%!%!%!!%%!!%!%!%!%%!%!%!!%?%?%!%!!!!?!?!!%?%?%%?!%!%%!!%%?%!%%!!!%?%!%?!!!!?%!!%%%%%!%!%!%!%!!?%%%%%!%%!??!%%!%!??!!%%!!%%%!%?%%%%%!%!?!%!%!!%!!?!?%%%%!?!%?%???!%?!%%%%%%%?!%%%%!%?%?!!%!?%%%%??!%%?%!%!%!%%%%!?%?%%?%%!!!%?%%!!?!%%!!%%%!!!!!!!%!!?!?%!!%%%%!???%??%%%%!!!%!%!!%?!!!!%%%%!%?%!!!%%%!!!%%%%!%!%?%?%!??!?!!%%%!%%!%%%%?!!!%!%!%!?%?%!%%%%!!%!!?%%!!!?%?%%%!%%!!%?!!%%%%%?!%!!?%?%%%%!%!?!%%??!!%?%!?!%!??!%???%!%%?%%%?%%!!!%!!!?%%%%!?%!?%!!%?!?!%%%%!??%!%%!?%%!%!!%%%%%!%!%!%??%?%???%%%%?!%!%%%?%!%%!%!!%%%!%?%%%?%%%%%!%!%%%!!%????!!%?%%!!%%%%%!%???%%!%!!?%%%%?%%%??%%%%%%!!%%!%!%%?!%?!%?%%%%%!%%%?!?!%!%%!!%%!!!!%!%%%%%??%!!?%%%?%%?%%!!%!%%%%?%%!!%%!!!%%?!!?%%%!?%!!%%%%%%%!%!?!%!!%!?!%%!!%%!%%%%%!!??%!!!%?%!!??!%%!%%%%%!%?!!%!%!%!%?!%!!!?!%!!!%%%??%!!!?%?!!%!%%%%%??!%%%!%%!%%%%%?%!!%!%??!%%!?!!%%%%!%%!%?!!%%!%!%%%!%%%!%?%!%%!!!%?!%!!!?%%?%%%?!%!??!%!!?!?!?!%?%?!!?!%%?!%?%%!%!%!?!%?%!?%!?%!!!??%!!!!%%%%%%%!?!!!%%!%!!??%%%!!?!%%?%%%%%%%!%?%%!!!!%%%!%%!%%!!%??%!%!?%%?!!%!%!?%!???!!!%!%%%%%!%??%!!!%%?%%!!?%%%!%%%%!%%%!!?!%!%!%%?%%!!%?%!%!!%%!!%?%!!%?%%%??%%!%%%%?!%%?!%%%%!%!!%!%?!!!%!!!!!%%???!%%%?%?!%!%!%??%?%%!?!%?%%?%!%%%%%!%!%%?%%!!%!%??!!%!!%%!!!%%%!!%!!!?%!%%%!!%!%!?!!?!%%!%%?!!?!%???%%!!?!%%!!??%??!%%!?%?!?!?!%%%%?!??%%%%%!%??%%!!!?!%%%!!?%!%%%!%!?!%%!!!%%%%%!%%%!!%??%%%!%%%!!!!!?%%!%!?%%%?%%?%?%%%%!%?%%!??%?!?%%%%?!!?%!%!!%%%%!?%%%!??%?%!!!%%%%!!!%%!?%!%!?%%!?%%%%??!%%!!%?!???%%%%!!%!%%%%?!%?!%%!!%%!!!?%%%!!%!%?!?%!!%!!%%%%%%%!?%%%%??%%!!%%%!%%%%%%%?%%%?!%!!%%!%%!%?%%%%!%%%!!%?!!!%!!?!%!?%%%%??!%?%!%!!!%??%%?%?!?!!%?!%%!!%%!!%%%%%%??%%%%%%%?%!%??!%%%%!%%%?!!%%!%!%?%%%%%%%?%!?!%?%!!%%%!%?!%%!?!!!%%!%%%%?!??!%!%%%!!!%%!!%!!!!%!%!!!!%%%%%?%%%%!!!%%!!!%%%!%%!!%%%!%%%%!!%%!%%!??!%%%%!!%%%!!%%!!?!!%!%?%?%%%?!%%!!%!?%%%!%%!%%?!%!!!!!%%%!!?%%%?%%!%?!??%?%%!%%!!%%%!%%%!!?!%!%%%!!!%?!%%!%!%!%%%?%%?!!?%%?!!%%?!!?%%?!!%?%?%%%%%%!?%!%%%%!%%%%!?!!%%!!?!!%?%!!%!?%!!%%%%%!%?%%%%%!%%%!%%?!!%?%%?%%%!!!%%!??%%%!%?%?!%%!?!?%?!%%!!%%%%%!%!?!%%%%!!%%%%%%%!%!%!%!%%!%!?!%%!!!!?%!!%%%%!?%%!%?!??!%%?%!%%!%%!!!%?%%%%!?!%%!%!%%!%%%!?%?%%%!%!!%%%!%%!%%!!!%%!!%?%%!?%?%!%%!%?%!?%%?%%!??%!%!!%%%%??%!?!%%!%!!!!!??%!?!%%%?!?!?%%%%%!!%%!%!!??%!%!%!%!%%%?%??!!?%%%??%%%%!?%%!!!!!%%!%?%!?%!?%%%%%%%%%!!%%%!%!?%%%!!%%%%?%%!%!%%%!%%%?!%%%??%%?%!!!%%%%%!??%?%%%%?%%!!!%%?%?%%%?!%%%%!%!%!!????!?%!?%!%%%!!!%?%%%%%!%!?%%%!%?!!!%%?%!%%%%!???%%%%%%%?%%%!?!!%%!%!?!%%!%%!!!?!%%%!!%%?%%%?%%%!%!%%?%%%!?!!%!!%%?!%%!!!%!%!%%?!%%%%%!%!?%%%%%???!%??%!%?%%%%%%%?%%?%%%%!%!%%%!?%%%!!!%!%!!!??!%%%%!%?!!!%%!!%%!!%!%%!!!!!?%!%!!%?%!!%?!%!%%?%!?!%%%!%%%!!!?!!%!!%?%?!!!%!%%!!%%%!%%!?%%!!?!!%!?!?%!!%%%%%!%%%%%!%%%!%!!!!!?!!%%!%!!%%%!%!%%%?%?%%%?%?!%%%?%!%%%!%%%%%!!!%!!!%%%?%%%%%%?%?%%?!%%%!?%?%%%?!%%?%!%%!%%%?%??%!%!%%%?!?%!?!%!%%!%%%?%%%!?%%!%%%?!!!!%!!%%?!%%?%%!%!?%%%%%!!?%%!%%?%!?!%%%%!?!?%%%%%%!!!?%!?%%%%!%%!%%!%!!!!?%%%%%%%%%!!!!%%!??%%!!%?%%%%?%!!!???!!!%%!%%%!??!!%%%!%%?!!!!%!!%!!%!%%%!%!%%?%!?%?!!!?%%?%??%%?!%%%%%%!%??%!?%?%!!?%!!?%%!!%?%?%%%?!%%??%%%!%!!!!?%%!%?%%%!?!%%!%!%%%!!!%?%%%!%?!%!%!%%%!!!!?%!!%!%?!%%%!?%%?%!!!!%%%%%%?!%!%!%?!!%%%%%?%?%%!%!%%%?!!!%%%%%!%%?!%%?%?%!%!%!!%%!!?%?!%!!!!%?!%?!%!%%%%!???%???!%%!!!?!!%%%!!%%?!!%!%%%%?!!?%%%%!%%!!%%%%%!?%!!%!%%!%?!!%%!%!?%?%%%%%%%!!!%%?!%!!!%%!%%%%%%?%!%%%%!%!!?????!%!!%%??%%?%?!%!!!%!!?%%%!%!%%%!!!%!%???!?!%!%%?%%%?%!%!%!%!%%!!!%%%%%%?%?%%!!!%!%!!!!%?!%%%%%!!%!%%!?!%%%%%%%%%??!%%!!???%%%?%%%%!%%%%?!!%%?!?!!?!!%!!!!%!??%!?%%%?%!%?%%!?%%%%!%!!!?%%%%!?!%!!%!?%!%!!!%%%?!!%?!?!%%!?%!%%!%%%%%!%%%?%%%%?%%!!%??%!!%?%!%%?!!!?!%%?!%%!%%%%!?%%!%%%!?%!%!%%%%!!!!%?!%!%?!%!%!%!%!?%%!?!?%!?!%%%%!?%%%%%%!%%?!?!%!%%%%!%%%?!%!%%?%%!!!!%!%??%?%%!!%%!%%?%!%!%!!%???%%%?%!!!?!!?%%!%%%%%%!!!!%???%?!%!?%%%%%!??%%%?%%%!!?!??!!%?%%%%!!!%?%%!%%%%?%%!%?!%!%%%!%%%%%!!%???!!%%%%%%%%!%%!!%%!%%?%%?%%!%%%%%%%%%%%??%%!%??%!?%!%!%%!!!?%!%%%%?%!!%%?%!!!%%!%%%%!%!?!%%!!!%%%?%%!%?%%!%%%%!!%%%!%!?%!%!?!?!?!%!!!%?%!%%%!%%?%%%%%!?%?%!?!%?!%!!!??!?!%%%?%!%%%!?%%%%%!%%!%!!??%!%!?%!%%%%%???!?%!!%!%?%!%%!!%!!%%!%!!%???!?!!!?%!!%%!%%!%%%!%%%%%%?!%%%%?%%!%?!!?%?%?%%!?%%?!%!%?%%%%%!%%?!!%%!%!%%%%!%!!!%?%%!?!%%??%%???%%!!!?%%!!%%!%!!?%!!?!%%%!%!!%%?!??!%%?%??!!%%%?%!%!?%%%%%%!!%%!%?%?%?%%%%!%!!%%%%!%!!?!%??!%%%!%!%??%?%??%%!%?%%%!%%?!%%%%!?%%!%%%%!?!%%?%%?!!%?%?%%%%!%?!?%%!!!%!%%%!??%!!%!!!%!?!!%!?%?%!?!%!!?%?%??!%%!%!?!?%!!!!??%!%%!?%%?%!!!%!%!%%%??!!%!%!?!!!%%!%!%%%!?%%%%!?!%!!%%%!%%%!?!?%!%?!%!!!%%!?%%%?!%%!!%!%!%?%!%%%%!%%!%!?%%!%?%?%%%!?%!%!%!!%%%%!!%!%%%%!!?%?%!%%??%%!!??!!%?%!%!!!!%!!!%!!?%%%%%?%%!%%!?%??!%!!%%!%%%?!?%!%%%?!%!!!!!?%%%%?%?!%%%!!%%?%%%!!!%!%!%%!%!%%%%%%?%%?%!?!%%!%!!%?!!%%%?%%?%!%%?%%%!%%%!%!%!%!!??!!??%%%%%%%%!!%%?!!%%%%%?%!!??%%%!!%!%%%?%!!?!%?%!%!%%%%?%??!%!%%%%!%%%%%!%%?!!?%!!?!%%%!%%!?!?%%!%!%?!%%!%?%?%!!!%%%%!%?!%%!%%%?!%%!%%!%%%%%!!?%%%?%%%!%%%%?!%%??!%%%%?%!!%%?%%%!!?!?!%?%!%!%?!%?%!%?%!!!?!!%!!%!%%!%!%!%!!!!%%!%!%!?!!%%%!?!!!?%%!%%!!%%!%??!%%!?%%!?%%%!%%!?!%?%%%%%%%?%!%!!%!!!%%%%!!!%!!??%?%%%??!!?%!!!%!!%%%??!%%??!%!!%!%!%%?!%%%%%%!%%!!%??%!%!%!%%!!?%%%%%%!!?!%%?!%%!%!%?%?%!%%!%%%%%!!!!!!!!%!%!%?%!?%!%!!!%%?%%%%%%%%%!%%%?!!%%%!%%?!%%!%!%??%%%%%%?!%?%!!%%%??%%%%?%%%??!%!!!!%%!!!%%%!%!?%%%??%?!%%!!?%!%!%!%%%!?%%??%!!!!!!!%%%%!%!!%%!!%%!!!%!!%%%%?%%??!!%?%%?!!!%%!!!%%%%%!%%!%%%%%%!!%%?%!!!!!?!?!!%?%%!!!!?!!!!%%%!!!%!%??!%?%%!!!%?%?%%%%%%?!!!%!%?!%!%!?!!%!%!!%??!?%?!%!%%%??%?!%%%??%?%?%%!!%!%%!%?!!%%%%!%!?!!%??!?!%%!!%!%%?%%!!?%%???%%?!%??%%%!%?%!%%%!%!!%?!??!%%!%%%%%%!%%!?%%%%!!!!?%!?!%%!!%??%%!?%%!%??%%!%%!!%%%%%%!%!!%%?%%%!!?%!%%????!!%!!!!!%????!%!%%!%!!?%?%?%%!%%%?!?!%!!%%%%%%!?%?%%!?!?%!!!%!!%!%%!!%%!%!%%%?%%!!%!%%!%!%%!?!?!!??%%%%!%!?!%?%%%%?!!!?!?!!?!%%!%%%!%!!%!!?!%%?%%%!!%%%!%%%%%%%!%!%!!?!!%!%?%??!%?!!?!!%!!%%!%!!!%!%!?!%!!%%%%?%!?!%?%?%!!?%%!?%?%%%%%%%%?!%!!%!%%%?!?%?!?!!?%!!!!%%%%%%%!!!!?%!!%?!%%%!!%?!???!!%!!%%!?%?!!%%%?%%%!??!!!%%!!%!?%%%!%!%!%%%!%?!%%?%!!??%%%?!!!!%??!?!!%!%%%!%!%%%%!%%%%!%?%%%!?%?%%!%%%%??%%%%%?%%%%!!%!%!%%!!!?%!!?!!!!!???%!%!!!%%%%!%??%??!!%%??%%%??%%%!%%%!!?!%?%?%%%%!%?%%!%?%%%%?!%%?!!!%!!%!?!%???%%%?%%!!!%!%%!%!%%%%!!%%!%%%!%%%!?%%%?!!%%%!%!!%%%%!%!?%%!%%!%!?%!!%!?%!?!%!!%%%%!?%%%%!!!%!%%!%%?%!!%%%?%%?%!!%!%!%%!?%%%%%%%%%?!%%!!!%?!%!%?%!%%?!!?%!?!%%%!!%!%!%!%%%%%%?%!?!!!%!!%%!%!%%!%%?%%?%!?%%!%!%!!!%%?!!!%!!%%%%%%!%!!%%%?%!%?%%%%?%%?%!%!!!%%%%!!%?%%!%%%%?%!%%?%%%!!%!!!!?%%?!%%%%%?%!!%%%%!!%%?%??!%%%%!%?!%!%!%??!%!%%!!%?!?%!!%?%!!!!!%%%!!!!?%%!%?%%%%!%%%!%?!%%%%?!%%!!!%??!?!!!!%!!%!!!%!?%?%%%!!!%%%?%%!!!%%!%?%!!?!%%%%%!!!?%%??!!%%!!%%%%?%?%!!%%!%%!%%%%%!%%%??!%%!%%!%%%%%%%????!!%?%%?!%%%%!%%%%!%!!%!%%?!%%%%%!?!%!%!%!!!%%??%!%?%!!%%%%!!!!%%%%%%%?!!%?!%%%!?%!?!!??!%?!%?%%%!!%%!%!%%%%!%?!?%%%?!!!%!%!%!%%?%?%!%%%%?%%!?!%%%%%!!!?!%%?!%!%?!??%%?!?!%%!%?%%!?%!?%!%!%!%%%?%?!!?!!%?%%%%%%!%!!%?%%?%%!%?!%%%%%!?!%%%??!%%!!%%%!!!!!%?%!%?!!%?!!?!%?!?%!?%?%%%???%!%%%%%%!?!!?!?%!%%!%?!?%?!?!%%!%%%%!%%?%%%%%??%!%%%!!%%%%!%%!%?%%!?!%!!%%%!!!%%%%??!%?!!!%?%%!%!%%%??%!%%%!%!??!?%%!%%%%%!!?%!%%!%%%%%%%!?!%!?!%%!!%?!%?%!?%%%%!%%?%?%!%!!%%!%!?%!%!!!%!%!%?%%%!%%!%!!%?!?%%!!%%%%?%!%?!!%%%!%!%%!!%!!%%?%!%%%%%%%%!!!??!%%%!!%%%!!?!%%%%?!%?!%!%%%!%%%%%%?!%?%!?!%!%!%?!%??%%%?%!%!!!%!%!%!?%%%!%%?%%%!%%%!!?!%%%?!?!%%%%%!%!!!!%%%%%%%?%!%%%%%?%%!!%%%%!!!?!!%!%!%%!%%%%!%%!%%!%%%%?!!!?%!???%%%!%%%%?%%%%%!%%%%!??%%!%?%%%??!%%?!?%?%%!!%%?!!%!!!%!%!?%!%!!%%%!%%%!!?!%%!!%%!%!!%%!%%%!!%!?%!!!%%%%!!!%%%?!??%%%!!%?%%!!!%?!%?!%!!!%%!!!%!?%?%%!%%!%%!!%!?!!?%!%?%%%%!%%!%!!?%%%!%%%%%!%!%!%?%!%!%%??%?%%?%%!%!!!%%%???%%!!!?!?%!!%%%!%!%!!%%!%%!%%?!!?%%!!%%%!?%!?!!?!%?!%!!!!%!!%%%%%%???%%!!?%!%%??!%%!!!!!%%!!%%?!!%%?%!?%!!!!!%!!%%%!!%!%?!%%%?%%%%%?!%%!%%?!%%%%???!%!!?!?%!%!!%!!%%%!!%%%%?!%??!!%!?%%%!?!%?!?%%%%%!!!%!%?%?%?%%!%?%%?%!!%!?%!%%!!??!%%%!!%?!%??%%%%%%?%!!!%%!%%%!%!%!!!%?!%%!%%!!%!!%%!!%!?%!%!??%??%!!%?!%!!!%!%%??%%!%%%%%!%?%%%?%?%%!%?!!!%%!%!!%%?!%!!%!?!%%%!!?!%?!%?%?!!!%%?%%!!%!!%%%%!!%!%%!%%%%%%?!!%%%!!%%!%?%!%!%?%!%!!!!%%!%!!%%?%!%!%!%%?!%!!!%!%!%%!?%%%%%?!%%!?!%!!%%%%!%!!%%%?%!?%%?%%%!%%%!%%%%%%!%%!!!!%!?!%%%!%!%%%%%%%??!%%??!!%!%!%!%%!!%%?!!!%%%%%%%!%%?%!%%%!?!!%%?%%!!%!!?%!%?%!!%!%%?%%!!!!!%!%!%?%!%%!??!%%%?!!%!%%!%!%?%%%%?%?!%%!!!!%!!?!%!%!%%%%%%!%%!!%?%%!!%%%?%!!!%!?%???%%%?%?!?%!!%%%%%%?%%!%!%%%%%!%?!%!!?!?%%!%%?%%!!!!%%%?%%?!%!!%%%?%%%!%%?%%%!%!%%%%%%?%!!?%%%!%!!!!%%%%!!!!%%%%%%!?%?!?%%!!!!%!?%!!%?%%%%%%?%%?%%%!!%!?%!!%%%!?!!%!%!%%%%!?%!%%%%!!!%?!%!%%!!%?!!%%%%%!!%?%?%!!!%%%%?%%%?%%%%%%!%%%!?%%%!?%!!%%!?%??!%%!%%%%!!!%!%%%!%!!%%%!%!%!%!!%?%!%%!%%%!!?!!%%!%%!!%%!!!%%%%??!!?%%%%!%%%??!??%%!?%?????%!!!%%!!!%!%%?%%%%%!%!%%%%%%%!%%%%%!%?%%?!%%%!!%%%%%!!%!?!!!!??%!!?%%!%!?!%?%!%%%%!!%%?!!%%%%%%!?%!%!?%%%%!???!%%!%%%!!?!?%%!%!!%%!!!?%?%!%!%%%%?%!?%%%??%%%?!%?%%!%%%?%!?%!%%?%!%%%?%!!??%?!%?%%!!!%!%%!%!?%%%%!!!?!?%%%!%%?%?!%?%!!%!?!%!%!%%%!%!!%!?!?!!%!%!?!%%!%%?!%%%!%%%?%?%?%!%%%!!!%%?%!%!!%!%%%%%!%!!!%?%%!%%%%!!%?%!!!!%!?!?!%%%%%?!%%%%%%?%?%!!?%!%!%%%%%%%!%%!?%!%!???%%!%%!%%%%?%%%%?%%!!%%%%!!!!?%!%!%%!%!%%??!!%?%%%%?%%%%%!%?!!?%!!?!!?!!!%%!?!?%%%%%!%!%???!?!%!%%%?!?!!?%%??%%?!%!%?%!%!%%!!%?!!!!%%?%%?%!?%!?%%!!?%?%%%!?%!%!?!!%%%%%%??%?!%%?!!!%%?!%%?%!%%%%?%%%!%?%%!?%%?!%%?!!%%%%!%!?%%%??%%?%%%???!%??!%%?%%!!%%?%?%%!!!?!%%??!%%!!%%!%!%?%%%%!%%????!%!%!!!%?%%!!%%??%%%!%?%%%!%!?!!!!?!%!%%!%%%?%%!%!?!%%%!!!%?%!?%%?!!!%%%%?!!!?%!?%%%!%?!%%%%!%%!%%%?!!%?%%%?!%?!%%!?!%%!%!%!!%%%!%?!!%%%?!%%!!?!%%%%%?%!%%!!%!%%%%%!%?%!?!!%%!??%%%!%%!%!%?%%!%%%!!!%!%!%!%%%%%?!!!!!%%?!%%!%%!??!??!!%?%%%!%!!%%%?%%%?!!%!%%%%!!%%!!!!?!!!%?!%!!%!!!%?!?%%%?%%??%!%%%%!?%%!%?%!%!%!?!%%%!%%?%!!%%!!!%!!??%%!!!!?!%?!?%!!!%!?%%%%%%?%?!%%%%%?!%%%%%%%%!?%%!!%%?%?%%%%%%%?%?%?%!?!!!%%%%!!%!%%%!!?%%?!%!?!%%!!?!%%%%%%%?%%?!%%?%!%!%%%!%?!!%%?!??%!%!%!!???!%?%!%%%%?!!!!%%%?!%%!!%%%%%%!!?%%%%%%%%%%%%??!?!%%!%%%!%!!!%%!?%%?%%!%%!%?%?%%%%%%!!!%%!%!!?%!!!%%?%%!%!!!!%%%!?%!?!%!%%%!?!%!?%%%!%?!%!?!%!%%%?%%?%!!!!?%!%%%%!%%%%%!!!%?%%!%%!%%!!!!!!?!%%!!%!??%%!?!!!%!%%%%?!?!%%%%%%%!?%!!%%!??%!!!%!%%??!?%!!%%%!%%??%!?%%!%%%?%?%!?%%!%!!!!%%?!!%?!?%!!%%??%!?%!?%????%%!%!%!?!%%!%%!?!%?%!!%%??!%?!%!%!!%%!?%!!%%%%!?%!%!%%%%%!%!%%%?!%%!%!%!%!?%?!%%?!?%%!%%!%!!!%%!!!?%%!!%%%%?!%?!??%%!!%%%!%!?%!!%%%%!?!%%!!?!%%%?%!?%%%!%%%!?!?%%!%%?%!?%!!?!%%!%??%??!!%%!!%???!!%!!%??%?!?%%?%%!!%?%%%!?%!!%%%%%%%%%%%%%!%!!?!!!!!%%%%!!?%%%%!%??!!%!%!!%%!%!%%!!!%%!%%!%?%!??%?%!!%%%%%!%!!%%!?%%!!?%%?!%!%?%!%%!%%%!?%?!%%%????%!!??%%%?!%%!%!!%?!!%%!!%%%%%?!!?!!%!%?%?%%%!%!!!!!!!%%%%?%!!!%%!!%%?!%!%%!!%%!!%!%!!!%!?%?!%%?%%%%!%!?!%?%!%!%!%%!?!%!?%!?%!?%%%%%?!?%!!!!?%%!!%%?!%?!!?%!!%%%?%%?%%%%!??%!%?!!%?!!?!%%%%!%?%!%%%!!!%%%!!!!!?!!%%!%?!!??%%!%?!%!?!?%%%%%?%%!%%!?!!?%!?%!?%!!!%!%%%%%%!!%!%!%%%%%!%!??!?%!!%?%%%%%!%%!!%%!%?%%%%!?!%%!%%%?%%!%%!!%?%%!%!%%?%!?%!%!!%!!!!%%%!%%%??!%?%%%!!!!%?%%?%%???%!%%!?%%%%!%%!!?%%%!?%!%?%?%!!%%!?%%?%!%%?!?%%!%!!!%!!%!!%!%%%!%???%?%??!%%%%%?!%!%%?!%?%%%!%??%??%%?!?%%%!%!%!%%???%%%?!%%?%%%!!%%%%!%%!%%%%!%?%%%!%!?%!%!%%%?!%!%%%%%!%%%!%!!!?%?!%%%!!?%!!!!!%%?%!!%!%??%%%??!?!!!%??%%%!%%!!%?%!!%%%?%??!!!%!%!?%%%?!?%%%?!!!?%?%%!!%?!%%!!!%%%!!%!%!?!%!!%%%%!?%%%%!%!?%%%%??!?%%%%%!%%%?!!%!?!%??%?%!!!%%!??!%%%!%%%!%%%!%%%?%!%%!%%!%%?%!!!!%!%%!!!%!!%!!%!?%%%!?%!%%!%%!!%%%!?!!%%%!!%!!!%%%!!!!%%??%!!!%!?%%!%?%!%!!!!%!%%%??!%!%%%!%%%%?!%%!%!%!%%!%%%??!%%%%!!%?!%%%%%!!?!!%%%%!%!%!!%!%!!%?%!%?%?!%!?%%?!%%%%!!?!?%%%!!%%!!?%%%?%%?%%!%?!%%!!!%%?%!?%!!%!%%%!???%!!%!%!?!%?%%?%!%%%!%?!?%%!%!%?!%!?!%!%!!!!??%!%??%%%!%%%!?!%!%%%!%%!%%%!%%?%?!!%%%%??%%%%?%!?!!?!%%%?!?%%?%%?!%??!!!?!%%%?!!!!?%!!%%?!!%%?%%!%!??%%!!%?!!%%%!%%%%!!%%!!?%%??%!!%%!?!?%???!%?!!?!?%%?%%%%%!!!%%!!%%?%!!!?!!!?%!!!?!??%!%?!?%%?!!%!?!%%%??!!!?%?!%%%%?%%!%!!!%!?%%!?!%%!?!!%??!?%!!?!%!!%%%%%%%?%%%%!%?%%%??%%%%%%!%%?!%!%%!%!%?%%!%!?!?!%!!!!?%%%%?!%%%%%%?%%%?%?%!%!!%!!%?%%!!!?%!!%?%??!!%%!!%??!!%%%!!%!!???%%%??!%!%%%!%???%?%!!%%%!!%?%!!?%!%%?!%?!%%%%%%!%!%!?%%!?!%%%!%%!%%!??!%%!%?%?%%!%?%!%?%%%%%%%!!!?%%%?%%!?%%%!!!!!%!%!!%?%%%%%?%%%?!%?!%%%%%!!%%?%!!!!!%?!%??!!!!%%%%?!%%!!!??%?%!%!%%!%%!%!%%!%!%%!%%!!!!!%%%?%!%%??%!%%?%%%%%%?!!%%?!??!%%!%?!?%%!!!%!%%!!!%?%!!!%%!!!!!%!?%?%%?%%%!%%!%%?!?%%%%!!?%!%%%?%%%?%%%%!%%??!%?%%!?%%!%%%%%%%!%%%%??!!%!%%%!!%?%!%!!!%!!!%?%%!%%%%%!%%%%%?!%?%??%!!?%%%!%%!%%!!%!!%%%!%%!%!%%!%!!!!?!%%%%!%?!%!%!!!????%!%!!%%%?%%!%%%!!%%?%%!%%?%%?!%!%!?!%%??%%%%?!!?%!!%%%%%!!!%!%!!%%%!??!!%??%!%%?!!%%!!?!!%?!%?!??%!!%%%%!!?%!!?%%!!?!%%!%!%!?!!!%%%%!%!!%%%%!%%%!%%!%!%!%%%!!%!!!%%%!?%?%%%%%%!!!%%!!!!%?%!%!!?!%%!%%%%!%%%%%%!%!!%%!?%!!!%!?%%!!?%%%%!?%%%%%!!!%!??!!!?%%!!%%!%!%?%?!%!!%%!%!%%!?%!!%%!!!%?%!!?!?!!%!%!!!!%!%?%!?%!!!?%?!!%??!!!!?%!%!!!!%%?!!?%!!%%!%??!!%%%%!?%%%!!%%!!%!%!!!?%%%%%%%?%%?%%%%%!%%!!!!%%?%!%%%%!!%!!%?%!!?!!!%%%%%??!%%!!?%%??%%%!!%!%!?%%%!?!%%%!%!!%%%?%%%%%!?!?%!!%%???%!%%!!!%?!%!%%?%!%!!!!?!!%!?%?%%!?%!%%%%%!%!%!%!%%%?%%?%%!%%%%?!%?!?%!%?%?!!%%!%%%%?%?%!!%!%%!!%?!???%%!%!%%%?%!%!!%?!%!%!?%!!%%%?%%!%%%!?%%!%??%!%%%!??%!%%%%!!%!%%!%?%?!%%%!!%%%%!%?!%%%!%?%%%%%%?!!%?!!%%?%%%%%%!%%%%!%!?!%%%%%%??!%%%%%%%%%%%!%%!!?!%%?%?%!%%%!!!!%%%?%?%%%?%?!?%!!%%!?!%%!?%?!%!%?%%!?%!%%%%%!!%%??!!!?%%%%%!%%?!%%%%%%!!?%?%!!!%!!?%??!%!!%!!%%!!%!%%%%%%!%%!??%%%?%!%%?!%!%!%!?%%!!%%%%%%%%?%??%!%!%!!!!%%%%!!%?%%?%?%%%!?!%%!%%%%%%!%?!%!%?!?!!?%%%!%%!!%!!%!%?!%%?%%!%%!!!?%%%!!!%%!%!%%!??%?%!!!%!%%%%??%!%?%!!%%?!!?!%!!%%%!!%%!!%!%!?%%!%?%%!?!??!%%!!!%%%?!!!??!!%!%!%?%!%!!!?%%%%!%?!%????!?!?%%%%!!!!%!%%%%%%??%%!%!!%?%%%%!?%%!!%?!%!%!!!!!%%%!!%?%%%!!%%!%!%?!%%%%%%!%!%!%?!%!!%!%%?%%!%%!%%%%%!%??!!%%%!?%%%!!!%%!!!?%%?!%%!?%?%!!%!%?!!!?%%?!??%?!?!!!%!!!?!!%!?%%!%%?%!%%%??!?%!%%?%%!%%%%!!??!?%%%??!?%!%%!%??%%?%%??!%!!!%%%%%?%%?%!!%%?%%%%??%%%%!%%%!??!%!%!!%%%%%%%%%%%?%%%%%?%%%!%%!?!%%!!?%%%%%%!?!%!%%%!!%!!?%%??!!!!?!!%?%%??%!!%%!%?%!%%!%%!%!%!!%%!?%?!?!!!!!!%!%%!?%!%%%?%%!%!%?%!%?%%%%!!%?%%%!???%%%!%%!%%%%%!%!%!!%!%!%%?%?%%!!%!???%!%%%%%%!%%%%%%%%?!!??%?%!%%!??%%%!%!!!?!?%%!%!%%!!%%??!!%!%%?!!!!!!!%%%!!!??%?!%%%?!!%%!!%%!!?%%?!!!%!?%!%%!?%%%%!%!!!!%!%!!%%?!?%%%%%%%!!!?!!!?%?!%?%%%%%%??!???%!!?!!%!%!?%%%%%!!!!!%??%%%%%%%%%?%?%%%?%?%%%%%%%%%!!%!!%%%%?%?!!!!!%!!?%%%?%??!!%%%?!%%!!?%%!?%%!?!!?%%?%%!%%?%%%%%%?!!%%!??%%!%%?%??%%?%?%!%%!%?!%??%%%%%!%!!!%!!!%%%!%?%?%%!!%!%!%!%%%%!%%%%%?%%%!%%%%!%%%!%!%?%%%%!!%!!!%%??%!!?!!??!??!!%%%%!!!%%!%%%%!!?!!%!!%??!!%!%!%!!!%%!%%%%%%?!!!%%%!%!!??%!%%%%%??!!??%!?!?!%!%?%!?%%%%!%%?!%!!!%%?%%!%?%!%%!?%?!!?!%?!!?%!%%?%!!%!!!!?%%%!!%%!?%!%%!%!!%!?%!%!!?!??%?%??%??!!!%!?!!%%?%?%%%%?!%%%!%%%?!%%%%!!?!!%?!!!!!%!!%!!?%%!%%%%%%!%%%%?!?%?%!!%??%%?%%!%%?!!%%%!!%%?%%?%%%%%%?%!!%%%?%%!!%%%%!%%?!%!%%%%%%%%%??%!%!!!!%%?%%?%%?!%??!%!%%?%%!%?%%%%?%%!??%%%%!%%%!!?%%?!%%%%??%!%?%!!?%!%%%%!!!%%!%%%%%!!%%!!%%%%!%?%%!!!!!??!%!!!???%!%%%%!%!!%!%!%!%?!!%%%%%!%%%%%!!!%!%%!!!%%%%!%!!?!%!%!%%!!!%%!%!?%%?%%???!!%!%%??%%!!!!%?!?!%?%%?!?!!?!%!?%!%%%%!%%!%%%%%?%!??!%%!%!!%%%?%%!!%!%%!%%!%??%?!!!%!%!%%%%!%%!!%%!!%%!?!%?%?%%%%!%%%??%%!!!%%!%!!!?!%%!%%!???%%%?!?!%!%??!!!!%!%%!!%!!%!!!!%!%%%%!!!%!!%%%%%???!%%!?%%?!!%?%%!%?%?%?!%%!?%!!?%%%!%!%%%!%!%!%?%!!%!%???%%!!%%%!!!!!!%!?!%?%!%!!%!%%%%%%?%%?%!!!%%%%%?%%?%%%%%%%%?!?%!%!%!%!%%%!%?!!%!!%%!!%?%%%%?%!!%%!%!!%%%?%%!%%%%?!!%%!%%??%%%?%%%?!%%?!!!!%??%%%??%%%?%%!%!!%%!!?!%!!%%!%!?%?!%%%!%!!??!%%!%%%%%?!!%%%%%!??%%%%%%!%%%%%%!%%%!%!!?!%%%!!!!!%!%%!?!%?!?%%%!!?!!%%%??%%?%%!%%%%%%%%??%!!!%!%!!%%!%!%!??!%?!%!?%%%!?!!!??!!?%%!?!%?!%?!%!?%?%%%?!?%!!?%%?%%?%%%%!%!!!?%!!%!!?!%%%%%?%%%%?!?%%%?%!%!??%?!!%%%%%!%?%?%%!!??%%%!%%%%%?%?%%%%%!%%!%!!!!!?%?%%%???!%%?!%?%%%?%!!?%%%%??%%?!?!!%%%%!!%%%!!%?%%?%?%!!%%!!%!!%%%!?%!%!%%??%%!%%!%%!?%!!%%%%!%%?!%%!?%%!%!%!!%?!!%!%%!%?!!?!%%%!?%%%%%%!!!!?!?%?!%%?%%%%%!!!!%!!%?!%%%%!!!%%%%!%?%%?!%%%?%%!%%%%!??%%%%!!%!%%%?%%!?!!%%!!%%%?%!%%!??!%%!!??!%%%%?%%!%?!?!%%!%!%%%?%%%%%!%%%%!?%??%%!!!?!%%%!%%%%%?%%%!!?%%!%!!%!?%%%?!%%??%%%!???!!!!!%%%%!%%!%%!!%??%%!!!!?%!%%%?%%%!%%!%!!!!%!%!!%%%%%%%!?%!!!?!!!%!!??%%!?%?%!!?%%!?!%%%%!%!%?%%?%!%??!!%%%!!%%???%!!%?%%!%%!%!!%%!!!%!%%!%%?!!%%!?%!?%!!??!%%!!%!%%%%%%?%!%%%%%%%!%!%%?%%%?%%%%!!%!%!!!?%?%%%!?!!!%%%?%!%%%!!!?%%!!%%%%%%?%!?!%!%!??%?!%%!?%%!%?!%%%!%%?!%!?!%!!%!%%%%%?%?!??%%%!?!%%?%%!?%%%%%!%%%%%?!?????%%%!%!!!!!?%!!%!%%!!?!%%!%%?%%%%%!!%%!!?%!%!!%%%%!%%%%!%?%%!%!?%?%%%!%%%!!!%?!%%%%%!!!!%%!??!!!%%!%%!!%?%?%%!%%!%%!%?%!!!%!!!%!%%%%%%!%!%%!%!!%!!?%!!%%%%?%!%%%%%%??%%%!%?!??%%%?!%!%?%!%%??%%%%!!!?%%!!%?%%!!!%%%%!%%%%%%!%!!%!%!!%!?%%!?%%!!!!??!%%%!?%?!!?%%!?!!!%%%!!?%!!!%%!?%%?!%%?!%!%!%%%%%?!!%??%!%%!%%%%!%!?%%%%!%!?%??%!%!%?%%%!?%%%%%%%%%%%!?%?!%!%!%%!%?!!!%?!!!!%%%%%!!!%!!%%%!%%!?%%!!!!!?%!!?!%!!%%%%%%%%!%!!%!!!%%!!!%%!!%!?%!!?!?%%!!!%!%%!%%%%%%%%%??!?!!%%%!!%?%?%?%?%?%??%?%%!%%!%!?%?!!!!%%!?%%%%!%%?%%!%!?%?!!%!%!%%!!!%!!!%!%%!%?!%%?%!!%!%%%?!%%!%%!%!%??!!!%?!!%%!%!%%%?!!!!!!!%?%%%?!%%%%%!!?%!!%%%%!%?%%%!!!?%?!?!%!%%!%%%%%!%%%?%!%%%!!%%!?%%%%?%?!?%?%%?!!!!%%?%%!%?%???%?%?!%%%!?!?%!!??%%!??!%%?!%%%%?%%%%!%%?%!%%%%%%%%%!%%%%?%%%?%!!%!%!%!%%%!%%!%??!!%%%!?%!%%?!%%%??%%%!!%%%??!%!%%??!!?%%!%%%??%%!!%?%?!!%!%!!!!!%%?%!%%?%%!%%%%%%%%%%%%!%?!!%!%!?!!%!%%%%!?%%%%%??%%%%!%!!!!%%%%!!?!%%%%%%!%!%?!%%%%!%%!?!!!!%%%?%%!!?!%%!!%?%!?%!?%%!%%!%?!%?%!!%!!!%%%%%?!!%%%%!?%%?!!%%!!%?%!%%?%?%!%%%!%%?%?%%!%%!?!%!%?!!%%%%!!%%!!!%%%%%?%!!!%%%%%%!?%%!%!%?%%%%!?%%?%%!%%%??%!%%%!!!%%!%%!?!?!%!!!!%%%!!%?!%!%%?%%!%!%!?!%%?%%!%!!!%!!!%!!%%%%!?%!???%!%%?%%%%?%!%%!%!%!!!!?%%%?%??!%%?!!%%!?!!%!%%!%?%%%!?%!%%%?!!!%?!%!!??!??%?!!%?%!%!%?%?%%!%%!%%%!%?%!??%%%%%?%%??%%!!%%??!!?!%!!%%!?!!%%!?!%%%?%!%%?%%%!%%?%%!%!%!!%%!?%%!%!!%%!%%?%!!%!!?%!!%%!?%%!!%%%%%%!%%!%?!!!!%%!!%%%?!!%!!!%%!?%?%%!!%?%!!%!%%!%!%?!?!%!!!%?!%?%??!%%%%%!?!%??!?!?%%?!%?!%%%!?!!!!?%??!!%%%?%!?!%!!!!%%?!%%!%!!%%?!??%%!?!?!%%!!%!%%?%!!%?%!%%!!%!??!!%!!!!!%%!%%?!%!%?%%%%?%!!%%%%!!!!!!%!%!?!%%%%%!!%?%??!%%%?%%!%!%??%%??!!%!%??!%%!%%?!!%%!!%!?%%!?%%%!?%!%!!%%%%!%!!%%%%!%!??%%!?%%%%%!%%%!!?!?!!?!%!!%???%%!%!%!%%%%?!?!!%%!!!!%%%%%%%!!?%%!%!%%%!!%?%%%%%!?%%%%%!%?%!%?!?%!%%!%%?!?%%!!%%%!!%!%!%?%%%!??!!!!%?!!%%%?!!!%!%?%!?%?%%%!%%%!?!?%%%%%%?%!!!!?%%!%%!!!%!!??%!%?%%!??!!%??!!%%!!%%%%!%!!%%!%%%%%%!!!%!!%%%%!!%!%?!%?%%!%%%%!%!!!%%!%!?%%?!!!%?%!%!?%%!?!!%?!%?%%!!%?%?!%%%!%%!?!!?%%?%%%!!!!?!%%%!!!!!%??!%?%%??!%?%?%%!!%!!!?%%!?%!%?!%%%!?%??%?%%!!!?!?%?%!%?!%%?%!%%?!?!?%%!!!!!?!%%%%?%%%!%%!%%%!%%?!%!!!%%!%%?%%?%%!%?%!%?!%%?!%!%%%%%%%%?%%!%%%?!?%?!?%%%??!!!%?!%%!???%%%!?%%!!!%%!?%%!!?!%%%%?!!%!!!%%%?!%%!%%%%%%!%%?!?!!%%%!%!!!%%!%%%!?%%?!?%!%%!!%%%!!!%%?%??!!%!%%%%%%%?%!%!%%!%!!!%%!%!%!%!%!?!%!%!%?%%%%?!%%%!%!%%%!%!!!!?%%%!!%%%%%%?!%%%%%%%%%?%!?%%%%%!%%%%?!!%!!!%!!?%%!%!!!!!%%%%%?%%!!%!!!!!%%%%!%%?%%%!!%!!!%%!%!%%%%?%%?%%%%%%?%%??%?%?%%%%!!%%!!%%??%%?%!!!!!!%%?!!!!?%?!%%?%%%??!!%?!?%%!%!?!!?%!%%%?%?%%!!?%!!%%%!%?!?%%%?%!?%!%%%%%%!!%!%!!??!%%?!%%%!!!%%%%%!!?!%%%!!%!%%!?!%!!!!!!!%?%!?!!!!?%!%?%%!%%?%%!%?%%%%%!!%!!!!%!%%!%!%?!?%%!%!??%%!%!!%!%%?%?%%%%%!!%!%!?!!!!%%?!!!!?!!!!!%%!?%?%%%?!?%%???%?!!?%%?!!!!?!!!??%%%?%%!%%?!%!%!%%%??!?!%?!!%%!%%!!!?%!!%%!!%!%!!!%!!%!??%!%%%%%??%%%!%%!%%%!??%%%%!%%%%?%!%%%%%!%?!!!!%!%%?!?%!%%%!%!!!%%!!%?!%?%!?%%!!%%!%!!%!!%%!%?%%!?%!%?%%%%!?!%%%%%%?%%!!%?%?%%%!%%?!?!%!!!%%?%?%??!!%!!?%!!!%%!!%%%%!%%%%%?!!!%!?!%%!%%?%%!%%?%%%!!!%%%!!%!?%?!?%%?%%!!!%%%!%%!!!!%?!!%!!%?!?%%%!%%!!%%%?!%!%%%?!%%%%%%%%%!%!!??!!!%%%%%!%%%%???%!!%%!%%!%?%!%%%!?%%!!!%?!%!??%%?%%?!!!%%%?%!%!%!%%??!%%%%%?%!!%%!%?!!!%!!!?!!%%!?%!!!%!%??%?!!?%!!!%?%!%??!%!%%%!?%%!%%!!%%!%!%%%!!%%%!%%%!%%!%%%?%%!?%!%!?%??%%%?%%?%!!??%%%!?%?!%?%?%%%%!!!!?%%%!%%!!%%?!!%!!%%?%%!!%!?%%!%!?%!!%%%%%!!!%!%!%?%%?%?!%!!%!?!%?%!!!%%%%%!%!%%??%%%?!%?!!%%%?!%?%%%%%%!%%%%!%!!!!!%%%%!%!!%%?!%!!%!%!%%%!??!%!%%%%!!%??%!?%%%%%?%%!??%%%%!!%%%%%?!!!?%?!%%!%??!%%%?%!!%%?%%!%%%?%!%%!?%%%!!%%%%?%%%!%%?!%%%%%%%%%%?%%?!%?%%!%!!%%?%!!%%!%%?%?!!%%%?%%!!%%%%%!%%!?%!!%%!?!??%%%!%%%?%?!%%%!%!%%!!%!!%??!?!!%!%!%%?%%!!!%!%%%!%?%?!!%??!%!!!%%%%!!%!%%!?%!!!%%%%%?%!?!!%?%!%%%?%%%%?%%!!%!?!%%?!%!!%%?%!%%%?!!??%!!?%%?%%!?!%%%?%!?%%!!!?%!!%!!!!!!?%%!!%%%%!%%!?%!%!%%!?!%%!!!!%%!?%??%!%?!!??!%?%%?%%!%!%?%%%%%!!%%%!!%%!!!!%?%?!??!?!%!!%!%%?%!!?!!?%%%%%!%!%?%!%%!?%%?%%%%!%!?%%!%%%!!%%%!%!%%!%%!!%%%??!!%!!%%%%!!%!%!!?!?%%%%%?!!%!?%%!?!%%%!%!%%?!!??!%%?%%!!!%!!%!!%%%%%!!%!?!%?%%?!%?!!%!%!!%%!!!!!%!%%%!%?!%!?%!%%!!%%%%%!!?!%!%?%!%!%%%%?!%?%%?!%!?%%!??!%%?%%!!!%%?%%!!%!%!?%%%%!%%%!!?!%%!%???!%?!!!!!%!%%!!%!%!?!%%!!?!%%%%%%%?%!%!!!!?!?!?%%%%%%%%%!?%!%%?!%!%%?%!%?%?%?%%%%?%%!%%%!!%%!%%?%?%%%!!%%%%%!!%!!%!%%%!%!!!%%?!?!%%!!%!%%%?%%?%%%!!!%?%%%!%%%!%%!??%%%%!%%!%?!%%!%!%??%?!%??!%%!%!?%?%%%%!!%?!!%?!!%?!%?%%!!?!%?!?%%!%%!%!%!?%!!!%%?%%%%%%%%%!!%%?%!%?%%?!!%%??!%!!!?%!%%?%%%%!!?!!%?!%!%!%?%%??%%?%!!%??%%?!!?%?!%?!%!%%%!%!%!?!!%%!%%%!%%??%%?%%%!%!!?!%%%%!?%%!!%%%%!%?%?!%%%%!%!%%%%%?!!!%%%%???%%!?%?%?%!!!%!%!!!!!%%%%%%%!%??%%!%??!%?%%!?%%%%%%?!!?!!??%!!!!!?%!%!%%!%%%%!%%%!!!!%!%!%!!%%!?%!?%!%%!!%%%%%%??!%!?%?!%%%!%%!%%!!%%%!!!%!?%%????!!%%!%!!?!%!%%!?%%!!!%!%!%!!%??%%%%?%%%!%%%%!?%%%%!%?%%!%!!!%%!!%!%!!%%%??%!%%%!!!!!%?%!?!!?!?%!!!!!!%!!!%!%%!?%%?!%%!!%%%%%?%!??!!?!!%!%%!!%%%%!%!!%!%!?!!%?!!!%!%%?!%%?!%%!?!!!%%%!%!???%%!!?!%??%!!?%!%%%%??!%!%!%?%%%%%%%?%!!?!%%%%?!%!!!?!%%%?!!%!%?%?!%%?!%!%%!%!%%%!%%?%%%?%?%%%%%%?!%%!!??!!?%%%!%%!??!!%%%!!%!%%!!?!%!!?!%%!!!!%!!%!?%%!%%!%%%%?!%%%!!%%!?%%%%%!!!%?!!!?%!!!!!%%!%%%!!!%!%!%%%!!!?%%!!!%!%!%!?!!!%%%%!%?!%%!%?%?%!!!!%!%?%!!%%%?!%?%!?!??%%%%%%%!?%%%!%%!!%!%%!%%%%%%%%%%%%%%%!%%!%!%%!?%%!%%%%%!!!!%!!!!?%%!%%%?!%???!%!!!!!%?%%!?!%!!%!!!!!?!%%%%?!%%%?%%!%%!?%%!?!!%?%%%%?!%%?!!%%?????%!%%?!%%!%!%%?!!%!!!!?!%%!%!%!%%%%?!%!!!!%%?!?!%%%?!%%!?!%%!%%!!%%%?%%??%!??!%!!?!%%%%!!?%!!%%!%!%%!?!%??!%!%%!!%%!%%%!%!?%??!%%!%%!%%%!!!%!!!%!!%%!%%?!%?%%?%!!%?%%??%%%??%%%%%%!%?!!%%%%?%?!!%%!!!%?!%!%!??!%%%%%%%%%%%%!%%?%!!%%??%%!%%?!%%!%%!%%?%%?%!?%?%%!?!%%!%%!??%%%!?%%%%!%!%%%?!%%%!%!%%%%%%?%!!!!!?!!%%?!%!%%!%!!%??%?%%%%%%?!!%!%!%!%%%?!?!!%%%%??!!?%!!%?%??%!?!%%%?%%?%!%%!?!!%!!%%%!?%?%%%%!%%%!!!??!%%!%%%%!!%%%?!%%%%?!!!??%%%?!%!%%!!%%?!!%%!??%!%%!%!!!%%!!?!?%%?!!!?%??%!%%%!%%!!?%!%%%!%%%!!!%!%%%!?%?!!?%%%!%!%!!%!%??!%!!!!!%%?!!?%!%!%??%!!%!?!!??%%!%!%%%%%?%%%!%%?!!!!%%!%?!!%!%%%?%%!%%?!!%%%!%!%%%%!!!%%!!%%!%%%!!%%%!%%%%%%??!!!%!!?!!%%!%%%?!%%!%%%?%!!!!%?%%!%%%!%?%!!!%!?%?%!!?!%%!!!!%!%%%??%%%%!%!%!%!!!%%!%%!%%%!?%%!%%%%%%%%%%?%%%%%%%??%?%%%!!%?!?%!?%%!%%!%%!%!%!!!%!%%???%!%%?%!!%%%%!%%?%%!!?!!!!%%%?%%!!%!?!?%%%%?%%!!%!%!!%!!!%%!%?%!!!!%%%!!!%%%%%!%?!%?%%%%!!%?!!%%%??!%!%%%!%!%!%?%%?%%!%!?%!?%%?!%!%%%%!!??!?!%!%!!%%%%!?%%!!%!??%?%!%!%%!%%%%%?!??%%!!?!%%%!%%%!%%!%%%%!!?!%!??%!!?%!!%%!%???%%%!%?!%%%!?%!%%!%!?%%%!%%%%?%??!!%%%?%!?!%?%%!?!!%!!!%!%!?!??!%%%!???%%!??%!?%%!%%%%!?%!%?!!?!%%!!?%!!!!??%!%%!?%!!%%%%%%?%!%?%!!%%%?!%%??%%%!%!%!%%%%%%%%?!%!%%%!?????%%%!%%!!!%%%%%!!%%%%??!?%%%%%%!!%%!!!!%%%!!!!%%%%%!%?%?%%!!??!%!!!%%%%%!!%%!!?%%%!!!?%???%?!%%?!!?!%%?%!?%!?!%!!!%%%%%!!%%?%%%!!!%%%!?%?!!%!?!%%%%?%%%%%!?%!!!%%?%!%%!%%?!%%%%%%?%%%?!%%?!%%?%!%!?!!!%%%!%%%?%?%?!%%!%%!%??%!?%!%%%!%%%!%%%!?%!!%!%%!%!%%!!!?%%!%%!!%!%!%%!!!%!?%%!!%!%%!%!%%!%?!!!%%%!!!%!%?%!!%!!%!!!%!%%!%!?%%%!%?%?%!%?!%%%!%!%%!%%!?%%!!%!?!?%!!%%%!!%!!%%!!%%%%%%%??%?!?!%!%%!%%!!%!%!?%!%%%!?!%?%!?!?%%%???!!%%???%!!!!!%%%%?%%%%%%!%!%%!%?!!!%%%%%%%?%?!?!%%!%!%%!?!!%!?%!?%!!%%%%%!?!?!??%%!%!!!%%%%!%%%%!!!!%!%!!%!!%%?%%%!?%?!!%?%!%!??%%%!%%%!!%%?%!?%?%?%%%%?!%!!!!%?!%?%%?!?%!%%!?!%%?%%?%%!?%!???!!!!!%%!%?%%!!%?%!?%%%%%?!!?%%!!!?%%!?%%%%!%%!%?%%%?!!!%%?!%!%%!%%!%%%?%!%!%%?%!%%!%??!!%%%%!!!%%%%%%!!!%%!!%!!!%?%!%%%%%%?%!!!%%%!%!%!%!?!?!?%%!%!!%%?%%!!?!%%%!%?%%?!%??%?!%!!!%%%!??!%%%%%%??!%%!%!??%%!!??!%!%??!!?%%%%!%%?%!%%!%%%%%%%!%%!!%%%%%!?%%%!%%%%%%%?%%!%%?%%%%%%!!%%!%%!?%!!%%%!%!%%!!%%??%!!%!%!!!!%!?%%?!%?%%??!?!!%%%!!!%!%%?!!!%%!!??%%%%%%%%??!?!%%%%%!%%!!%%%%%%!%!?%!!!%!!!?%%%?%!%!%!??%%!!!?!%%!%!%%%%!%!!%%%%!%!%!%!!!%?!??%%%??%!!%%!%?%%%!?!%%!!?%?!!?%%%!%%%???!??!??%%??%!%!!?%%!%?!%%%!!!?%?%!%!%?!%!?!!%%!!%!%%!%!%!%%?%!%?!!!%?%%!%%!%%%%%?%%%?!!!!%%??%!%!?%%!%?!?%%%??!!%%%?!%%%%!!%%!!!??%%?%!%?%%%%%!!%!%%%%%!%!%!%%%!%%!%%!?!!!!!%!%!%%!!%!!!!%?%!%!!!!%%%%?%%!!!?%%?!%!?!?!%%%!!%%%%!%?%%?%!?%%!%%?!!%%!!!%%!!%%%!%%?%!%%?%?%!!!%??%%%?%%?%%?%%%!!?%%%!!!!%%%!!!!%?%%?!!%%!!%!%!!%%%%%!!?!%!%%%?%%!!%%!%!!!!%?!%%%!!!%?%%%!%%!?%%?!!%!%%!%%!%!!!%?%?!%%%%!??!%%%!!%%%%%%%%!!!%%!?%!%%%!?%%!!!?%%%!!%%%!%!?!!%!!!%%!%?%%%%!%%%?%!%!!%%%!!%%!!?!%!%%%%%?%??%%%?%%%%%??!!%?%!%%%!!%%!!%%!%!%%%!%%%!?!!%%!!!%%%%%!!!%!%%%!%%%!!%%%?!!!?!??!%%%!%!?!!??%%%%%%!!%%!%!!!%%%%%?!%%?%%!%?%!%!!??%!!!!%%?!!!!%%%%!%?!%%?%!%%!%!?%?%%%%!%??%!!%%%%%%%%%!!?%??%?%%?!%%!%?!!%%?%%??%%%!%%%?!?!?%?%?!%??!%%%%%%%%?%!!?!!!%%!!!!?!?%%!%!%!%%?!%!??!?%??!!?%%%?%!!!?%?%!!%%%!!%%?%%%%%!%%%!%%%!%%?%%%!%%!?!?!!%!!!!%!!!!%!%!%??%!%!%!!!??!?!%?!%%!%%!!!?!!%???!!?!%%!%%%??%?!%!%%?%!%!!%%%!%%!%%?!%%%!%%%!?%!!%?%??!%!!%!!!?%%!%!?%%??%%!%%?%%%!!%%!%%!%%?%%%?%%!!!!%!?!!!%%%%?!!%!!!%%?%%?!!%?%%%!!!!%!!!!%%%%!%%!?%!!%!%!%!%%?!?!%!!?%%%!?!!%??%!%??%%%%?!%%%%%?%!?%!?%!!??%?%!!%%???!!%%?%%!!?!%?%!%?%%?%%?!%%%??!!%%!!!?%%%!!%!!?%!%%%!%!%!!?%!!!%%!!?%%%!%?%%!!%%??%!!!!!%%!%%%%!%!%!%%%%%%%!%%!%%%%%%%%!!%?%!%!%%%%%!%!?!%?%%!?%%!%%!?!?!%!?!%%%%%%!%%!%??%!!%!%!%%!%?%%!%!!%%%!!?%%?!%%%%?%!%?%!%%%%!%%%%%!!%%%%!!?%!!%!%!!%%!!!??%?%%?%%!%%%%%?%!!!%!?!%%%!!%!!%%%!?%%!!!!%?%%?%?%!?%%!!!!%!!%%?!!!%%%!?!%!!%?!??%%!!%!%%%%!!%%%%!%%?!%%!?!!!%%?!??%!?%!!?!%%%%!%%%%%%%!!!?%!!%%?%%?!%%!%!%%!%%%!??%%%%%!?!!%!!%?%!?!%?%%!!%%!!?!%%%%!?!!?%!!?!?%?%!?!!!%!!%!!?!!?!%%!%%%?%!%%?%%!!?%%!?%%%%!%?!!!!%!!!%?!%%!!!?!%!?!!%%!%%%%?!%!%?%?%!%!%%%!%%%?%!!%%%%!!?%%???%%!%%?%!!%!!?!%%%%?%%!%%!%%!%%?%?%%%!%%!%!!%%!%%%???%%?%!%%!!%%%%%!!!%%%%%%!%%%%?%!?!?!%!!%!!?%%%%%?%!%!!!%%!??%?%?%%%%!%%%%%!?%%!%?!!%%%!!%%%!??%??!!%%!!%%!%!%%%!%?%!%%%%!%%%%%?!?!%!%?!%%!!%%%%%!?%%%?%!!!?!!?%%%!%!%%%?!!%%!?%?!!!!?!%?%%!!%!?%!%%!?!%?!!%!%?%!?%%?%!%!%?%%!%%%?%?%%%%!%??!!?%!%!%%!??!%!%%%%!%!%%!%%?%%%%!?%!?%%!??%???!!??!!??%%!!??!%!?%!!%%!%!%!%%!!%!%%?!%%!%!!%%??!?!%!??%%%%?%%?!%?%%%%?!%%?%!!%!%?%!!%!%%%?!%?!%%%!%%%!%!%%!?%%%!%%%%!!?%!%?%!!%?%!%%?%?%?!!%?%!%!%!%%?%%%%%!%?!%%?%%??%%?%%!?!!?%%%?!%!!?%!%?%!?!!%!%!?%%!!%?%!%%%%!%??!?%%?!%%%!%%%!!!!%!%%!%%!%%!??%%%??!?!?%!?!!%%?!!!%%%!!!%?!!!%?%%??!%!!!%!?%!%?!%%%%!??!???%!%%%!%%?%%%?!!!!%!%!%!%%?%!!%!%!%?%%%%!!!%!%!%%?!!%!%%?!!%%%?%!!!!%!%!%!%?!%!%%%%!%!!%%?%%%%%%?%%%?!?%%!%%%??%!%!!%?%%!!?!%?%!%%%%!?!?!!%!??%!!!!%?%?!!!!?!?!%!!?!?!!%%!%%?%!?%%!%%?!!%%%?!!!!%%!!%??%?!%%%!%%!!!!%%!%%!!!?%%%!!?%%??%!%!?!??%!%?%%!%!%%%?%!?!%%!?!!!??%%%%!%%%?!!!!!%%%%%%%%?%?!%%%%%%%%??!?!%%%%!%?%?%!%%%?!?%!%!!%?!!??!!%%!%!?%%%%!%%!?%?%%?%?%!!?%%%!!!!%%%%%?%!%%%%!!?%!?%%!%!?%!%%%!!%%%%!%%%!!!%%!%%?%%!??%?!!%%%%%?%%%%%%?%!??!%?!%?!?%%!!!%!!???!?!%?%%??!??!!%%%?!%%%%!?%?%!!%?%?%!%?%%%!%!%%%!%%%%%%?!%%%!%%%?!!%%%%?!!%%%%%%%%!%%?%%!?!%???%%!%%!?!%!???%%!%%!%%?!%%%?!!%?%%%%!%?%!%%!%!%%%!!!!!!%!!%%?%?%?!!%%%?%!%%%%!?%%!%%%?%%???%!%!%!%%?!%%%%!!!!?%!!%!%%%???!%%%!!?%??!!%%!!%!!!!%%%%%%%!!?%%!!!?!!%%!%%%?!!!!%!%%%%%%!%!!!!%%%!%!!%%%%?!!%!%!%%!???%!%!%!!?%!!?%%??%%%%??!%?%%!!?%%%%!%!%%!%!?%!%%%!%!%?!!%%?%!??!%%%!%%%%!!%!%!%!%!%%%%%%%%%%%!%%?%?%!%%?!!%?%%!%%!%%%?!%!?%%!?!!!!%!?%?%%%!!%!!%%%%%!%!!%%!%%?!%?%!%!%%%??%%!%!!!%%!%!%%%%%?!%!!!!%%!!%%!%%!%?%!!!!!?%?%??%!%%%%!%%!?%%%%!!%%!%?%%%!%!!%%!%!!%%!!%!?!!!?%%??%!%%!%??%!%%%%%%%!!%??%?!!!%%!%!%?!?!!%?%%%%!%!%?!?%%%%!!%%??%%!%?!%%?%%%!%%!%!%?!%%%%%!%!?%!%!!%?!??%!%!!%%%!%%%?%%%!?!?%%??!%%%!%%%!%%!??%%%?!%!%%%!%%%%!%%%?%?!%%!%!%!!?%%%???%!%%%?!!!!?!!!%%%%?!%?%!%%%!%%!!!%%!%%%?%%%%!?%!!!%%%???%%%%?!?!%%?!%!!%?%!%!%?!%!%!!!!%%%!!??!!%!?%%%!%!!?%%!%?%%%%%%%!!?%%?!!%%%?!?!!%!!%!!%!%!!!%?%!!%!!!%!!?%%!?!%!%!!%!%!?%!!!?!%%%%%%?!!%!!%?!?!%!!%%%!!%?%%%%!!%?%%%%!%%?%!?%%%%!!%%!!%%?%%%%%%%!%?%?%!%%!%%%!%%!?!!%?%%%!!!!%%!%?!?%%%%?!!!!%%%%%%!%%%%?!!!?!%!%%%!%!%%??%?%%!!!!%?%!?%%?%!?!!!%%%!%?%%%?!!%!!!%%!%%%?%!%?%?!%%%%%%%%?%%%?!%!?%!!%!%%!%?%!%?%%?%%!!%?!!%?!!!?!%!!?!%!?!%%%?!%%%?!%%%!%!%%!!!%%!!%?!!!!!%!%!%!!?%%%%??%%?%%!!!!!%%!%!%!!%!%!!!%%%!%%!!!%!!!%!!%??%%?%%%??!%!%%%!!!?%%%%%!!%?%%?!%%??!%%?%!%?%?!!!!%!!??%%%!!!!!?%!!%%%%%%%%%%%!%?!!?!%%!!!%%%%%!%%%%!%%!%!?%?%%?%%%!?%!!!!%!%%%!!!?!!%!%%%%%%%%?!!%%%!%%??!%?%?!!!!!%!%?!%!%!%%?%%%%!%%%%%%!%%!!%%%?!%%%!?!%%%!%!%!!!!%%%%!%!%?!%%?!??!!?%%%%%?%!?!!!%%%%%!%%%%!%??%!!%!!%%%%%%!%%%%?%!!%!%%!???%??!!?%!%%%?%%!?%%!?%%!!!!%%%!%?%%%!%%!?!!?%%?!!%?%%%!%%?%%%!%?!!%!!!!?%%!%!%%%%!%!%!%?!!?%!%%%%%!!%?%?%?!%!?!!%%??!?%!%%%?!%%!!!%!%%!%!%!%%?%%!!?%?%%!%!%%!%%%%%%%!!?%%?%?%!%?%%!%%!???%%?%%%%?%%!%?%?%%%%%!!?!%?%%%%?%%%%%%!!!%?%!?%%!%?!%%%!?%!%!?%%!?!%!!%%??!?%%%!!%!%!!%%%%%!!!!%%%%!%!%%%%%???!%%%???!?%%%?!!!??%%%!!?!?%%%%%%!%!!%%%%!?%!%%%%!%!!%%%?%!%%%!%%!%%%%!%%%%!!%%?!%%%%?%%!!?%%%!?%%!%!!%!!%!%%%%!%!%%!!?%!!%!%%!!!?%!%%!!!%!!!?!!%%?!%!!!??%?%?%!%?!!%!?%?!%!%!%%!%%%!!??%%!?%%!%%!%?%%?%%!%%%!!%%%?!%%!%!!?!%%%%!%?%?%!!%!%%%%!%%%!%!?%!!???%?%!!%!%!?%!?%%?!?%!!!!!%%!?%%%%!!%?!%%!%!?!??%%%!%%%??!%%%!!!%%%%?%?%%%%%%!?%!?!!?!%%%%%%!%!?!?!%?%%%!%%!%!?!!%!%!%%!?%%?!?%!%?%%?!%?!??%!%!?%?%?!%%%?!%%%%%%?%%!!%!%%??%??%!?%!!%!%!?!%!!%!?!%%%???%??%!?%%%!%!%%%%%%!%%!?%!!%!%?%!%%%!!%!%!%?!%%%!!%!%%%!!%%?%?%%%!!?%!%?%%!!%%%%%?!%%!?%%?%?%%%!!?!!!!!%%!?%!!?!?!%!??!%%?%%%%?%!%!?!?%%%%%!%%!%%%?%!%%?%?!??!!!!%?!%?%%!%?%?!?%!%%?%%!%!!%%!!!%%!%%!?%!%%%!?!?%%?%%!!%!%!%%%?!!%%?%!%!!!?!?%?%%!?%%!?%!%?!!%%!!!%???%!%?!%%!%????!%%%!?!%%?%%%!!%%%%%%%!!?%?!!%!%%%!!!%%%?!?!%%??%!!??%%?%??%%!!!%%!!%!%!??%???%?!%%%!!!!%!!%%%?!%%%%!%%%!!?%%!!??%!!!?!?%?!?!%!!!?%!?%?%%??%%%%%%%?!%%%!!%!!%%?!%?%?!%%%!%%!%%!%%?!%?%??%%!%!%%!!?%!?!%?%%??!%%%%%%!%!!%!?%!!%!??!%%%%%%?%%%%!%?!%!%%%!%%!%?%?%%!?!%%%??!%!!%%%!?!!?%%!%???!%%%!%!!!%%!!??%!??%!!!!!?%!%!!%!%!!!%%!!!!!%!%%!??%%?%!%%%%?!%%%?%!%%!!?%%%!%!!%!%?!!!%!%!!!!!%!%!!%%%!?%%!%%%%!%?%%!%!%%!???!%%?!%%%%!??!%!%%!??!??%%!?%!!!%%%%!%%!?%%%%?!%%!%%%????%%%%?!!%%!!%%%%!!%%!%!!%!%!%!?%!%%%%!%??%%%?%%%%%!%????%%!?%%%%%!!!!%%!%%%??%??!!!!!?%%%!?%!!!!?%?%?!%!??%%%?%%!!%%!%%%!!%!%!??!!!%%%%%%?!%%%%%?%%??!!%!%%?%%%!%!%!%%?!!%!%%?%!?!??!%?%%!!%%%??%!!!%!???%!%%?%%%%%%%%%%!!%%%%%%%%%!!??!%%!!%%!%%?%!%!%%!!%!%%!%!!!%%%!%%!%%?!%!??!%%%%?%!%!%%??%!%%!%%?%%?!%?!!!!?%%?!%%?%!?!!!%?%%%!%!!!??%%%!%?%?%%%!%%%%%%%!%%!%%%?%!!%%?%!%%!!!%!%%!%?%!%!?%!%%!!%%!!!%?%%!!%%%%%%%%?%!%??!!%%%!??!?!!%!%!?%%!!!!%?!!%%%%%!!?%!%%%!%%?%%%%%?%%%?%!!%%%%%!%%!!!!!%%%%?!%?%?%??%?%%?%?!%%%!?!%!%!!!%%!%!!%%?!%!!!?!%!!%!!%%!%%!%!%%%%%!?%%%%?!!!!%%!%%!?!%%?!%%!%!!??%!%!!%!!%!%?!!!%%%?%!!??!??%!!!%!%%!%?!!%??%%?%!?%?%????%%%?!!%!!%%%%!!%%!%?!!!!%%?%%?!%%!%!!!%%?!%%!?%%%%%%%!?%%%%!!!%%!%%%!!!%%!!%%%%%%%!%%%%?!!%%%!%!!%%!?%%%?%%!!%%%!!%%!!%!%!%?%%%!%!%?%%!!??%%!%!!!!%%%%?%%%!!!%%!%%%%!!%?!!!%?%%!%%!?%!%%!!??%%%!??%?!%%%!%%%!!%%%%%!%%!!?%??%%!!%!%?%!!%%!!!!%!?!!!%%%%%!%%%%%%!%!%!%%%%%??!%%%%%%?%%%%!!!!%!%?%%!%%%!%?%%%!!%%!%%!%%%?%?!!?%?%!!?%%!%%!!!!!!%%?!?!?%%%?!%%!%%?%!%!!?%%%!!!%%%%?!%!!%!%%!!%?%%%!?!%!%?%!?%%%%?%?!?!!%%!!!!%!%!?%!%!%%%%?!%%%?%!%%%!!?%!!!?!!%%%%!!!?!%!?%!%%%!?!!!%?%%!?!%?!!%%!%!?!%!%!?%!!%%!!?%!!%?%%%%!%?!%%%!%%!%?!??%?%!%%!?%%%%%%%!?!?%%%?!?%?%%%!%!%!%!!!%??%%%%%%%%?%!%?%!%%%!%!!%%?!%%%!%%%%?%%!%?%%%%%%!!%%%!!%%!%%!?%?!!%?%%!%%!%%!?%%?%!%%?!!!%%%??%%%?%!%%%!!!?%!%%%!%!%%%%!?%!%!%%%%!!?!?!%%?%!%?!!!!!%!%!%?%?!%%?%%%%!?%%%%!!%??!!?%!%?%!?%!?%%%!?%!%%%!?!%%%!%%!%%%??%?!%?!%%!!!!!%?%?%?!!%%!%!%!%!%%!!?%%%!%?%!?%%%%%%??!%!%!?!!!!%%?!%%!!??%!???%%?!?%!%!!!!!%!%%%??!%%?%!!!%%!!%%!!%%%!!?%%%!%%!!%!!%!%%%%%%%!?%%!%%!!%!!%%%?%!%%%%%?%!!%??%%?!%%?!???%%%??%%%%?!?!%%?!%!!%!%%?!%%!?!!%%%%%!%%!%%!%%%!%%?%???!!!%?!!!%%!!%%%%%%!!?!!%%!!!%!?%%%%%%%%%!%%%!!!%%%%!%!!!??!!%?%%!%%%?%!%!??%?%%?%!%%%%?%%%!%?%!%?!!%?!%%?%?!!?!%!%%!%%????%%!?%??%%?!%%?%?!%??%!?!!!!??%%%!%!%%!%%%!!%%!%?%?%%!%%!?!?!!!?%?%%%%%!%%!??%!!?%%?!%!%%%?%?%!%?%!?!!%%!%%!!%!%%%%?!!!%!%%!!!%???%!!?%??%%%%%!%%!%%!!%%%!%%!!%?%%%%%%!!%?%%%%!%!%!!%%?%!%!%!%?!%%%!%%?!%???%%%???!%!%!!%!%%!?%%%%??%?%?%?%?%?%%%!%!%!!!%!!!!%!!!!%%%%!%%%%!!%%!!%%!!!?%%%?%%!%%%%!%%!!!%!%!!!%?%%!!%?!%!%??!%%%!??%!?%%%%!??%%!%%??%?%?%%%?!%%%%%!?%%!!?%!?!!!!?%%%%??!?%%%%!!%!!%%%!?%%!!?%!!!!!%!?%%%%!%!%%?%!%!%%!%%%!%!%%?!!!%%%%!%!?%%!%%?!%%!!?!!%?!!%%%%%?!?%%?%?!!%!?!?!%?%!%%!!%!%%%!!!?%%?!!!!!%!%%%%%%!!%!!?!!%%!?%%%!!%%!%?%???!!!?%?%%%???%%!!%!?!%%!???%!%!!?!%%%!%%%%%%?!%!!!%!%%!%!?!%%%!%!!%%%%!!!!?%??%?%!%!%!%%%?%%?%!!!%!%!!%%%%%?!!!%!?%!%%%?%?!!!!!?%!%%%!!!?%??%!!!%!!%!%?!!%?!%?!!%%%?%!%%?%!?!%?%%?%%?!%%!%??%!%%%%!%!%!!?!!%%!%!!%?!!%%%%?!!!?!%?%!%!%%!!%!!%%!?!!%%%?!?%%%!%!!?%?!!?!%?!?!!!%%%%!?%?%%%?!??%%?%?!%%%%!%?!%!%%!!%%%%%%%!!?%?%%?%!!!?!?%!%!!%!%%%?!%%!!%%%%!%%%%%%%!%??!%%!%!!%%%%%%!%%%%!%%%???%%!!%?%%%??%%??%%?%%!!%%?%%%%%!!?!%??%!%!%%%%!%!%%%%?%%%%%%%!%!%!?!!!!!?%!?!%?%%%%%!%%?!%%!!%%!%%%!%!!%!%!!%%%%!%?!%!?%!%%!!%%!%%%%%%%%!%%!%!?%%%!?!!?%%!%?!%!%!?%!!%%%!?!%!%?!!?!!%%%??!?%!%!!%%!%?%%?%!??%!!%!?%?%%!!!%%!?%%!%!%?%%%?!?!%!%%?%%%!?!%??%!%%!%!%?!!?%!%!%!??%??%%!!!!%%%%!%%?%%%?%%%%%%!!!!??!!%!%%?!!%%!!%%%%%%%%!?%!%%%?!??%!%%%%!%?%%%%%%%??%!%!!!%??!%%!%!???%%%%%?!?%%%%!!!%!!%%!!!%!%!?%%%%!?%%?!%%!%!!%%?%%%%!!!%!!!?!%%%%?!!?%!%!!%?!?!%?!!!?%%%!!%!%%%?!!!%%?!!!%%?%%!!%!!!!!%!%%%!?%%%?%%?!!%%?!??!%%?%??!?!!?%%??%%%%!!%%!%?%%%%?!%!%%!!%!?%!%!%%!!?!!!!!!%!%!%%!%%%!?%%!!!!??%%?!??%!%!!%??!!!%%?!!%%%%%!%%%%!%!!!!%!!!!%%%%!%%%%!%%%%%?%!?%?!%%?%!%%?!??%%!!?!%!%?%?!!?%%%!%?%%?%%%%%%%%%!%!%!!%%%!%%!%%!!!%%??%!%%?%!!!!!%%!!%!?%%!%!%%!%?!%!?%%!%!?%%%!%%%%%!?%!%%%%%%!%?%!%?!!%%%%?%%%%?%?!?!!?%!!%!!?%?%%%%?!?%??%%%%!?%!%!%!%?%%??%?%!%%%!%%%?!!%%!!%!%%!%%%!%!%!!%!?%%!?%?!%!!?%!!!%?%%!!%??!!!%!%%?!??%%!????%%!?%!!%%!!?!%!%!!?!%%!!%%!%?%%!!%!%!%%%%%!%!?%%%!%!%%%!%???!%%???%%?%%?%?%%%%?%%%%!?%!!???!%%%%%?%??%%%%%!?%!%!?%!!!?%!!!%?%%!%%!%!???!!%!!!!?!%%%%?%!!?%%%%%?%!!%!%%%!%?%%%%!%%!!!%%%%!%%%?!%!!%%%!%%?!?%!%%%%%?%%?!%%?%%%%%!!!!?!%??!?%?!!?%%%!?%%%?%!%%??%%!!%%!%%?!!!!%!????!%!?!%?%!%%!%!%!?!%%!%!%?%%%!?!%%%%%!?%?%?%%!%%!%%%%%%!?%%%%%%!%%%%!?!%%%!%!!!%?%%%%%!%!!%?!%!?!%%%!%!%%%!!%!!!?%%%!?%%???%!%!?%%%?%!%?!!%%%!!?!?!!!%!!?%!%!!?%%?%%!?%%%!!%??%%%%!?%!!%%%!%%!!%!!%%!??!!%?%%!!%?%%%!%%!%%%!%%!%!%%%?!!%%?%!??%!%%?%%!!%?%!!!%!%%?%!%%%!!???%!%%%?%%!%?%%?%?%%%?%%%?!%!!!%?%?%!!%!%!%!%!!%?!?!%%!!??!!!%!?!!!%%%?%%!?!!%???%%??!%%%%!%!!%%%!%!%!%?!?!?!%%%!!%?%!!!?%!!%?!?%?!%%%!%?%!%%!%?%%!%!%?%!%!?%%%%%!?%%!!!!%%%%%%?!!?%%%!%!!???!!%!!!!%?%?%%%!?%!?%%%!!%%!%?!!!!%?%%%?%%!!%!%?%!%!!%??%!!%%!!!%!!%?!%???%!%%%!%%!%!%%%%!%?!%%%%?!!!!%!?!%!%!!?!%%!%%%%?%!%%%!!!%!?!!!%%%!!%!!!%!!%!%!%%?!!%!!!%!%!???!!%!?%%!!%%!!?%%%%?%%%?%!?%!%%!!%%%?!%%?%!!%!!%%?!!?%%%%%?!%!!!!%%!!%%%?!!%%?!!?%!!%%!%%!%!!%%?!?!%!%%%!%%%!%%?!%??!%%%%!??!?%!%%%%%!%%%?%?%!%!!!?%!!!%%!%!!!!!!%%%!?!%%?%%%?%?%!%?%!!!%?!!%!!!%!%!%!%%?%!%%?%!!!!!!!%!!!?!%?!?%!!?%!!!!%%%!%%%%%!!%%%!%!%%?%!%%?%%%%!?!%!!!%!%%?%%!%%%%%%!!??!?!%%%!%??!!??%!?%?%?!%%?%?!%?%%%%!%!%!%%%!%%%!%!%!%%%%!!!!%%%%?%%%!?%%!?%!%%%!%%!%%%%?!??!%?!!%!!%!!!%%%?!%!!?!%!%?!%%?%?%%%?%%!%!%?!!?!?!%?%!?!!%!%%!?%!%%%%%!%%?!%%%%%%%!?%%!!%%%%%%%?%!%?%!!%?!!?%?!?!?%?%!!!%?%??%?%%%%!%%!?%%?%%!!%?%!?%%%!%!%%%%!!%%%%?!%?%!!!!!%%?%!?%?%?%!?%!?%!!!%?!?%?!?!%!!!!!!%?%!!!%%%%%%?!%%??%%!%!!!!%?!!?!%%%%?%?%%?%%?%%%!!?!%!%%%!!?!%%?%?!!!%!%!!%%%?%!!!!%!%!%%%!%!%%%!?%!!!%%?!%!!!%%!%%!!!%%%%%!?%%!??%%?%%!?%%!!%!%!%%%%!%!%%%!%!%%%?%%!%%%!???!?!%!!%!%!?%%?%%%!%%!!!?%!!!!!%!%!!%%!!%?!%%%!?!!?%%%%%?!%%!!!?%%!?%?%?!??!!!%?%??!%%?!%!%%%%!%%%!%%!!!???!!!!%%!!?%!%%%%%!?%?%!%%%%%%%?%?%!%??!!?%!!%%%!!!?%%%!%?%!%%%!%%%!%%%%!?%!%!%%?%%%!!!!!%%%%!!!%%%!!%%!!?%%!%!!??!!???!!%??!!%%%%!!?%%%%!%!%%%?%!?!%%%%!!!!%?!%!!!%!!%?%%!%%!%!%?%%%!!%?%!!%%!!!%%%?%!!!!?!?%!?!!!%%!!?%%%%%%?!%!!%!%%%!%?!%%%!%%!!%%!%%!!%%%!%%?!%%%!!%%%%!!!%?%%%!!%%%%?!!%%%!!!??!!%?%!%!?!%%%%%?%?!%%%?%%!!!!?%!!!?!%%!%!%?!!!%%%!!%?%%%?%%%%%%%!!%!%?%%?%!%%!%!%!%???%%%!%!%!?%?!%?!!%!%%?%%%!%%%%%%???%!%%?!%?%!?!%!!?%!%?%%%!%%%!%%%%!?!!%%?!!?%!!??!!%!%!?%?%!%%!!?%%%%?%%%%?!!%%?!%%%%!%%%%?%%%%??%%!?%!%%%%!??!!!%%%!%%?%%!!%%!!%!?!?!%%%!!!!%%%%%%%?!!?%%?%?%!%%%%%%??!%%%%%%%%%%%!%%%!!!%?!?%?!%%?%!%%!!%%!%%%%!!?%%?%%?%?%?%!%%%%%!!!?!!?!%!?%%%%!%%%?!%%?%%!%?!?!!!?%?!??%%?%%!?%%%?%%%%?%!%%?%!!%!%%%!%%%!?%%!!!?%%%%%%%%%?!%%!%%!%!%?!!!!?!%!?!%%!!%%%%!?%!!%%?!!%!?%!!?%!?%!!%%%%!!%%%?!%%%?%!?%?%%!%%%%%!?%%!%!?%!!%%%?%?%?%%!%%%!%!%%!!%%%????%?!?!%%%%!%??!%%%%!%%!%!!?%%!!?%!%%?%?!%%%!!!%%?%%!!!!%%%%%%!%!!!!%%%%%?!!%!%%%!!!%%!%!!%%%!%%!%%%!!?!%?%%?!%?%!!!%!%?%%%%%%!!!%!%%%%%%%!!!%!!%?%!%%%%!!%%%%%!!!%!%%?%!%%%!%?%?%!!%!%!!%%%%%?%%%%%%%%%!%%%?!?!%%%?!%?!?!%%%!%%!%%!%%?%%!!???%%!%%?%!%?!%%!%!%!!%!?!!%%%%%?%%!%%!%%%%%!!%!%%!!??!%%%%%%%!!%%!?!!%!%!!?%!?%?%!%?%!%!!!%!%%?!%%%%%%!?!!%!!%?%!!??%!%%!%%?%!%!!!!%!%?%?!%%%!!!%!%%?%%?%%!%%???%!%%%!!%%!!%!%?%%%!%%!%%?!!!!%%!%%%?!%%%?!!%%%%%%!!!%?!%!!!%??!%%?!???!!%%%%%!!!%%!%%??!!?%!%%%%!!%%?!%%%?%%?%?%!%%!%!!!!%!!!%!%?%!%!!%%!%%!!%%!%!?%%!%?!!!%%%%!!%%%!%?%?%!%!!!%!%%%!%!!!!?%%?!!%%!%%?%!?%!%?!!!%%!?%!%!%%%?!%?!?%!%%?%%!!!%!!?%!!!%!?%!!!%%%!%?%%!%%%%%!%!!%!!?%%!%%%!%%%%%%%%%%?!%%%?%%!%!!!%%%%%!?!??%?%?!!???!?%%?!!!%%%%!%%%!%%!!?%%?!%%%%%%!%%!%%?%!!%?!%!%%?!%%%%?%%!%!!%%%!%%!?!!%%%!!!%!%%%%%!!%!%%%!%?%%%!%!%%%?%?%!%!%%!%%%%!%%%??%%!%!%%%?%!%!%?%??%%%%?%%?%%%!!%?!!%%%!!%!%%%?%%!%!%%?%%%%%?!%??%%%?%%!?!%!%!%%%??%?!%%!!!!%!%%!%?%%%?%?%??%%?!%??!%%%!%!??%!%??!%%!!%?!?%!%!?!%%?%%?%!!%%%%!%%!!%!!%?%?%!!!%%!%??%?%%%%?%%!%!%!?%%%%!%?!?!!%%!?!!%%!%?!!!%!%%!!!%?%??%!!%%!!%%%%?%%!%!%%%%!%!?%!%!%!%%%%!!%??%!?!!!%%%?!%%%%%?%!?%%%!%%%!%%??!%!%%%?!%!?!?%%!%?%?!!!%%%!!%%!%!?!?!%%!%?%!!%!!!%%!!!!!??%%!%!%%%%%%?!!!%%%%%!??%!!%?%!!%!?!%%%!%%!?%%!?!%%!!%%!?%!%!%!%?!!!%?%?!?%!%!%%%%!!%!%%%%%%%!%%?!!!?!%!!!?!%?!??!?%%%!?%%%%%%?!%%!%?%!%?%%%%%!!%?%%?%!%!%%?!%!%!%!%%!%%%%!!%%??%??%!%!%??%?!!?%!%%?!!!%?!%?!%%%!%%%!?!!%%!?%%%%%??!!!%?%!%%%!!%!%%!%?%%!?%!%!!%??%!!%!?!!%%%!%%%%?%?!!%%%%%??!%%%%?%?%?!!%%%?!%!!!%!?!!??%!%!!%!!%%%?%%!!!%%!%!!!%!!!%%%%!%?%!?!%!%%??%?%!%!!%!%?%!%%%%!!!!!?%%%?%?%%%?!%%??!!%%!!%!!?!!!%%!!?%!!!?%%%%!%%%!?%%%%%%%%?!%%!!!!%%%!!!%?%%?%!%?!!?%%%%%!%%%%%%?%%?!!?!%!!!!%%%%?!!%%?!!%!!!!%?%??!%%??!%!%%%?%%%%!!!%%%!%!%%!?%%%%%%!?%%%!!!%!%!%!%%?%!!%!%%%!!?!%?%?%!?!%?%?!!%?%?%!!%%%%%%%%!!%?%!??%!%!%%!%!?%%%%%%%%%%!!!!%!%%%!?!%%?%%%%?!!??%??!%%%%%!%%!%!?%%%?%%!!%%%%?!!?%%%?!%!?!%%%!%%%%%?%!?!?%?%!!%%%!!%%%!%%!%%?%%%!!!?!%!?!%%%%%???%%!%%%!%%?!!!??%!!%?%!?%??%?%!%%%!!?!!%%!%%%%!%!%%?%%!?!%%?%%!!%!!%%??!?%%%?%%???!%%%%%%%??%%!%?%%%!%%%!!%!?!%%%?%!%!%!%!!%!%%!%!?!%%%!%%!?!?%!!%%%%?!%%?%%?!%?%!!?!%%!%%%%!!%!!%%!%!%%!%%??!?%!%%%%!%%?!%!%!??%%%?%%!?!?%%!!?%%!%!!??%%%!%?!!%%%%!%%!%!%%%%%!!%??%!%!?%%!!!!%%%?%!%%!!?%!!%!%!!%!!%%%??%???!!%%!%!!%!%!%!?%%%!%%?%%%!%??%%%%?!%%%!??!%%!!%!!%%%%%%?%%%?%%!%!!!?%%%%!!%!?%!%%%!%%%%%!%%?!%%!?%%%!%?%!%%%!!%%?!%!%%%!%!%?!%!!?%%%%%!!?%%%!%!%%%!%?!%!??!!!%!!%!%!%?%!!%%%%!?!%%!!!%%?!%%%%%%!%%%%?%%!%!%!?%%%!!?!?%%%!?!!%!?%%??%%%%!?%!!??!%?%%%!!!%?%%%%?%?!%!?%??!%%%!!%%%%!%!??%%%?!!!%!%?%%%!%!?!%!%!?%%!?%%%?%%!%%?%?!!%%%%!%%?!?!%?!!%??%!%%!!!%!!!%?%??!!!!%%!%%%!?!!%!%?%!%!!!!%?%%!!%%?%!??%%%!?%%!%?!%%!!%%!%?%?%%%%%%%!%!%?%%%???%%!%??%!!%!?!!%%%%%!%%!%%%!%%%%%!!!!%%!?%%!%?%%!%%%?%%!%%%%!!%!!%%?!!%%%!!%!%!%%%!?%?!%%!%%%!?%%!!%!%?!!?%%%%?%!%!%!%!%%!!?%!%?!%??%!%%!!!?%%!?!?%%%!!?!%%%!%?!?%?!%!%??%!!%!%!%!%%?!%!%!%?!!%?!%%%?%%!??!!!%?%%?%???%%?%%%!!!?%%%!%%%!%!%!!!??%%%%!!%!!%!!%?!!%%%!?!%%?%!%!%%%!!?!!%%??%!%!%!%!%%%!%!??!%%!%?%%%%%%!%%!!%!??%%?%!?%!%!!%%%%!%?%??%!!%%!!%%!%%%!!%%?!%%%%??!!%!%!!!!%!%?!?%?????%!%%!?!%!!%%%%%?%!!!%!?!!!%?%!!!!?%!%%??!%??!!!?%!?%?%!!?%%%%%!?%%!%%%%%!!%%?!!%!?%%!!%?%%!!!%%%!%%%!%%!!%!!%%?%!%%%?%??!!%%%!!!%%!?!%?%%!!!%%!%%?!%!?%!%!%%%?%%%!%?%%%%!%%%%%!%!!%!?!%!!%?!!%?!!%!!??%%%!%%!%!!%%%%!%?%%%??%?!%!%?%%%%?%%%?!%%%%%%%!%%%!!%%!%%??%%%%%%%!%%%!!%!%?!?%%%%%%!!%%?!!!!?!%!%??!!!%!!%!???!%!?!%?%!!%!%?!%!!?%!%!%!%?!%!%?!?%!%%%%%%!%%%!!%%!?%%%!!%%%!!!%%!!%%%%?%!%?!!%?!%?%%%!!%%%%!!%!?%%!?!%!!%%!%?!%%!%%!%%?%?%!?%?!%%%%?%%%%%!?!%!?%%?%%!?%!%!%%%!!%?%%%?!%%%?%!%!!!%?!%!?%%!%%?%%!%!%%%!%!?%?%??%!%!%!%!%%!!!%%%!%%%%!!!!%!?!%?%!!%!%?%!%?%%?%!!%%%%%?%?!%?!%!!!%!!?%!!!%%%?%%%!!%!%!%!!%??%%?!!%?!%%%!%?%%%%!!!!%%!??!?%!%?%!!%!%!%%!!!!%%!!%%!!%%?%?!%%!!%%!%%%!!!?%%%%%%??%!!!?%%%%!?!!??%%!?!%%%!?!%%%!!!!%%%%%%!%%%%!%%%%%!!?!%%!!!%%?%%%%%%%%!%?%%%?%?%%%!%%!??%%!%%%%!%!?%?!%!!?%%!%%?!?%%%%%%!%%!!!%%?!!%%!!%%%!!!%%!%%!%!%?%%%%!!!!%!!!%!!%%??%!%%!%!%!%?%%??%!???%%!%!?%%!?!??!!?%%!%!%%?%%%%%%!!%%%!%%?%%!%?!%%?%!!%%%!%%!!!%%%%?%%%%%!!%%%!%%!!?!%%!%%%?%%!%%?%%%??!!%!%%%%!%%!%?%!!%%%?%%??!???%%%?%%%%!!!%!%%?!%?!!!!%%!%!%%%!%?%%!!%%%!?!??!!%%%!!%!%%%!%%%!??%?%%!!%%%%%!!%%%!!??%!!!?!%!%%%??!%%?!!!%?!%?!!!?%!%!?!!!%%?%?!?%%%??!!%%!%!%?%!!%%!%?%%!!!%%!%!!?!?%%%??!?!!%!?%%!%%%!!%!!%%!!!%%??%%?!%?%%!%%%%%!%%%%%%%!%%%?%%!!!%!!%%%??%%%!!!?%????%%%%%%!?!%%%%?!?%%%!%?%??%%!!!!%%?%%%!%?%%%!%%%%?%%!!??!%???%%?!!?%%%!%!!%!!%%%%!%!%%%!%%?%!?%!%%!!%!%?!%?!%!%%!%!???%%%!%%%??!%%??%%%!!%%!!%!%!?%%%!%%?!%%%%!%%%!%%!%!%?!%?%%%%%%%!?!%!%!!%!%!%%%%!?%?%!%!?!!?%%!%!!!%!%%!%%%!?%%%!!!%%%%%!%!%!?%!%?!%%%!!%%!%%!!!%%?%!%%%!!%??%%%?!%!%%!!!!!!%%?!%!%%%!%??%%%%%%%?%!%%%%%%%!!?%%%!?!!%?%%%!?%%!?%%%%%%!%!!%%?!%!?%?%!%!?!!%%%%!!%%!?%%%!%!%!%?%%?%%%%!%?!!?!%!!?%!!%%%%%%%%%?!%%%%%%?%?%%%%%?%%%%?!%%%%%%%%%%%%!!%%%%?%!!!%%%%%?!!?%%!%%%%%!?%%%%%%!!?!!???%!??%?%%%!%%!%%!%%%%%%%%%!!!%!%%!%!!%?%%?!%%!%%%%%%%!%!%?!?%%?%!%!%%%?%%?%!?%%?!?!!%%!%?!!?!!!%%%%%%%%?%%!%!!%%!%!%%??!!%%!!%!%%!?!?%!%?!%!!%%%%%!%%%!%%!!%!%?%%%!%%%?%%!!%%%%?!%%?%!!%%!%%%?!!!%!%%%%%!%?!!%!!!%%%%%!%%%%%?%%?!%%%!%%?%!!!%%%%???%!!%%?%%!!!%%!%%!??%!%%%!%%!%%!?%!??%%%??%!!!!??!!%%??%!!??%?!!%%%?!%!%?%!?%!%!%%?!%!?%%%!%!%!?%?%?%?!?%!%%!%%%!%%%%%%!%%%%%%%%?%%?%??!!?%!%?!?%%!%!%%%?%!%%!!?%?!?%!%%%!!!!%%%%!%!%%?!%%!!?%%!!!!%%%!!?%%%!?!!!?%!!%?%??%!%%!%?!!!%%??!!%%%%%%!!?!%%!%!%%%!!%%%%?%!!%%%%%!%!%!!!!%!%??!%!!!%!!!%!?!?!!%%!?%%?%?!%!%?%!%?%!%!!!!%%!%?!%%%%%%!!!%??%!%!%%?%%%!%%%!%!!%!%!!!!%%%?!%%%%%!%%%%%?!!%!!%%!%%%??%!!!%!%??%%!?%!%!!!?!!%%%!%!%%%?%%%!%?%%!!!!?%%!!????!!!!%%%%!!%%!!%?!!%%!%%%!%!%?%?!%!%?!?!!!%%!%%!!?%%%?%%!%?!%!?%%%!%!?!%%!!!%?%?!??%%%!!%%%!!%%%!!%%!!%%?%%!%!%?%%%!%%!!%!!%%?!!%%!%!!%!%?!?%?%%!!%%%!%?%!%%%?!!%%??!%!%%%%%!!%%%%%!%!%!!%!!!%%!%%??!%%!%%%!%%!%%!!?%%!!!!!%%!!!%!!%!%%%!!!!?!%%%%%%%!!?%%%??!!%%?!?%???%!??%!!!!!%!?!%!!%%?%!!%%%!%%?%!!%!%!!!%%!%?%%%%!?%%?%?%%!?!!!!%!!%?!%!%%!%!!%?%%%!!!%!%!!!%%!%%!%%%!!?!?%%%?!%%%%!!?%?!!!!!%!%%%%%%?%!?%!!!?%!!!%%??!?!!!%%!%??%%%%%!%%%!%!%!!?%%%%!?%?!?%%%!%!%%%%%!!%?!%!!!!!%?%%?%%%!%%%%?!%!!%%%?%?%%!!%!%??%%%%%!%?%!%?%!!%?%%?%!??!%%%%%%?!%%?%%%%%%%?%%?%%!%%%!%%%%%%%!%!%!%%%%!%?%%!%%%!!%%%?!!?%!?%%%!?%!%%!!%!!!%!%!!!!%%%%?%!%%%%%??%!%%!%%%?!!%%%!!%!%%%!!?!%%%%%?!!%!?%!%!%!!%!?!%??!!!%?!!!%?!%%%%%%%%?%%%%!%!%!!!?%%!!?!%?%!!%%!?%%!!?!%%%%%!?!%?%%%%%%%%!?!%?!%!!!%%!%%!?!!%%%%%%%?%%?%!!%!!!%%%%%%%%%%!?%?%?!?!%%%%?%?%%%!?!%!%!%?!%%%?!%%!??%?!%%?!%%%%!!%!%??!%??%%?!%!%%%?!%!?%%%%?!%!!%!!!!%!!%%%??!!%?%!%!!%!!!!%!?%%%%%%?%%%!%%%%%%!?%?%!%!?%%?!!%?%%!%!??!%%!%!!!%%%?!!%?!?%!!!?%!%???%!%!!!%!?!!?!?!%!%%%%!%?!!!%%%!!?!%!!%%%%%%%!%!%!%!%%%%%%?!%!!!!%%%!!%%??%!%%%%!??%%%%%%%?%?%?%%?!%!!%?!%??%!%%?!%?%%%%%?!!%!%%%!!%%%!!!%%%?%!%!!!%%%!%?%%%?!%!!?!%%!%?!%%%%!%!!!%?%?%?%%!%%!%!%%!%!%!%%??%?%!%%%%!%!%!%!%%%!!?%!%%!?!%?!%??%%%%%!!%?%!?%!!%%!!%%%%%%!!%?!%!%!%??%!?%%!%!%!!??%!?!!!!%%%%!%%!!!??!%!%?%!%!%!%%?%%%!%%%?%!!!%%!%%%%!%!%%%%!?!%!%%%!?%%%!%%?!?!%!%!?!!%!?!!%!!%%?%%%%!%%!%%!%%%%?%%?!%%%%?!%%%!%?!%!!%!!%%%%!%%%%%!%%!?%%!%%%!!!%!!%!!%!?%?%%%!?%!!?%!?!!!%%?!!!%??%!?%%?%%?%%?%!%?!%%%%%!!!%!%%%%%%!?!?%?%!!?!!!%???%!%%%%??%?!?%?!%%%!%!!?%%!!%%??%%!%%%!%%!%!?%??%?%%%?%?%?%??%!!?!?%%?!!%%!!%!%%%!%%%!%!!?!%!??!%!%%%!%?!!!!%%!?%?%%%!%%%?!%!%!!?%%??!%%%%!!%%?!%?%%!!!%%%%%%%%%%%!???%%%!!!!%?%!!!%?%%%?%%%?%??%%%%%?%%!?%%!?!!!%!%!%%%!%?%?!!!!!!%!!%?!%%!%%?%%!%%!!!!%!%!%!?%%??%%%%!?!!?!?!%%?%?!!%%?!%!%!%%%!%!%?!%???!%%???!?!?!%%?!!!!?!!%%%?!?%??!%%%%%?%%??%%%!%%!!%%??!!%%%%%%!%%%%??%!!!?%?!%%%%?%?%?!!!%!!!%!!!!%!!%%!!?!%??%%%%%%%!%?!%%?!%!!%!%!!!!!!%%%%%!?!?%%%?!%%%%%%!%!?%%!?%!!%%%!%!%!%%!%??!!%!%!!%?%??%%!%!%%?!%%!!%!??!!%?%%%!!%!%?%!?!%%%%?%!%?%%%!%%%%%%%?%%%?%!!%!%%%%%!%??!!%!?%?%%?%?%!!!%%!!%%!%%%%?%%!?!%%!%%%%%!%!?%%!%!%?!%!%!%%!%?!!!%%%?!%!?%!%%?%%!%??!!!!%!%!%?%!?!%!?!%?!!!%!??%!%?!%%%%!%!!!%%!?!?!!%%?%%%!%!?!?%!?%!%%?%?%%%%%!!?%%!%?%!%%%%?%!%%%!!%%!%!%!%!%%?!%?%%?%!%%?%!%%%!%%%%%%!!!%!%!%%%%%%!%!%!%!%?!%%!%%%!?!!%!!!?%?%?!!%!%??!?%!?%%%!!%%%%!%%!!?%!%%%!%!?%!%%?%?%!%%%!%%%%!!??%!%!!%%%!!%%%%%!%%!!%!%%%%%!%%!?%!???!%!%%%!%%%%%?%?%%%%%%%%%%!%!!%%%!!%??%?%!%!?%!%?!%!!!%!!%!?%!!%!%%%%?%?!!%?!%%%!%%%%!!%%%!??%!%%%!%!?%%%%!%%%?%?!!%%!%%!%%%!!!%%%!!?!!%%%%%%?%%%?!%%%%%!!%%%??!%%!?%%%%%%%%?%!!!!%%%%?%!!%%%%%??%%%!!%%!%!!!!%%!%!%%%?!!!%?%!!%!?%%%!%%?!!%%!%%?!!%!!%%?%!!?!!??!%%%!!%%??%%!%%%?!!?!%%%%??%%%%!?!%!%%%!%!!%%!%%??!!%%???!!%%%%!!%%!!!%%!%?%!%!?!%%!!!%%?%!!%%%%!%%!%%!!?!%?!?!!%%%%%!%!!!%!%%!??%%?!%%%??%!%!!%!%!%!!%!!%!!!!!%%!%%%%!%%%%%!?%%%!!!?%!%%%%%?%%%!%%%%!%%%%?!%!%%?!%%!%%?%%?!?!%%!%%!%!?!%%!!%?!%!!%%!%?%!!%!!%!%?%!%%?%?%%%%%%%!!%%%!%?%?%%%!%!%%%%%!%!?%%%%!%?!!?!!!?%%!!!!%%%%!!??!%!!%!!?%!%%!?%%!%%?!%%%%%?!%!?!%?%?%%!!%%??%!%%%%!%%!???!%!?!%!%?%?%%%!!!%%!%!%%%?%%?%?!!!!!?%!%%%%?!%!%!%%!%!!%%!%%%%!??%%%?!!%!?%%%!%%!%%?!!?%?%!%%%!%%!!%!??!%%%%!%%%?!%%?%?%!%??!?!%%!!!?%?!!!!%%!?!%%!%!%%!%!!!?%%?%%%%!!!%%%!%!%%%%%??????%%!%%%?!%!!?%!??%%%!!%%%??!!%%%!?!%?%?!?!?%?%%%%%%?!!!%!%%!%??!%%!%%%%!%!!?!%%!?%?!!!%!%?!?%?!%?%%%!%%!!?%%!?%!%!%%%!??!%!%%%!!%%!%%%%!?!!!!!%%?%%!%!!!?%!!%?%!%?!%?%?%?%%!!%%!%%!?!%%%%!%%!!!%%?%%!!!!!!?%!%!%!??!%%!?%%%!%%!%?!%%?!!%?%!!%%!!%?%!%!?!?%?!%!?%%!%%!!%?!%%?%%!!%?!!%??%%?!%%!%!%%%?!%!%%?!!%%%%%?%!????!%!?!%!%!%%!!!%%?!%%!%%%!!?%%%%%%!%!%%%%!%!%%!%%%%!%!?%%%%?%?%?%!!?!%!?!%!%%?%%%%%??!%%??%!!%!?%!%?!!!%%%%%!!?%%?!%%!?%%!?%!%%%%?%!%?!!!%%%%%?%%!?%!%%%%%?%%%%%?%?%%%%???%%%%%!%%%%%!!?!%%%%%!%!%%%!!?%?%?%?%%%!%%%!%!%%!!!??!!!!%!%%?%%!!!%%!%%%?!?%?%?!%%%%?!!%%!%??%%%%%??%%%?%!?%%%?%?!??%%%?!%!!%!%?%%%%!?%%!!!%???!!?%%%!%%%%!%%!%%%!!!%!!%%%%?%%!?%%%%%!?!%?%%%!!!!?%!%!!%?%%?%%!?%!%!?!!%%!?%!!%%%?%%%?%?!!!%%!%%!%%!%%%!%!%%%?%%%?!%!!%!%%!%%%?!%!!%?!%%%%%!!%?%?%?%%%%?%!!%?%%?!!?!%?!%%????%!?%%!%%?!!%?%?%?!!%?%%?!%!%!!%%%%%?!%!?%%%%!!%?%?%!%%?%!!%%%%%!!?!%%%!%%%!?%%%%!%!!%!%%%!!%!?%%!!%%!!%%?%!?%!%!%!%%?%%??%!%!%!%?%%!%%%%%??!%!%!?!%%%!!%!!%!!!%%%%%?%%%%?%%!%!!!!?!%%%%%%!?!!!?%%%%%!!!!%!!!%%%%%!?%%%%%!%%%%%!%%%%?%??!!!%!%%!%%!!?%%%!?!?!%%?%!?%?!!!%!??%%%%??%%%%%!?%%!!%!%%?!%%%!!!!%!!%!%!!!%!!!?!%!?!%!?%%!%!!%%%%!?%%%!?%!%?!!!%%!?!?%?!?%%%?%!%!!!%!%%%!%%%%!?%%%%%%%%?!%!?%%%?%%%!%?%%%?!?!%%%%!!%!%??%!%??!%!%%?!!!?!??!!!!%%!%?%%!!!%?%%!!!?%%!%%!!%?%??%%!%%%?%%%!!%?%%%!?!%%%%%%%%?!%%!%?%?!?!?!?!?!%%!%%???%%!%!%%%%!%!!!!!!%!%!!%?%%!%??%!%!%%!?%!!%%!%!!%%%!?%%!?!%%%!%%%%!%%%?!%!%?%%!%%%%!%%!!%!!%%!!!!%%!%??!%%%%!!!%%%%!%!!?!!%!!!!!%%%!%%%!?%?!?!%!%??!?!!!%?%%?%!%%!?!?!%%%?%!??%%%!%%%!%!%!%%%%%?!!%!!!!%!!!%%%%!%!%%%!%%%!?%!%%!%%%!!%%%!!!!%%%%%!!!?%!!%!!!?%!%!%%%%?!%!%%%?%??%%%????!%?%!%%%?%%%!?%!%%%?%?!?%!%!?%%!!??%!!!%!%!!!!?%%%?!%!%!?!%%!!%?%%!%%?%%%!?%%%%?%%%%%%!%%%!%?!%%%%!??!!?%!%??%!?%?%%!!%?!!!%?%?%%!%!%!%%%?%%%!!!??%!%?!%%%!%%%%%!?%!%%%%!%%%?!!%!%%%!?!?!%%%%?!%?%!%!!???%!%%%%%!???%!%!!%%!!%?%!%!!!!!%!%!?%%!%?%!!?!%?!!%?%%!%%%%%%?%%%!%%!%%?!%%!%%%??%!%?%!!?%!%%%%%%!!%!!!!%?%!%%?%?%!%%%!%!!%%!??%%!?%%!!%%%?!%!!!!!%!?%??%?%%%%?%%%!%%!?!%!%!?%!%%%%?%%?!!!%?%%%%%!!%?%%%%?%%%!%%%%%%%%%!!%%%!!!%!?!??%%%%%!%%%!%%??%%!%%?!?%!%!!!%!%!!!%?%?%%!%!!%!!?!!%!?%%!%!%%!%%%?%?!!%%%%??%!?!%!%%!%%??%?%?%%%%!%!%!!!%!%??%%%!%!!%%!%%%%%%%%%?%%?%%?%%%?%?!!%!%%!!%%!!%%!!!%%!%%%!%?%?%%%%!%!!?!!%?%!!%!%%?!%!!?%!%!%%%!!%!?!%!%!%?!?!!%%!!!%!???%%!!%%!%%!%?%!!!!?%%%%!!!%%!!!!!!!%%%!%%?!??%!%%%!%%%%%%!%%!!%%%!!%%%!!!!??!%%%%%?!%%!!%%%%!%%%%!!!%%%%%%!?%?%!%!?!!%%!!%%%??%%%!%!%%%%?%%%!!%!%!%%!%%%!%%!%%%%%!%%!%!%%%?!!%%?%%!!!%!?%%%!%!?!%%?!%%%%%!%!%%%%%!!!%%%?%?!?%?%!%!%!%%%%%!%!%%?!?!!%%!!!%!!%!%?!???%!!???%%!%!%!!%?%%!?!?%%%!!!%%?%%%?%?%!%%%%%%%%!!?!!%?!?%!%!%%%%!!!!!?!%!%?%?%%%%%%!!%%%!%%!!!!%%%%?!%!%%!?!?%?%!%!%%?%%!??!!!%%!!!%%?!%?%%?!%!!%%!%%%%!?%%%%!!!!?%%%?%?%!??%%!%!?%%%%%!!!%%%%!!%%%???%%!!!!?%!!%!%!!%%%?!%%%!%%!%%!%!%%!%%%%%!?!%%?!!%!!!!?%?%?%!!!%!%%?!%!%!%!!%!%!?!%?!!!?%%?%!%?!%!!!!!!!!%!?%%%%%%!%!%!%%!%%%?%!%%!!%!%%!%!?!??%%%!%!%!!%!%%!????%%%?!%%%!%!!%%!!%%%!!!%!%!!??!%!%?%%!?%%!%%!!?%%%??%%%!??%!%%!%!%??%?!%%!%%%%%?%%!!?!!%%%%%!%!%!%?!!%!??%%%%?%!%%%%%%%??!%?%%!!?!%??!!%%!%%%%%!!%%%%!%!!!%!!?%?%%%%?%!%?!%!%%%%%!?%%!%%!%%%!%!%!!%%!%%?%%%!%%%?%%%%!%?%!?%%!!?!%?%%%!??!%!!%%%%!%??%!%%%%%!!%!%???!!??%%!?!%%%%!!!!%%%%?%?!!%%%!%!!??%%!!??!%!%?!%%%!!!%!!!%!%!%?%%%?!?!%!?%%%!!%!!?%%%!!%%!!!!%!%!%%%??!%!%%!%!%!%!%?!%%!!!?%%!?%?%%!?%%!%?%!!%?!%%%%!?%%?%!%!%%%%!!!%!%!?%!!!!?!%%?%??!%!%%%%%%%!!?%!%%!?!%!%%!%%!%!%!!%%%!%%?!%!%%?%!%!??!!%?!%%%!%?%!%%%%%%%?!!!%%!!?%?!%%??%%%%%!!%%?%!%%!%%!%%%!!!?!%%%!%?%!%%%%!%?%?%%%!%!%!%%!%?%%%!?!??%!!%%?!%%?%???!!!!%?%%!%???!%!?%%!%!?%%%!!%%%%!%%!!%%%%%%!%%!%!!!!%%%!!%%??%!!%!%%%%!!%%%%%!%!%!%?!%!!%%%%!%%%%?%%!%?!%%!?!%!!!!!???!%?%!?%!?%%!!!%!%%%%?%%?!%!!%!%!!%?%?!!%!!?%!%?%%%%!!%!%%%!%%?%!%!%!%?%%%?%%?!%%?%?!!!%?%%?!?!%?%!!%!%??%!!??%!??!!?%?!%%%%!%!!%%%!?%%?%%%?%!?%%%%!?!!!%!%!?%!%%!%!%?%?%!?!%!!?%!?!%%%%%%!?%!%%?!%!%!%!!%!%!!%!%!!%!%!!%?%%%?%%%!%?%!%%%%!%!%!!%%!%!?!!!%??%!%%%!!%!!%!!%?!%!%!%%%!%%%%!%%??%%!!!??%%%?%?%!%%?%%!%?%%%!%?%%%!!%%%?%!%!%%%!!??%!%%?!!%%???!!%%%%%!%!%%%?!%!?%!%??%!%??!?!%%!?%?%%%!%%!%%!!%%?%%%%!?%%%%!?%%?%%!%?!%?%%%%%%?%%%%%!%!%!%%!%!!%%?!%%%?!!?!%!!%!%%%%!%%%!??!!?%%??%%%%%!!?%%%%%!%%%%?%!!%?!%?%%%!!%!%!%%?!!!!!%%!!?!%!%!%%?%?%%!!%%%?!%!?%%!%?%!%?!!%%?!!%!?!!%%?%!%%%!%!??%%?!?%%?%%!!!!?%%!!%%!%%%%??%!?!!!!!%!!%!%%%%?!!%!%!!%?!?!!!%%%%%%%!?!%%%%%%%!%%%%?%?%%%%%!!?%!%!%?!!!!%%!!!!!%%%!%!?!?%!%%!!!!!%%!%!%%??!!!%!??%%?!?!!%!%%%%?!!%?%!%%!%%!%!?%%%%%?%!%?%%%!%!!?%?%!%!%!!??%%??!%?%!??!?!%!%%?%%%%!??%%%!!!%!!%!?%%%%!!%%%?!!?%!%%!?%%??%%!%%!!%!%%!!!!??%!!%%??%??!?%!!%!%%!!%%!%?%%!!??%?!%!!%?%?!%??%%!%%%!%?%%?%%!%%!%?%!!%!%%?!%!!%%!%!%%%!?%!%%!%??%!!%??!!%!!!%!%%!%!!%!%!%?%!?!%?%%%!%%%%%!%%!!%!%!!%%%%%!%%!!%%%!%%!!!??%%%%%%%%%%!%%%%%%%%!%%?%!??!%%?%%%!?!!%%!%%%!%%!%%%%!%!??%?%%%%!%??%!!?%!%??!%%?!??%%!!%!%??%!!!%%%%!%?%%!?%?%?%%%?%!!%!%?%%%!%!!%!!%!!%%%%%%?!!%!?%%!!%?%!?%%%!?%!%%%%!%!%!%!?%%%!!!%%?%!!!?%%%!%%!!%!%%!%?!!%!?%!%%%%?%%%?!%!!%%!!!!!?%%%!%!%!?%?!%!%!%!?%%!%%%!!?%%!%!!%%%!%!%%%%!?%%%%?%%%%%%!?%!%!!?%%%%?!%!%%!??!?%%%%%%!!%%!%?!%%?%!!%!%%!?%?!%%!%!!!%%!!%%%!?!%!%?%!!!%%%%%?%%!%%?%?%%%%%??%%!%%?%!%?!%?!!?!!?%!%%%%!%%%!%%!%%?%%!!%!%%!?%???!%!!%!%!!%???%%%??!%!%%?%?%%!!%!!%%%??!%!%!!%%%!%%%!%%?%!%!!?%?%%%!!!%!!%!%!?%%!?!!!!!%%%!!%%%%%%???%!%%%%%%!%!%%!%?!???%%%%%%%?!?%!?!!%%?%!??%?%!!%!!!!!%%%!%!%%%!!?!%!%?!!%??%%%!%%%%?!%!%??%!?!%%!%%%%%!!?!%!%%?!%?!!%%%!%%!%?!?!!%%?%%%!%%!%?!!%%%!%%!%!!!%%?%%!!?%%%%%!%%!%%%%%%%!%%!%!%!%!%?!?!?%?%!?%!!%?!%!%%!!?!%%%!!!%!%!%%!!?%!!?%!%!%?%?%!%%%!!%?%?!%!!!%!%%?%?!?!%!!!%%%%%!?!%!%!!%?%%%?%%?%%%!%%%%%%%!!%%%!%!%?!%!?!%!?%%%%%!!?!?%!%%!?%%!?%%!%%?!!!%%%!%%%%?%!!%?!%!%?!!!%!?!%%%!%%!%!%%!%%%%%?%%?%%%?!!%??!%%?%!%!%%!?!%!!!%%!!!%!!%%%!%%!%%%%?!?%%%%!%%%!%?!%%!!%!!?%!?%!!%??!!%!%%!!%%?%%!%?!!?%%%%%%??!%%!!!%!?%%?%!%?!%?!%%%!!?%!!%%%?%%%?!%%?%!!%%!%%!?%!%!%%?%%!%%%%%%%?!%!!!%?%!!%!%%!?!!%!?%%%!%%%?%%!%%%%%%!%!%%%!%%%!??%!!%%%%%?%!%%%%??%%!%!?%!?!%?%%%!!!%!?%%%%%!!%%??%!!?%??%!%?!%%%!?%!!!%%%%?%%%!%!%!%!!!%!%?%!!%!!!%!?%?%!?%???%%!!!?%%?!%%%!?%!%%%%!%!!%%!?%%!!%%%%?%%%!%%?%%?%!%%%%%%%!%%%?%%!%?!?!!!!!??%%%!%%??!%%%%!??%?%?%%%%%%%%!%!%%%!!%?%!!!!%%%%??!%%?%?%%?%%%%!!!?!!%??%!%%%%%%%%%??%!%%%!??%!!!%%!!%!%!!%%%!%%%!%?!!%%!!!%%!!%?%%%%!!%%%!!!!%%%!%!?!?%?!%%%!%?!%!%%!%!!%%???%%!%%%!!%??!%!?%!%%%%%%!%!!!%%!!!%%!%%?%%%%%%%?%%!%!!%%!%!%!%!!!%!%!?%%%%%%%%%!?%!%%!!%!%??%%%!%%%%!%%%!!%%%!%!%%%!!%!%?!!?%!%%%!!??%!%?!!%!!!!%%%!!!%!%!%??!%%%%?%%%!%%!%%%!?!%!%%!%%%!?%%!%%?%%%!%%?%!?%%%!%!!%!%?!!%?%?%!?!%%%!%%%%!!!!!?!%!?%%%%?%?%!%%!%!!!%%!%%?!??!%%%!%%%%?%%%?!!%%!!%%!!!!%!%%?%%!%%%%%%%%?%%?%!??%%%?!%!?!!%%!!!%%?!!%%%%%!!%?%%!%?!!!%?!%%!!%%!?!!%%!!!!%?%%%!??!!?%%%!!!!!?%??%%!%%???%%!!%%%%!!%%%%??!%!!!%!%!!%!%!?!?!%%!!?%!%%%!!?!%!!%!%!%%%%%%%%%%!%!!%%?%%%!%%!%!%!%%%?%??%%?%%%%!%!%%?!%%%%%?!!%%%?%?!!?%!!!!%!%!!%%%!%!%!%%%%%!%%!!!%%%!%%%!%%%%?!%?%%??!%%%?%!??!?%?%!%!%!%%?!!?!%%?%%%%!!%%%!%%!%%?%%%??!?%%!%%!!%!!%!!%!%!?!!%%?!!%%%!%%%%?%%%!!%%!?%%%%!!%?%!%%!%%!%%!!!%!%!!!%??!%%!!!%%!!!!%!!?!%%%%%!%%?!%!%!%!%?%!?%!%!!!%%%?%!%!%!%%%%%?%%%!!%%?%!%%%%!!?%%%?!!%!%%%%?!%%?%?!%%%!%%%???!%!%%%!%??!??%!%%%??%!??!%!!!%%%%!%%%%?!!??%%%?%%!!%!!!!?%?%!?%%!!?!!!?!%%!!%!!!%%!!%%!!%?!!%?%%?%?%??%!%%%%?!!%%%?!!%%?!!!%!%%%!%?!%!%%%%!%%%!%!!?%!%%%!?!%?!?%?%%%!%?!%%%%%%?%!!%%?!?%!%!%!%%%%%!%?!!!!%%!%%%?!!%!!%!!?%%!%!%%%!!%!?%%%?!!%?%%?%%%!?!%?%%?!%%!%?!%%%!!!%!?%%!%%!?%%%%!!%??%%!?%%%%%%%%%%!%%%!?%??%%?%?%%!%?%?!!!!?!!?%!?!%!%!%!%%!!%%!%!%%!?%?%%!!%??%%%!%%???%!%!%%%%%!!?!%!%?%!%!!!??%!%%?%?!%!?!%%%??!%!!!!!!!%%%%%!!%%%%?!%??!%!%%%%%%%%!!%!!%!%?!!!%%%??!%%!%!!%!%?!%!%??!?!%?%%!%?!%!?!%!%!!!%!!%%%%?!%!!!!?!!?%!%%!!?!?%?!%%%%%?%!%%?%??%%%!%!%%!%%%!%!%%!!%!!%%%%!%%%??!!%%%%%%!%%%?%%!%!%!!?!%%%!%%??%%%%%%%%%%?%%?%!!%%%!%!!!!%%?%!%%%%%%!%%%?!%!%%%!%%%?!!%!!%%%!?%!?!%?%%%!%%%!?%?%!!?!%%%!%%%%!!%%!%?%%?%?%%!!%!!%%%!!!!%!!!?%%%%!%%%?%?%!?!%?%!!!!%!%!%!?!!%%!%%%%%?!%%%!%%!%!%%??%??!%!%!%?%??%%%!%%%%!%%!%!!%%???!?%%!?!?%%!!?%%%?%%%%!?!%%%%!%%!!!%%%!!??!!!%!?%%%%?%!%!%!%!%?%!%!!%!%%%!!?!!??!%!%!%%??!!!%!!%%%%!%!%%%%!%%%%!%!!!!%%?%??%!?!%%!%%%%%%?%!%?%%%!?%%!!!!%!%!%%!!?%%%%%!?%?%!%?%%!%?%%%%!%??%!%!%!%%!%!!?!%!%%!?!!%?!%!%%%!%%%%%%%?!%%!%%??%!%!%?!?!!%!?!%%%%!!%!!%?%?!?!%%!%%!!!!%!!%!!%%%!!?!%!!!!!%%!!%?%??%!?%?!%%?%?%%!%%?%%!%?%??%!%!!%%!!?%%%%%?!!!%!%!%!%!?%?%%!%?%%!%!?%%?%%%%!??%??%?!%?%!%!?!%%%%%%!%!!%%?!!%%%!!%%%%??!%%%!?%%!%%?%%%!!%%%%%?%%?!?%!!%!!%%!%%!!%%!%!%?%???!?%!!!?!%%%%?!%%%%!!%?%!%%%!%%!%%??%!%%!%?%%%%!!%!%!!!!%%!%!!!%%%!%%!%%%!!!%!%!!?%%%?%!%%!?%!!%!%!%%%%!%%!!!?!!!?%%%%%!%%%%!%!%?%%!!!!%%%?!!%!%!!%%?%!?%!?%!%%!!??!%!!%%!%!%%%%!!??%%%!%!?!?%!!%%?!!!!%?%%?%%%!%?%!!%%?!%?%!%?%%%??%?%??%%%!%%%%%!%??%%?%?%?%!!%!%?!%%?%%?%!!!!%??%%%!%%?!%!?%%%?!%%%%!%!!!?%!?!%!%!%!%%%%!%!%?%%!%%!!?!?%%!%!%!?%%%?%%!%!!%%%%?!%%%%?%%!%%??%?%%!!%!%?!%%!%%?!%???%%!%?%%%%!?%?%%%%!%!%%!%?!%%?%!!!?!%!!%?%!!%!!%%%!%%%!%%%%%%%%%%!%%%!%!%?%?%?!%!%%%!%??%!%?!!%!%!%%%!%%!!!?%%%%%!?%%!%%%?!!%%%%%%%!%?!?%!%%??%%%?!!%%!%%%!!?%?%%%?!!%%%!%??%!%%%%?!!%%!!%%!?!!%%%%%%%%!!%?!!?!%%%%?%?!%%?!%%%?!%%??%???%%!!%!%!%%%?%%!%!%%!!!%!!%!%%?!%%%%!!%!%%%!%%%%%!!%%%!%%%%!!!!!!!%%%!?!?%!%?%??%!%!!%%%%!%%%?!?!!!!!%!?!%!!?%???!!%!%?%%!!%%!!?!%%!!%!?%?%%%!?%!%?%?%%!!??%%!!!%!%%%?%%%!?%%?!!%!%!!%!%%%%%!!%?%%%?!!%%%%%%!%%!%?%%!%%%%%%?!%!?%??%!!%%%%%%%%%%%%!%?%!?%!%%%???%!!%!!!!%!%%%%!%%!%%%!%??%!!!%%?%?!%%?%%%%?%%%!!%%%!??%!%!%!!?%!!??!!!??%!%%?!%%%!%?!%%!!%%%!%!%!?%%%?%!%!%!!?!%%%%?!%%!!%!!%%%!%%?%%%%%%%!%!%?%%%%!?!!%%%%?%???%!%%??!%%!!?%%!%%%%%%%%%!%!%?!!%!?!!%!!%!%?%?%!%?%%?%%%!??%%%?%%%%%!%%!%?!!%%%!%%!!%%?%!%!??%%?!%%%%%%%!!%!%%%%%!%%!!!!!!%!!!%%??!%?%%!?%?%%%%!!?!%%%?%%?!%%!%%%?!?%?%!!!!%%!%!!!?!!%%!%%%%!?!%%%!?!!%?!%?%%%!?%!%%%%%%%!!!%?%%!!!!%!!%%!!%!%?!!%%%%%!%!%%%?%%!%!?%!!%%%%!%%%%%%%%%%%%!!!%!?!%%%%%%%%%%?%!!%%?!%!?!%%%%%%%!%?%%?%%!%%!%!%%%%!!?%!!%!%!%%%!??!!%!!%%%!%%!!%?%%?%!??!!!?%%%%%%??%%%!?!%%%!!!%%!%!%???!%!!?%!?%%%%%%!!%%?%?%!?%%!%?%!%%%%?%!%?!%!??!?%%%%!%?!!!?!!!!!?%%!%%!%!%%%%?%%%%%%%%??!%!%?%%%?!!%!%!!%%!?%%!!!%!!!!!!?!!!%%%!?%!%%%!%%??%!?%?!%%%?%!%!%!??%%%!!%!!??!!%!%!%%!%%%%%%?%?!!%?%%%%%%%?%!%?%!%%%!%%?%%!?%!%%!!%!!!%!%%%%%%!!!%?!!%%?%%!%%!%%%%!?%%!%?!?%?%!%!%?%!!?%%%?%!%%?%!!!!%%?%%%%%?%??%%!%!%%%%!%%%%!?%?%%%%%?!%?%%%%?!!%?!!%?%?!%!%%%?!?!%!%%%%!%!!%!%%!!%%%%%%!%%%?%%!!!!!??%%?%%%%%?!!!%!%%?%!!!%%%!%!%%%?%%!%?!?%%?%!%%%!%!%!%%!!?%%%%%%?%%%!%?%%!%%%%%!%%%%%%%!?%%!!%?!?!%!%%%!%?%%?%!!?!??%%%?%?%%%?%!%%!?%!!!%%%!%%??!%%?!%??!?%%?%!?!%%!!%?!!%!%%%%%%%%?!?!%?!!!%%!!!%!?%%%%!!%%!%?%%!%!!??%%%%!%?%%?%%%%!%%!%!!!%!!%??%%?!!?!?%!?!%%%!!%!!!%?%%%?!?%!%!%%%!!!!%!!%?%%!%%?!?!%%%?%!?%%%!!!%!%!%!%%!!%%%%!!%!%%!??!!%%!%?%%%?!!%%!!%!%!!%!!%?%%%%%!%%%%%%%%!%%%!?%%?%%!!%%%?%%%%!!!?!?%!!%%%%!?%%?!%%%%%!!%!!%%%%!!!!!%!!!%%?!%%%?%%%%%%%!%?!%%%!!%!!%%%%%?!%%%%%!??!!!%!%!%%%?!!%%!!%%%%%!%?%!%%!!%?!%%!?%??%??%%?!!%!?%!%?%!%!!!!!%!%%?%%%!%%%%!!%!!!!!%?%%??%%%%%?%!%%%%!%!%%??!!!%!!!%%%%!!!%%!?%!?%%%%!%?%%!%%%!%%%?%!!%!%%?!!?%!!!%%%%%?%%%?%%?%!%??!%?%?!%%!%!!?!!%%%?%?%%%!%!!%%!%?%%%%%%%%?!!%%?%!%!!%%%%%!%%%?!%!!%%%!!?!!!%%?%%%%%%%!?%%?%%%?!?!%!!!?!!!!%%!?!%!%!!!%!?!%??%!??%%!%%%?%%%%!?%%%%%%!%????%?%!!?!%??%%%%%%%?%%?%%!!%%%!!%%?%?!!?%!%!!%%%!?%%%???%?!!?!%!%%!!%%!?!%%%%?%%!%%%%%%%%!%%%%?%%%%%?!%?%?!!!?%%%?%%%%?%%!?%%!%%??%!%!!%%?%!%!?%??%%%!%!?!%%%?%%?%%%%!%%%?%?%%?!?!%%!%%%%%%??!%%%?!!%%!!%!!!%%?!!%%!%?!!%%??!?!??%?%%!!!%?!%%!?%%!!!!!!%%%%%?!??!%%%?%%!%!%!%!!?%!!%%?!%%!??%??%?!?!%?%%!%!!%%!%%%!%!%?%%!!%!%!?%?%%?!%%?!?!!?%%%!!%?%!%%?!?%!!!!!%%??!!%?!%!%!?%!%!%!!%!!!?!?!!%!!?!%%!?!%?%%?%!%?!%!?!%!%!??%%?!??%?%!!%%??%!%?%!%!%!!!!!%!%%%?%!%!%?%!%%%!%??%%!?%?%???!?%?%?!%%%!?%??%%%%!!%!?%%%!%!%!!%%?!%%%%%%%!!!%!%?!%%%?!%??%%??%%%%?%!??%!!?!!%%%%%%!!?%!%%%!%%%!%!%%%%%%%%%%%%%!!%!?%!%!%%??!!%%%?!%!%%%%!%?%?!!%?%%%%%%!?!?!%%%!%%!!%?%!!!%%!!?%%?%%!!%%%!!?%!?!!%!?!!%!!!%%!!!!?%!!!?%%%??!!!%!!%!%?%%?%!%%%!!!!!%!!!%%%!%?%?%??%%%!!%!!?!%%?!%!%%!?%!%%!?!%!!%%%%%%%!%%!!?!!%!%?%%?%%%!%%%%!!!%%?!!!%!%?%%%!%!%%!%%?%!%!%!%?!!%!%?%%?!?!%!?%?!%%!%!%%%?%%?!%!!%%%!??!!!!%!%%!!%%%?%!?!!!?!%!%!%%!%!!%%?!?%%%%%?!!!?%%!%!!?%!%%%!%!%%!!%%%!%%!%%%%!%!!!%!%!!!!%!%%?%%%%!%?%%%%%%!%%!%!!%!%?%%%!!!!?%?%?!%!%%%%%%%!%%!%!!!?!!%??%!!%!%%???%%%!%%%!!%!!!%!%?%%%%!%?%!%%%!?%?%!!%%%?%?%!%!!!%%%%!?!!!%!?%!%!!!!?%%!%!?%?%!!!%?!!!%%%%!%?!%%%%?!!%%%!%%!?!%%%!!%?%!%%%!!!!%?!%!%%!!%!!%%%%!!%%%%?%%%!?!%%%!%%!%!!!?%!!%!%?!?!!!%!!%????%!%%!%!!!!%?%!%!%%%!%!%!?%%!%!!%!!!!%!!%!!!!!%!!%??!%!%%%%!%!%%%!?%!%%?%!%%!??%%!%%?!%%%??%!!%?%!??!%%!!??%??%%?%%%%%%%%!%!!%!??!?%?%!!!!!!!!%!!%!!!%%?%?%%?%!%%!%!%!%%%%!!%!%?%%!%!!!%%%!%%%!!%%?%%?%!%?!!?!?%??%%%%%%%!!%%?%?%%%!%%%?%!%%%!!?!%!!?!%?%%!!%!?%!!%?%%!?!!??%!?%?%%??!?%%%%?%!%%%%!%!!%%%!??%!%!%%%%!!?!?%?!!?%!!%!!%!%!!%?!%!?%%?!%!!!%?%!%???%!!%%%%%%%?%%%!!!!%%%%%!%%!??%!%!%%!!%%!%!?%%?!%%!%!!!?%!%!!!%??%%%%!%!%?%???!!%%%!!??%%%%%%!?!?!%%!!!%?!!?!!!!?!%?!?!?%%!%%?%!?!%%%!!%!?%!%%!!%%!%!%%?!%%%!!%%%!?!!%!?%%!!%!!%!%%!%%!%%!%!%!%%??%%!!%???%%%!!!%!%??!?%!%??!%%!%!%!%!??!%!%!%%%%%!?!%!!?%!%!%%%%!%%%%!?%%!!%%%%%??%%%%%?%!!%!%!%%?%%%!?!?%?%%?%!!%%%?!?%%%%!%%%?%!!!%%!!%!%!?!%!%?!?!!%%%??%?!!!!%!!%!%?!??%%!%??%!%!!%?%%%%!?%%%%%%?!!%%?!%%%%!%??%%??%!%!%%!??%!!?%%?!%!%!!%%!!?%!%%!?!!?%!!??%%!%%%%%!%?%%!?%%%%%!????!!!!!%!!!%?!%%!%%?%?!%%%%!%?!%%?!%%!%!%%!!%???%%?%!!%%%%%%!%!%?%!%%!!!?%%!%!%!!!%!%!?%%!%!!!!?!!%!%%!??%%%!!?!%%?%!!?%!?!!%%!%%!%%?%!!!%%%%%%!%?!!%%!%%%?!%%%!!%?!!%!!%!!%?!?!?%!!!%%!%??%!%%%%!?!!?!%?%%%!%%%!%%%!%!%%%!?%!!!%%??%!??%%%!?%%%?%??%?%!%!!!?!%%?!%%%%%!!!%%%!?!%?%!%%!%%%!!%%!!%??%!!!%!%?!%%%?!!%!!%!%!!?!!!!%%?%!!!%??!!%!?%%!!%!%?%?!%?%!?%?!?%%!!%%!!!%!%%?%!%%!%!!?%!!%!%%!!!%!%%!%!%%%!%!!%%%!%!!%%!?!%!!?!!!!!?!?!!%!%!%%%!%%%!?%%?%!!%?%!%!%?%!!%!%%!!%%!%!!%??%?%!%%!!%%%%!%??%!%?%!?%!?!!%?%!!!!%%%!?!%!%?%%%%%%!!%%%!%!%?%%!%!?%%?!!???%%%!%%!!!!!%%!%%%?%!%%%!%%?!!!!%?%?!?%%???!!!!!!!?!%!?!%%%%!!!%??!!?!!%%!?%%??%%!!!%%%!%%!!%!?!!%%%%%??%!!!%?%%%%%!?!?!!?!%!!?!!%??!?%!!!!?!%!%?%?!!!?!%!%%!%!%!%!%!%%%!?%%%%!?%%?!%%?!?%!!%?!%%!!%%%%%!!%%?%%!%?%%?%%!!!!!%?%%%!%?!%%%!%%%%!%%!!%?!!!!!%%!%!%%%??%?%?!%%!%%%%%%%%!%%%?%!%?%?%!?%!!!?%%!!!?!!!%!%%!!%?!%!!!%%!?!%!!!??%%!?%%%!%%?%%%!!%!?%%%%!?%!%%%?%%!!%?!!%?!%%?!%??%%?%%!%%%??!!?%!%%%!??!!!?%?!!%!%%!%!!%!%%!?%?%%%!%!%!!%?%%!?%%%%%!%!%%%%!%%!%%!!!?%??%%%%!!%%?%?%!?!!%%%%%%%!%!!%!%!%%%!!%%!%%!?!%?%!%%!???%%!%?%%?%%%!%?%%%?%!?%!%!%!!!%!!??%!%!%!!!%%%%%?%%!!%?%!?%%%!!?%?%!!!!%%%%!?!%%!%%%!%%?%!%!!%%%!%%!%!%%?%!?!!!?!!!%??!%%!%%?!!!!!!!%%%!%!?!!%!%!%!!!!%!%?!%%?!!%?%%%!?%%!!%??%!!??!%%%%%%?!%%?%%?%%%!!??%!%!%?!!?%%%%!!%!%%!%?%%!%!!%%!%%%%!%%%????!?!%?!%!%%?!%%!?%%%%!???%%!%%%?%!%!!?!%%%%%!!%%%%%%!!??%%%%!!%%!!!%!%?!!!!!%!!%!!!?%%!?%%%%%%%%%!%%?%?%!%%!%%%!???%%?!!%!!%%%!?!!%%%%%?%!!?%%!%?%!!%!!%%!???!%%!!!!%!%!%%%%%?!!!%?%!%?%?%!!!!%!%%?%!?%%%!%!?%%%!?%%!?!%!%%%!!%?!!%%%%%!!!?%%%!%?!%%!%%%?%!%%%?%%%!%%???%!%!%?%%!%%?!!!%?%!%%!%%!%!%%%!%?!???%!%!!?%%!!!!%!%???!?%%?!!!%%?%%%??!%%!%!?%%!!%!%%%?%%%%!%%%?!?!!!?!%?!?!%!%%%%!?%%%%!!!%%%%?!%%%%%!%%!%%%!?%%%%!%??%%%!%%%!%%!%?!%%%!?!%!%%?!%%%!%%!!%%!%%%%%%%!!%!!!!%%!?%%!%%%%?%?%?!?%?!%!%%?%!?%%%?%%%%%%!?%%%%%!%%%?%%%%!%%%%!%?!!%%%?%?!%!!!!!!???%!!??%!!%?!%%!!!!%%!?%!!%%?%!%%%!!!%?!%%%%%?%%??%!?%!!!%%??!%!!%!!%%%!???!??%%??!%!%%%!%%!%!%%!?%!%!%!!!!%!!!?!!!%!!%?%?!%!%!%%%!%%%!?!!!%?!?%!%%!%%?!%%!%%?!%?%%%%!??%?%!?%!?%!!%!%!%!!%!!%%!?%???%%?!?%%!!%!%!%%!%!?!%%%%%?%%!!?%%!!%%%!!%!?!!!!!!%%%%%%!%%%!?!%%%%?!!%%!!!%?!%!%?!%%%%!%%%??!%%%!!%%!%%%??!%%%%%?%%!%%%%%?%%%!%%%%!%%%!%!%?%%%!%%%???%!%%%?%%%!!%??%!!?!%%!%!%%??%!!%%%%%%??%!%!%%?%%!!!!!??!!!?%!%!!%!%%%?%!%%!!!!!%!%%!?%%!%%?%%!%!%%%%!??!!%!!%?!%!?%!!!%%!%%%?%!!?!%%%%!!!%%!%%?!!%%%%!%!?!!%?%?%%%%?%!!%%%%%?!%%!?%%?!?%!!!!?%%%%%!%%%%!%%%%!!!%!%!?%%%%!%!%!!!?!%%%%!%?!%%!%%!%?%?!%!!%%%%!!%%%?!%!%?%%%%%%%!!%%%%%!%!%!%%%%%?%%%%%%%!%??%!!%%?!%!?%?%!%????!!!%%%%%!?%!?%!%?%!%?!!%%%%%!%%%%%!%%!%%!!%!!!%%!%?!!!?!%?%?%%%%%%%?!%!!%%!!!%!%!%%!%!!%?!?%%?!!%?!!?!?%%!!%!%%%%%?!!!%%%%%%%%%%%%!!?!!!%!%%!??!???%!!?%%%!!?%??%%%??!%%%%%!%%!%!%??%!?!%%?!%!%!?!%%!%%%%!%!!?%%!!%!%%%!%%%%?!?%%%%!!!%?!!%%??%%?!%!!%%!%!!!%!%?%!%%!%?%?%%%!!?%%!!!%!?%%%%!%%!?%!!!%%%%!%!!!!%?%!%%%%!%%!%%%!!%!%%!!%!!!!!%!%%%%!?%%!%?%!?%?%%?!!%%%%?%%!!!!%%%%%%%?%%%!%%%%!%!?%!!%%%%%!!%!%%%%%%%???%!%%!%!!%%%%%?%??!??%%%%%%!?%%!%%%%%%!!%%!%%%%%%%?!%%%!%?%%%%!!%%%%%%!!!!!%!!%!!%?%%!!%%??%%!!%!%!?!!%%%%%%%%%%!!%%%%?%!%?!%?%!?%?%%%!!%???!!?%%!%%%!!!?%%%%%??!!!%??!!?!!!!!%%%?!!?!%!?%%%%?%?!!%!%%?!!%?!%%!%%!!%%!%!%%?%%?!?%?!!%%%%%!%%%?!!%%%%!?!%!%!!%?!!!%!%!!!!!!%!%%%?!!!!%%!%!%%!?%%%!!%!!?!%?%%!%%!!!%%!!!%%%!%%!%%!!!!%?%%!!%%%%%!%%?!!%%!!%???%%?!%%%!!%%?%!%??%!%!%?%?%%%%%!!%??!?%%%%%?%%!%?!?%%%!%!%%!?!!%!!%%!?!!?%??%%!!!?!%%!%!!!%!%!?%!%!%!%!%%%%?%%%%%%%%!?%%!%%%!!?!%%%!!!%!?!!%%%?%!!!%%?%!!!%!!?%%!!!?%%!!%%??%?%??%!!%!%%!%%!!%!%%%%?%%%??%%?!%%!%%%!%?%??%%%%!%%%%!!!!!???!%%!%%!?%%%%%%%%%!%!?!??%%?!!%%%!!!?%%%%!%%?%%!%!%!%?!!%%!%%%????%!!%!%%?%%!!!%!%%!%!%!%%!!%???!%!!%!??!!!%!%%!%?%!%?!?!%%!?!!?%%!%!%!%%%%?%%?%?!?!?%%%!%!!%%%?%!%%!%%?!?%%%!!!%%%!%!???!%%%%?%%!!%?%%?!!%%%%?%%?%%%%%??%%!?%%!%%%!%%!%%!%%%%%?%%!%!%?%%%%%!!!%!%!%%?%!%%!!%?!?!!%!%!!%!!%!%!%%!?%!%%!!!!%%?%!!!!%%%!!%!%!%!%!%%!!%%?!?!%%%!?!%?!%!!%!!%?%!%%%!%?%%%%!!!!%%!%?%!!!%%!!!%%!!!%?!%!%?!%!?%%%?!!!%%!!%!%??%%??%?%%?%%?%%%%%%%?%%!%!%!!%%!%%!!%%!%?!%?!%%?%?%%%!??!%%!!%?%?!!%%!%%%?%!%!%?!%!%%!?%?%%?%%%%%%!!%!?!%!!%%!!???!!%%%?!!%!%%!?!!!!%!?%!%?!%%%!!%%?!%%?%%!%%!!%%%%!%?!?%%!%%!!%%%?%%?!?%%!!??!%%??!??%%%%!!!!?%!%%%!%%%%!%!%%?%%?%%%?%?%!%!%%!%?%%%%%%%!?!%?%%%?%%!%?!%!!!%!!!%?!%!%???%%!%%%%%%!%%%!!%%!!!!%!%%!!!!!%%!%!!%%%%?!??!%%%%%%!%%!!%%!%%%%%%%?%?!%%!%!!%%%!%!?!%?!!?%??%%%%?!!%!!?%%??%%%%%%%!%%%%?%%%!?!!%!!!%?!%!%?%!!%!%!!%%!??!!??%%%!%!!%!!%%%?!!%!%%%!%?!!!%!!?%%%?!!!%!??%?%!?%?!?!!%!!!%%!!%?%%%%%!%!%!%%%!?%%!!%?%%%!%!??%!%%!%!!?!!!!%%!?!%?!%%%!!%?!?!%%%%%!?%%%%%%%?!%!%%%!!!!!!%!!?%%?%%!%%?%%%%%%!%?%%%!%%?%%%?!%%!%%!%%?!%!%%!!%!!!%%%%!%%%%?%%?%%!%%%!%!%!%?%%!!%!!!!!%%!%%%%?!?!!%!!?%%%?%?%?%%%!%%!?!!%%%%%!!%!?%?%%%%%?%%!!!!%%%%!!!!%%?!!?%!%%!!%%%%!?!?%%!!%!%!?%%???!%%!%!%%%!%%?%%%?!%!!%??%!%%!!!!!!%%!%!!%%!!%!?%??%!!?!%%%%%?%!!?!%%!%?%%%?%!!?%!!??!?%%%??%%!%??!%%!%!%??!!?!%%?%%%!%?%%%!%%%%%%!%%%!!%%%%%%%!?%!!?%!!%%!!?!%?%%?%?%??!%?!%%%%!%%%%%%!%!!%%!%%!??!!?%!!!?!!?%?%!%%!%!%!%!%%%!!!%!%%%%!!?!!???%?!%?%!%!!!%%%%?!!%%!%!??%%?%%!?%%%!%%!%%%%%!%%!??%!%%!%%?!?%%%!%%!??%%?!%??%?%%!%!!!%!%%%?%!?!!%%%!%%!%!%!!%%%?%!?%%?%%%%%???!!!?%%%%%%??!%!%?%%%%!%%%%!%?%%%%!!?%!!!%%%?%%!%??!%%!?!!!%%!%!%%%%!%%%%!?%!?%%%!!%%%!%%%!!!%%%?!?%!%%!%??%%%%%%!%?!!%%%%!%%!%%?%%%%!%!%!%?%!%%?%%%%!!!??%!!?%?%?%!%?!!%!%!!%%!!?!?!%?!%?!%!%%??%!%%%%%?!?!!!!%%!%!?!?!?%!?%%?%%!!%!?%%%%!%?%?!%!%!%%%!%!%%%?!?%!?%%?!%%%%!%!%%!%%%%%!!!%%%%%!%!!?%%%%%%%!%?!%%%%%%%%%%!!?!%!!!!!!%!!!%%%%?!?%%!%?!%!%%%?!%%!?%!%!?%%%?%%!?!%!%!%!!!%%?%%%!!!%!!!!%%%!?!!%!!!%%?!!??%?%?%?%!%%%?%?!?!%!!!%%%!!%%%!!?%!!%??!%%%!!%%!!!!!%%!!%!?!%!!!%%!!!!!%%%%%!??!!!?!!!!%!%%!%!?!!%%?!%%%%%%%%%?%%?%!!!!!%!?!%!%??!!?!%%%!%%%?%%%%!%%%?%?%?%?!%!!?%%?%!?%%?%!%%!%%%%%%%%!%%%?%?%??!%%%%%!%?!%!?%%%%?!!%!?!?%%!?!?%?%%?!??!%%!%!?!%%!%!!%!?!%!%!?%?%%%%!!%%!!%%?!!!!!!??%?%%%?!!!??%%%%?%!%%%%???!!?!!%%!!?!%%!!!%!%!%%%%%%%!%?!%!%%%!%!!%%!%?%%%!!!%!%%?%?!%%?%!!%%%%%%!?%?%%!!?!%%??!!%!!!!%%%!!%%!%%!!!%%?!!??!!?%!%%?!!?!%%%%%!%%%!??%!!!!!%%!!?%%%!%!!%!%?!!!?!%?!%%?!%!%%?!%!!!?!%%%%?%%!%%??%!!%%!%!!?%%!!!%??!%!!?!!%!?%%!%?%!!%!???%??%!?%%%?%!!!%?%?%%!%%!%%?!!%?!%%%!%?!!%!!%!!!!%!%?%%%!%%%?%?%?%%?%!%!%!?!%?%!??%%?!%%%!%!%%%?!?!???%!!!%??%!?%!!%!%!%%?!%!?%!!!%?!%%%%%!%?%?%%%%%%!!%%%%!?%?%%%!!%!%!%%%%%%%!%%%!%!%%?!?%?%%%%%!%%!!%!!!!!%%!%%!!%%!%?!?!??%!?%%%%%!!?%!%!!%!?%???!%%?%%%%%%!?%%!%%?%%%%?%%%%%%%!%%!?!%%%!%!%!%!%%!!!!%??%%!?%%?!?%!%!!%%%%!%?!?!?!?%%%%%%%%%!!!%%%%!%%%%%!%%!!?!?%%%%%%?!%%!!?!%%!%%%%%!?%!%%!!!!!?%%!%%!?%%?%?!%%!!%?%%%?%%?!??!%!?%%?%%!!%!%?%%!?!%%%!?!???%!?%?%!%%%%!%!%?%!!!%%%%??!!%%%!?%!%%!?!?%%%!!?%!!%??%!!%%%%%%?!!%!!!??%!%!!??%!%%!!%%%%?%%%!?%!%!?%%%%!!!%??%%%%??%????%%%!%!!?%!%!%%%%%%??%!!%!%?!?!%%!!%%?%%%!%%%!!%%!!%%!?%%%%%%%!%!!%%%!%!%!%?%!?!!%!!%!%%!%%%%?%%!!!!!%%?%!?%%!%%%!!%%!!?!%??!%?%!%!%%%%???!!!?!%%?%%!%!!%?!%!%%%%!!!!?!!%!%%!!%!!%!!!!!??%!!!?%%???%%!!!%%%%%!!%%%!%%%!!%!!!%%?%%!%%%%%%%!!!!%!%!%!%%!%!!%%%%%!!!%!!%%?%?%!%!!%%!%!%%!%%%!!?!%!%?%!%%%!%?%!!%!!?%!%?%%%?!%%%%%!??%!%!!%%%%?%!%?!%?!%%%%%%!%%%%%!%!%!%!%%?%%?!?%%!%%%%!%!!%?!!?!%?%%%!!!?!%%%!%?!%%??%!%!!?%%!!!%!!%%??%?%%%%!!?%%!!!!%%%%!!%!!%%!%!%???%!%!%?!%%?!%%%?!?%%%!!%%!%%!%%!!%!%!%%%%?%!%%!%!%%!!%?!%%?%!%!?%!%?%!%%%%!!?%!?%%%!?!!%!%!%%%%!%%%%?%%%?%%%?%%%%??%!!!!%%!!%%%%%%!!!%!!%%!%??!%!!!%%?%!!%???!%%!!!%??%%%!!!!?%%%%%?%%!%?!!%?%?%%%!!!!%??!%%%!%!!!%!%!?!!%!%%!%?!!%?%??%!!%!!!!?%!?!!!!?!!!!%??!!%%%!!?%%%%%!?%?%%%!!%%%!%%?%%!?%%!%%?%!?!!%!!!%!!%!!!%%!!!?!%!%?!%%%!!?!!%?!!!!!!!%%%%?%!%%%%%%%!!!?%%%%?!%!%%!%%%%%!!%%!%?%%!%?%!%%!%?%%?%%%?%!%!!!!?%!%%!!%?%%%%%!%%?%%?%!%!?%%!?%?!?%%?!%%?%%!!%%?%!%!!!?!%%%%!%??!!?%%%!%%%%%%?%%%%!%????%%!%!%?!?!!%!%%%!??%!!%?!%%%!!!%!%?%?!!%%!%!%%!?!?!!!?!%?%%%?%%???%%%!!%?!!?!!!!%!%%%!!?%%!?!%%!%%!!!!!?%?%%!%%!%%!%%%!%!!!%%!?%!%%!%%?!%?%!!%?%?%?%%?%?%!!!%%!%%!?!?!?!!?%%%%?%??!%%!%??!%!!%!!!?!!%%%%%%!%!!!!!!%%%%%?%!%!!!%!%!!!!%%%!!!%!!%!%!!!%%%%?%!!%%?!%%!%%?%!!%%%%%%%??!!?%!%!%%%!!%%!%%!!?!!%!%!?%!%%!?!%%!!!!!%?%%%!!!%?%%%!%!%%%!%%?!%!%?%%!%%!%!!%%!!!%%%%!%!?%?!%%%%!%?%!%%!%!%%!!%!?!%%%?%%!?%?%%%%!?%!!?!%%%!%%!%%!!!?%??%%%%?!%!%%?%%%!%!!?%%%%?%%%%%?%!%!?%%%%%!!!%%%%%?%%?!%%%!%%?!!%!%%%%%?%%%%%!!%%!!!!%%!%?%!??!!?%%?%?!%%!?%?%!!!%%!!%%?%%??!?!%!!!%%%%%%?%%%%%%?%!%!%!%!!%%?%%%%!%%??%?!%%%%%%%%%!!%?%?!!%!%%?!!!%%%!!%%!?%%!!?%%?!%!!%%!!%%%?!?%!%?%%!!?!%!!!!!%!?%!!!%%%!?%%!%%%!%!!%%!!%%%%%?!?%?!%%%%%%!?!!?%??!%%%?%%!%%%!%%!%%!!!!!%%!!!??!!%%!?!!?%!%%%?!?!%%%!%!!%%?!!%!!!%%%!%%%%%%%%??%%?!?!!!%!!%%%%?%%?!!%?%%%!!%%%!!!%!?%%!%%%?!!??%%%%%?%%!%??%%%!%%!!!!%%!%%%!?%%!%?%?%%!??!%!%!!%%%!%%!%?%!??%!%!!%%!%%?%!%?!%%!?%%?%%%!!%!%!%%?%%%!%!%?%!%!!?%!%%?!%?%!?!%%?!!!?%%%%!!!?!%%%?%!%%%%%!%!!!%%!!!!%!!%%%%!?!!%!%%%%%!%%%!%%%%?!!%%!%!%!%%!!%%!%!??!%?%!!?%%!%?%?%%!%!%!!%!%?%%!%!!%!%!%!!%%%%!%%!%%%?%?%%?!%%!%!???!!?%%!?%?!%!%!%%?!!!?!?!%?%!%%?!%%%!??%?!!%!%!%%%?%%%%%!%!%?!!!!!!!!%!!%!%!!%%!%%!!?%!!!!%%%%!!%??!%!%!%!!%%%%%%%?!%%%%???!!!!%!!?%%!?!!?!%%!%!%!?%!%?%%?%??%%!??!%%!?%?%%!?%%%%!!!%??!%!%!?!?%?%%?%!!%?!!%!%!%?!%%%!%%%?%%%%%!%!%!%%%?%%%%?%!%!!!?%??%%%%!%!%?%%%!!!!%!%%%!%%!%?%%%%%%?!!?!%!%!%%%!%!!%%!%%%!?%%%!%!%?!%!?!%!%%!!!?!%%%!!!%?%!?%%!%!?!%?!!?%%?%%!%%!%%!%!%!?%%%?!!%%%%%%!!%%%%?%!%!%!%%%!?%?%%%%!%??%!?%%%%!%%%%!%%!%!%!%%?!!?%!!%!%%!!%!%!!%%?%!!%%%!%!!!?!!!%%?!%%?%!!!!%%%%!!%!?!!!%!%%!???%%%!%!%%%!?!%!?%?!%%%%!%%%!?%?!%?!!%!?%!!?%%!%??!%!!!!?!!!!?%!??%%!%!?!!%!!!%!!!%??%%%%?%?%%%!!%%!%!!?%%%%%?!%!?!%%?%!??%%%%!%%!!!?!!%!?%%%!%%%!!?!%?%%%!%?!!%?%%?%?%%%!!!%%!??%%?%!%!%%%!%%!!?%%%!!%!%%%!%!%!%!!!%%?%?%%%%!%!!!%!%%%%!!%%!%!!!!%!?!%%%!%%%!?%%%%!%%%%%?!?%!?!%%!%%%?!%!!?!%!!?%%%%!%??!?!%%%!!!!!%!!%%!?%?!%%%!%?%%%%??!%%!!%%%%%!%!%%?%!%?%%!%??!%!%%!!!?%%!!%!??%%%%%!%%?%%?%!!%!%%!!%!%%!!!%%%%%%%%%?%%%%%%!?!%?%%!%%!%!!?!%%%%?!%%%!%!!%%!%%%%%!?!?%%%!%%%%!?!%%%!?!!%?%%%%!!??!%!%?%%!?!%%%!!%%!!!%%%%%%%!!%?!%!??%%%%!!??!%!%?!!!!!!%%%?%!!?%%%?%!?%!!%%%!!%%%%!!%?%!%%?%!!%!!%%!%%%%%%%!?!%?!!!%!?%%!!%%?%%%?%!?!!?!!%!%!!!!%%!!??!%!!%!!!%!%%!%%!?!!%!%%!!!%%%%%!?%%%!%!!%%%!!%!%%%%%?!%%!%!%%%!!!%?!%!?!%!!%??%%%!%!%%%!!%!%%?%!!%?!%%%!%%?%%??%!!%%?!!%?%?%%!%%!%%%!%?!%!?%%!?!??%!?!?!?%%%!%!!%%!?%%%!!%%!%%!!!%?%!%!%!%%%!?!!%%%!!%%%!!%!!%?%%%%!%%%%%%%?%?%?!%!%!%!%?%%!!!!%%!%%!%!%%%?!%?%%!?%%!!%%??%%%%!?%%???%!%!!%%!%??%%%!!!!!!!?%!%?!!%?!!%%!%!!%%!?!!!%!?%%?!?%%%!!%!!%!%%?%%%?!%%%%%%!!%!%?%!%!!!%%!!%?%%%%!%!?!!%!??!!!%?!%!??!%%%!!%%%!!%!%!!!%%!%!%!!??%%%!%!!%%?%%?!!%%?%???!!%!%!!%%!%%%!%%!!?!%%%!!%%%%%%%!!?!%%%%!%%!!!%!%!!?%%!!%%%%!!!%!%%%%!%!%!!!%%%!%!%%??%%%!%%!???!?!%%%!!%%!%%%!!!!%?%!%!!%%%!!!%??%?!%!!%!??!!%!%!%%!?!%?%?%%%%!!%?%!!%%!%!!!?!%!%!%!!!!!%%%!!!?!!?%%%%!%%!!%?!%%!%%%%%?!!%%?%%%??%%?!!%??!!%!!%!!%!!%%!?!!%%%%!!%!!!!!??%%?!%%%!??!?!!%??!%??%!?!%%!%!!?!!??%%?!%!!!!!%%%%%%??!%?%%%!%%%?%?!!%??%!?!?%!!%!?!%!!%%%!%%?!!%%%%!%?%%?%??!!%!!!%!!?%%!%!%!!%!%?%!%%%!!??!%%!!?!??%%!%%%?%!%%%?%!!!?!%!?%%%!!%%!%!!%!!!%?%%%%%!%!%%%????!%!!%%%%%%%%!?%%!%!!%%!%%?%%%!?!?%%%!??%!%?%%%!?!%%!%!%%!!%!!?!!!??%?%?%!%%%?%%!%%!!%%%!%?!!!%!%%!%!%%!!!?%!!%?%%%%%!%!%%%%%%%%!!%%%!!?%!!%??!!%%!%%!%%%!%?%??%!?%!%%%%??%%%%%%%?%%%%!%%%!!%!!%?%%!!!?!%?!!!!!!!!%%%???!%!%%!??%%%%%%!!%%%?%%%?!%%%%!%!%%%?%?!!!!!?%?!!%?!!%%?!%!?!!!%!!%!!??%?!!%%%%!?%%?%%%!%%?%!%%!%!%%??!%%!!%!!!%!!%%%!%!%%?%%%%%%%%!%!!%%%?!%%%%%!%%%?%!%%!!!%??!%%%%!??!%%%!%%!%?%%%!?%%?%%%%%%?%%%%%!?%?%%?%!!%%!?%%?%!%!%!%%%!%!%?%!!%!!!%!%%%!?%%%%%%?%%!%%?!%!%%!%%!%!%%?%%!%%?%%%??%%%?%%?!??%%??%%!!!!%%%%%%!!%%!%%%!!?!?%?!%?!%%%!%!%!!%?!%??%%%?!?%%%!%%%!?!%%%!%%?%%!%!!!%!%!%!%?%!!?%?%!%!?!!!?%%!?%%%%%?!%%%!%!%%!!!?!%%%%!%!%%%!%%%%!!!!!?%?%%!?!%%!!!!%%%%%!%?%%%%?!??!%%%%%!%%!%!!%!%!%%%%!!!!%%%%%!!%%!%%%!%%!%%%%%!%%?!?%%%%!%%?%%!%!%%!?!?!!?!!?%?!?!?%%%%????!!%?%!!%!%??!?%!?!%%%%%!!???!?!!%%?%%%%?%%%!!?!%!%?!%%%!!!%!!%%%%%%%%%%%!?!%%!!%%%%%!!%!!?%%%!%%!!%%%%??%%!!!??!%%%!!!!!%?!%!%%!!!!!%%%%!!%?!%%?%%%?%%%%!?!%?!%%!!!!!%%%!!%!%%%%?%!!!!!%!!?%%%%!!!%!!?%?%%!%%%!!%%%%?!%?%?%!%?%?%%!%!!!!!!??!!?%%%%?!%%%%?!?!%%%%%!%%%!%%%!%!%%%!%%%!??!?%%%!!!%%!?!%%%!%%?%%!!!?%!!!??%%?%%%%%%?!%%!%%%%%!%!%!?%?%!??%%%!%?%???%??!?%%%!%%!%%?!%??!%?%%%%!!%?!!%%%!%!!%!!!?!%%?!%%?!%%!!??%%!!!!%!!%?%!!?%?%%!%%!!%!%!%!%?%%?%%?!%??!%%!!!%%!%!%%!!%!%!?%?!!!%%!%!!%!%?%%%!?!!!?%?%%%%%!%?%%%%!%!?%?!%!!?%%???!!%%%!!%%%?%%!!%%%!!%%%%!?!%!%%!!%!%!%%!%!??%!%!?!%%?!?!!%?%!%%%%!%!!!%!??%%?%!!!%%!%%%!!!!!%?%!%%?!%%%!?%%?!!!%!%%%!??!%?%?!!!!%?%%?!!%%!%%!%!%%!!!!%%%%%!!?%!%?!%!!!??%%!%%%%%%!%%?%??%??!%!!%%!%%!%!%%%!!?%%%!%%!%!?%%??!!!%%!%%!!!%!??%%%%!%?%%!%!!%?%%%%%%!%?!%%%%%%%%!!?%!!??%%?%?!%%!%!%?%%%%%!!%!!?%%!!%!%!%!%%?!!!?%!%%%!%?%!%%?%!!%%!%!%!%?!%%%!!!%%!?!%!%!???!!%%%?%%%?!%%%?%!!!%%!!%!%!?%!%%%%%%%%!!?%!%!%!?!!%%%?%!%%!%%%!?!!!%%?!%?%%%?%?%!!!?!%%??%!%%!!%!???%%%%!%!%?%!!%%!!!%!!%%%!?%!?%%!??!??!?%!%%%%%%%%%!?!?%!?!?!%!%!?%%?%%%%??%%!%%?!%???!?%!%!%!!%%!?%%?%!?%!%%%%?%!%?!!%!%!%%!%?%!%!%!!!%?%%%????!!?!%%%%!!!%%%%!!!!%!%!%%!?%%!%!%!?%%!!!%!!%!%%%!?!!%!%%!%!!%!%!%!%?!!%%%?%?!?%%%%%%%!!!%%%!%??%%%%%%%?%!!!!?%%%?%!?!?!%???!!!%%!%%%!%%%!%!%%%!!%%%%!%%%%!!%%!?%%!%%?%%%!%%!%!!%!!!%!%%?!%%!!!%%!%%%?!!%??!%?!!%%%%%?!?%?%%!?!!?%%!%?%?%!%%!%!!%?!%!%!!!?%%%?%%%%%%%%!%%%%?%%%!%%%%!%?%!%!!!%!%!!%!!%%!??!!%%%!!%%?%%%%!!%?%?%!!??!%!?!%!%!!?%%%???%!%!%%%%%?%%%%!?!%%!!%!%%?%%?!%!!%!?%??%!!!!?%!!%!%?%%!%%%%!%%%%%!!?%%!!%!%??%%!%?%%%%!%!?!%!%%!!%%%%!!?%!!%%?!%?!%%!%%%!?%%%%%!!?%%%!%%%!!!?!%%?!%!!%%!%!%%%!?%!%!%!%?!!%%%%%%%%%%?%%%!?%?!%?!!!!%!!%!!!!!%%%%%%!!???!!%%%%%%!%!!%%%%%!%%%!%%%%%%!?%%!?!%%%%??!%%%!?%%%%%?!%!!!%!%!!?%?!%%!!%!%?!%!%!%%%?!!%?%%%%?%??%%!?%??!%!%?!%%%!!%%%%%!%%%%%%!?%!?!%!?!!%%%!!!%?%%?%!!%!!%%%%??%%%!%%!!%!!%!!!%!%!%!!??!%!?%?!!%%%%?!!%%%!%%!!!?!!%%!%%%%!%%?%???%??%%%%!%%%%%%%!!!%!%%!%%%%!%!?!%!%%%!!?%%%!%!%!!!!%%!%%%!%?%!%!!%%?%!%?!??!%%!!!%!!!%!%?!%%!!%?%%!????%?%%%!%%??%%%%!!?!%?!!%!%%%%%%!%%%?%%%%%??!?%!%%!!!!?%%%%!?!%!!??%%!?%!%%%%!%%%%%!!%%!!%%%?!%!!%?%?!?%?%%!%?!!?%%!%%%%!?%!%%!!!%%?%%!!%!%%%%!%%!!%%%%%?%!%%?%?%?%!%%%?!?!?%!!%!!%?!!%%!%?!%%!!?!%!!?%!%!%%??!%%?%%%!%!!?%!!%%!!?!!??%!%%%!%!!?%%!%%%%%?%%%?%!!?!%!?%!!%%%!%%?!%?!%!!!!!%%?%?!!!%!%%%%%!%?!!!!%%%!?!!!%!%%%?%%%%%%?%?%%%!?!!!!!!?%??!?!!!%%!!%?%!%!!%%%!%%!%?%%%%!%!%%!%%!!?!?!%!!?%%%!??%%?%%!!%%%?!!%?%?%!%?%!!?%%%?!!!!!%%!%%?!?%!%%!!%!%!!%%!%!%??%%!%%!!!%?!!!%!%%!!!?%%!%%!%%%!!?!%?!%!%%!?%%%!%%!!!!!?%%!%!?%!?!%%!!%?!%!%!!?!!!?!%%%??!%!%%%!%%%!?%%%?!%?!!!%%?%%?%?%%%??%??%!%?!%%!!%!%%%%%%%%%??%?%!%?%%%%!?%!%!?!!!%%%%!%%?!%!%!!%%!%!!!!!%%!%!!%%??!%?%%?!%%!!%%!%%%?%%%!%%%%!%%%!%!%!!!!%%%!%!%%%!%!%%%%?%%%%%!!?%!%!%%%!?!!!%%%%?%?%%!%%!!%%?%!!!%%!%??%%!%!%%%%!!!%%%!!%%!%%!?!!!!%%%%%%%%%!!!!!!%%%%?!?%%%?%%?%%!!%%!%%%!%%?!%!%%!%%%%!!!!!!!!%!%%!%%%%?%!!%!!%?%??!%%%%%%%?%%?!?!!%!!?%%?%%?!!%!!%!!!!!%?!!%!%%!%%%!%!!!%!!?!%%%%?!%%%%%%!!!%%%!!%%%%!!%!%?!??%%!%%!%?%%%?%!%!?%!??!?%??!%??%%%!%%%%?!%!!%%%!%%!?%%%%%!%!!!!%?!%%?%!!%!!%?%?%!!!%?%!%%%%??!%?!%!%!%!%!%%%%%!!!!??!!%%!%%%%%%!%!%?!%%%%!!%%!!!%%!%%!%?!!!%%%%!!!%%!%???!!%%!!?!%%%%?%!?%?%?%!%%%!!%%?%!!!!?%?!%!!%!?%%%?%%!%!?%%%!%%!%!!%%%!%%?%%%%%!%%%!??!%!%%?!%%%!!%%?!!%?%%!%??%%!%!%?%??!%%??!%!?%%!?!!%%?!!%%!%?!%!??%%%%!!%%%!%%!?%%!%!??%!%%!%%%?!!?%!%%%!?!!?!%!??%?!!%!!!%%%!%%!%!!!%?%%!?!!%%?%?%%%%!%!%!!%%?%?%!!!!!%%%%%%?%%%%?%%!!%%%%?%!!%%%!%!%!!%!!?!!%%!!!%%!%!%%%!%%?!%%!!%%!!%?%%!!?!%%%!!%%%!!%%%%%%!!%!%%%!!!%%%!%%%%%!!%!?!%!%!%%%%%!?!!?!??!!%%%%!%?!!%!!%%!?%!%%%%%?%%!?%?%!%%!?!%!!!??!!%%?!!%!!!%?!!%?!%%!!%%!!?%!!!%%!%%!?!%%!!%%??%!!!??!%%?%!!?%??!%%!%%!!!!?!?%%%!!%%!%%!%?!?!%%!%!%???%!!?%%!!!%%!!?%!!%!%%%%%%!%%!%%%%%%!%?%%%%?!%!%%!??%!?%%%?%%!%%!%%%!%!%?!%%!%!?%!!!%?!!!!!%%%!?%%??%?%??!!!%%!%!!!!!!!%%?!!%!%%!%!!!!%%%!%!!%%%?%%!%%%!%%??!!!%%?%%%!!!!%??!%%%?%?%?%!%%!?!%!%%!%!%%!%?%%%!!%%%!?%%%%%!!!?%%%!%%%%!!%%?!%!!%!!?%!!%???%%%%%%?%!%?!?!!%%?%?%%!?%%?%%%!%%%!%%!%!%%?%!!%!%!%!!%%?!%!!%!%?%!!!!%!%%%!?%%%%%!!%?%%?%%!!%%!!%!!%!%!%?!%!?%%?!!?!?%%%!?%%%%%!?!%%???%%!%!!%%??%%%?%%?%%%%%?!%?%!%?!%%%?%!!%%%%%?%%%?%!%!%!%%%!%!!%%!?%%%%?!!%%?%?%%??!%%%%%%%%%!%!!!!%!%!%?%!%%?%%?!%!??%%%%%!%%%?!%%%!!%?!!!%!!!%!!!%?%%%%!!%!!%%?!%%!%!?!!!%%??%%!%%%%%!%%!??!??%!!%!!?%!%?%!%!%?!%!!!!%%%??%!%!%%!%%%%?!%!%!%!!?%%%!%!!!%%!!!!?%!%??!!!?%?%%%!!%%!%%!%!?%!???!!?%!%%%%%%%%!!!!%!?%!!!?%%%%%!!%?%%%!%?!%!%%%!%?!!%%!%%!??%!%%%%%%%%%%!%%%%!!%%%%!??!?%?!%%!%%!!!?%!%!!%!!%%%!??%!!%!!%!???%%!%%%???%%%!!!!%%!!%!%!!%%?%%%!%!?!?!!%!%%%%!!?!!%%%!%!!%!%!?%!?%%%!%%%%!%%%%!%!%!!%?%???%%%!?!%!%%%?!%?%%%?!%%%!%?%%!%?%%%!%?%%?%%!%?!%%%!%%!%%%?%!%!!?%!????%??%!!?%%%%!%%!%%!!!%!%%?%%%!!??!%!%!!!%!%?%%%%!!!%%?!%%?!!!%%???%%%?%%!%%!?!!%%!!%%%!%%%!!%%%!!%%%!%%%!!!%!%%!%?%?%%%?%!%!%%?!%%?%?!!!%%%%!!!!!%!%%!%!%%%%?!!!?%%%%%%!%!%!!!!%%!!!!!%%%!%?%!???%?%!!%?!!?%!%%%??%%?%!?%%%!%!!!%%??%?!%!%%!%%%!%%!?%%%%%?%!%?!?!%?!!?%?!!%%%%!%?!%%%%%?!%%%!!%%!%?%%!?%%%%?%%%%%%!%%!%?%??!??%?!%%%!?%!!%%%%%!%?!!!%%!%%%!%?!!!?%?%!%%%%%!!%%!%%!%!?%!?!!%!?%!%%!%!?!?%%!%%%%!%!%??%!%%!!%!%??!%!!?!%?!?!%!!%??%??!!%!?!!%!%?!!%%!%!!%%!%%?!?%%?%%%!?%!!?%%%%%%!?%%!!%!?%%!%!!!%??%%%%%%%!%!%%!!%%%!!%%?%%%?!!!!!!%%%%?%?%?!%%%!%?%!%%!%!%!%%%!!!?!%%%!?!%%!!%%%%%!%%!!%?%?!%!%!%%?%!%!%!!%!?!%!%!%%!?%?%!?%!%%?%%%%!!%%%%%%%?%!!??%!!%%!%?%!%%%%!%!%%%?!%%%?!!!!%%%%!!%%%!!%!%?%%%%!%%%%%!%%%!%%!!%!???%%?%?%%!?!?%?!%%%%!%?!!%!?!%%!%!!%%?%?!??%!%%?%%!%?%%?%%%%%%!!!!%%!?%%%%%!??!%%!!?%%!!%%?%!%%%?!%%?%%%?%%!%%%%!%%%%!!%%%!%!!%%?!%%!!!%%!?%?!!%%?%!!%?%?!!%!!!!%!%%%%!%!%!%%%?!%%!%%%%%%%!%%??%?%%%!?!%!%%%!!%?!!%%%!%%%%?%%%!!??%%%!!!%%?%%%!%%!%?%%%!!%%!%!?%?%%!!%%!%?%!!?!!%?%!!??%!%%!?!!%%!!?%%%!?%?%%!?!!%!!%%%%!%!%%!!!%!%!%?!%%!!%%%?%?%!%?!%!%%%%%%!%!!%!%!!?!%%%%%%??%%%%!?%%?%%!%!%%!%!%%!!!%!!%!!?!!%%!??%!%?!%%%%%?!??!?!%%%%%%?%!!!?%!!?%%!?!!?!%?!%%!%!%%%%%!%%%!%%%%!%%?!%%?%?%%!?!?%!%%%%%!%%!%??%%?%%!!%%?%%??%?%%!%%%%?%%%?%!%!!%!!?%?%%!%!%%%%?!%?!%!!%%?!!%!!!%!%%%%%%!!!%!?%%%?!%?!%%%%%?!!!%%!%%%%!%%%%!%?!!?%%%%!%!?!!!%%%?%%!%%!%%!%%??!?%!%%%!!!%!%%%%%!%%?%!!??%%%!%%!??%?%%%%?!%!!!%%!%!?!??!!%!%?%!??!%%!!!%!%?!?!!%!?%!!?%!!%%?%?%!!?!!%%%%!%!%%?!!%!%%%?!?%!!%%%%%%%!!?!%?%%%!!%%%!%%!%!%%%!!!!%!%%!%?%%%!?%%!!%!%%?!?!!!?%??%!!!%%?%%!?!!%!%%!!%%%!%??!?%!%!!!!%%!%%!?%!!?%%%%%%%?!%%!%!!%%%!%!!?%!%!?!%!%%!%!!?!%%%!%%!%%%%%!%!%%%%%!!%!?%?!!%%%%!!%%!%!!%%!!%%%%!?!?!?%%!!!!%!?%%?%%%%%!?!%?%!!%?!!%!%%%!!!%%%%!!!!!%%%%%%%!%?%%%!%%%%!%!!%%%%!%!%!%!!%%%!%!%??!%!!!?%%?%%%!!!!!!!!!%%%%%%!!!%%?!!!!%%!%!%!?%!??%%%%!!%!?!!?!?%%%!%%%%!!??%%%%!!!??%%%%%!!%!%!?%!!%?!?%%%%?!!%%!!!!%!%!%!?!!!%%%!%%?%!%%%?%%?%?!!%!%%!%!?%%?!?!%!%%%?%!!!%%!?%%?!%%%%%%%%%?%%%?!%%!%%!%!%!!!%!%%???%?%!!%%!%%%?!%%%%%!!%!%!%%%!!%?%!?%%%%?!%!%%%%?%!?%%%!%%!%!%?%%!?%%%?%%!%?!!!%%%!%!%%!%?%%!?%?%!!%%%?%%!!!!!!%%%%?!!!!?%%!%%!%%!%!?%!?!!!%%%%%??%%!!%%%%?!!%%??!???%%%!!%%%%!%!%!%%!%%%%!!%!%!!%%!?!%%%!!%%?%%%%%?%%?%?%!%!%!%%%%??%?%!?!?!!!?!%?%%!?%!!%?%?%!!%%??%?!%%!%!!%!%%!%??!%%%!?%%!%%%%%!?!!%%!!!%!%!%%%%?%%!!%%?%%!%?%%%?%%!%%!%!%!%!%!?%%%!%?!!!%!%%!!!!!!%%!%!!%?%?%!%%%%!%%%%!?%%?%!!%%%%%??!?!%%!%?%!!!??!!!!!%%!%!%%%!!%%%!%%%%%%!??%!%%!%%%%%?!%%!!%%??%!!%%%%%!%!??%!%!?!!%?!%?%%?!%!%%!%%%%!??%%%!%!%%%%??%%?%%!%?%?!%%!!?%%%!%!!!%%!!%%!!!%?%%%%!%?%%?%%!%%?%%%%%%%%?%???!?%!!!?%!%??%?!!%?!%%%!%?%%%!!!!!!!%%?%%?!%%!%%?!%!!?!%%%%%%!%%?!!!%%%!!%!%%!!?%%!%!!!!?%!!??!%%%%%?%%!%!!%%!%?%%??%%!!!!?!!!!%%!%%%%%?%?!%%?!%%%!?%%?%%%!%?%%?%!%!?!!%??!!%%%!??%%?%%!?%%%%%!%%??%!!%!!%%%?%?%%!%%!%%%%%?!!%?!%%%%%%%%%%%!%!?%%!%?%?%%%%%!!!%!%%!%%!%?!%!%?!!!%!!!%%!%?%%!%!!%%%%?%!?!!%?%!%??!?!!?%!%!%!?%%!%?!%%?!%%!??!?%%?%%!!!!%?%%?%%%%%%?%?!?%!%%?%%%%%%%%!?%?%%!%%%%%!?!!!!??%%!%%!!%!%!%!!%%!%%%%%!!!!?%%!!!%%%%!!%!?!%!%%%!%%%!%%!%%%%%%%%%!%%%%?!!!!?%%%%!?%%!%%!%%%!%%!%%?%!?%%%%%!??!%%?%!%!%!?%%%?%?%?%!!!!%!?%?%!!!!%??%%%%???%?%%?%?!!%%!%%!!%!%%%!%?%%?%?%?!!%!%%!!!!%?%%%!%?%?%?%!%!%%?%%!?!%?%%?%%%%%??%!%!?!%!?%%!!!%!!!%%%%!%%%!%%%??%%%!!!!%?%!%!%!!%!?%%!!?%!???%??!!%?!??%%%%!%!%!!%%%%!!!?!!%%%%%%!%%!%%%!%%%%?%??%%%%!!%%??!%%!!??%!%%%%!!%!!?!%%%!!%%%?%!?%%%!%?%?%?%%!!!%%??%%!!!?!%!%%%%!?!?%!%?%%?%!%%%!!!!!%%%%!!!%?!%!%%?%!%!?%%%?!%?%%?%?%?%%?%%%%%!%%?!%!!%?%??!!?%?!%!%!%!!?%!!%%!%%!??!%!!?%%!%%%%!!%!%%!%%%%%?!%!%!%%%!!!%%!?!%!%%%!?!!?!%%%%%%%?%!!%%?%!!?%!!%!?%!!!%%?!%?!%%%!!!%!%!%%%%%!%??!%%!!%!!!??%%%??!%?%!%!%?%!%%!!%%%?!!!!%%%%!!%%?!!?%%!%?!%%%%%!???%%!!!%?!%??!!?%!!%?%!%!!!%!%!%%!!?%?%%%?%?%%!?!%%?!!%!!%!%%!%%%!%%%%%??!?%%%%!???%?%%%%!!%?!%!?%!!!%!!%?%%%?%?%?%%!!!%!!!!%%%!!!?!%!%??%%!%?%%%%%?%%?%!%!%%%%%!%!%!%!%%%%%%%%%%??!!%!%%!!!!!%!%%?%!!!%%??%!%!?%%%!%!!!%%%!%%%!%!%!%!%%??%%%%?%%??%%!!?!%!!%%!%!%%%!!?%!?%%%!!%%!!!!!!!%%%%?%!%%!%%!?!!!%%!%%?!!!%!%%%%!%%?!%?!%%%%!!!%!!%%!%%!?%!%!!%?!??%%?!%?%!!!!?!?!!%!%!?!%%!!!!!%?%%?%%%%%!%!%!%%%?!%!!??%%!!!%%?%%%%!%%%%?%%%%%%!%!%%!!!%??!?!%?!!?!%%%?%!%%%%!!!??%?!!!!%%!%%%%%%!%?%?%%%%!?%!%!%%!%%!%%!%!?%!%!%%%?!!%?%%!%%!%!!?!?!%?%???%%!!%%%%!%!%%%!%%!??!?!%%?!!?%?!?%!!%!!%!!?%!%%%%??%%???%%!%%!%%!%!?%!%!%%%%???!!!%%%??!%%%?!%?%%%%%%%!??%!!!%!?%%%!%!%?%!!%%?%%!%?%??%%!?!%%!!!%%%%%!%??%!!%%%!%!!!!?%!!%?%!%%!!%%%%!!%?!?!?!%!%??!%%%??%%%%?%%?!%?!!?%%!%%!%%%%%!%!!!!?%%!%%!%!%!%%?%%??%%!!!%!%!!%?!!?!?%%!!%%?%%%!!%%%%?!%!!%%!%??!%%%!%%!!%!!%!%%?%?!%!!%!!%%%!%%%?%%%!!%?!!%%?%??%%!?%%%%!%?%%!%!?%%%%%!%%%%!%??%%!!?%!!!%%?!%%%!?%!%!%?%?%!!%!%%%?%%%!!%%?!%!?%%!?%?!%%?%%!?%!%%%!%%%%?%!!%?!?!%?%%!%%!%!%%!%?%%%%?%%%%%%!%%!%!!?%%!%%!%%%%?!%%?!!???%!!?!!%%??!%!%!!%%!??!%!%%%?!!?!??!!%%!%%!%%%%%%%%%!%?%%!%!!!%?%?%%%!%!%%%!%%%%?%!%%%%%!%%!%%%%%!?!%%!%%%!!???!%!%??!%%%!?%?%%!!%?%%!%!!!!%!?!%%%%!!!!?%%!%%?!%%%%%!%%?%??%???!!%!!%%?%??%%!%!%??!%?!!%?%!%%%%!!!!?%?%!!?!!%%?!%%?%!%%!?%?%%%!!%%!%?!%%!!%!%!!!%%?%%!!?%%!?%%??%%?!!%!%!%%!?%%%!%%%%!%%!%%%??!?%%%!%!%!!%!!?%%%!%?%!%%%%%!%%%!!%%%%%%!%??%?%?%%!?%!%??!%!%?%!?%!!?!!??%%?%!%!?%%!!?%!%!%%%%?!!!!%!%%!%!!!%?!%%?%?!%%?%%?%%%%%%!?%%%%?%%!%%%!%?!!%!!?%%?%%!?%%%!%?%%%?%?%!%?%%%%!%%%%%%!%%!!%!!%%?%!%%%%??%!?!%!!%!!%!%?%??%%!!!%!%?%?%!%!?%?%!%!%!%%%!%%%%%???%!%!%%!!%?!%%%!%!%%%?!%!%!%!!%%!!?%%%?!!%%!%%?%!!!!?%?%??%!%%%%??%%!%!%?%%!!!!!!!%%%!!%!%?%%!?%%%%!%?%%%%!!%%!%%%!%?%!%!%%?!!%!?%%!?%!%!?%%!%%%?!%%%??!%!%??!%%??%!%??%%%%!%?%%%%?%!%%!?%%?!%!!%!%!%%?!?!!%!!!!%!!!?%%!!!%%!%??!%?!%%%%?!%!%%!!?!%%!?!%%!?%%%%%!%!!%!?!%%!%%!?%%!%%???!??!%!!!%%%%%!!%%!!??%%!%%??%%%!%%%%%%%%!%%?!%?!?%!?%%%%!?%%%!?%%!%%!%%%%%%!!?%%!!!!?%?!!!%%!%%?!!!%???%??%%%?!%??!%%%%%%%?!?%%!!%!!%!%!%%??%%??!!?%!?%?%!!?%%%%%%!%!%!!!%%%??%!!%?%??%?!%?%%%?%!!%%?%%%!%!%?!%%%?%?!!%%!%!%??%%%!%%%!!!%%!%%%%%%%%!?!!%!%%!%?%?!!?!?%%!!!%!%%!!?%!!%%%%%%%%?%%!%%%%?%!!%%%?!%!?%?!%?!!?%!%%!?%%!%%!%!!%!!%%!%!%%!?!%?%!!?!?%%%%%!!%!%%%%!%%!!%!%%??!!!!?!%%%!%?%!%%!%%%%!!!%!%%!%?%?!%!%!%!%%%%!?!!!%!%%!%?%%!!?!??%!%?%!%!!%?!%???%!%!!%!%%%%!%%%%?%!?!!?!%?%!!%%??%!%%!%!%?!%!%!%!%!!%%!!%%%!!%%!!%??%%%!!%%%%%%%!!%!%?%%!%%!%%!%%!!%%%%%%?%!?!%!%%%%%?!!!!%?!!?!%%!%!!%!%%!?!?%%%!!?!%%%%%%%!%%!%!!%?!%%!%%%%%%%!%!?!%%!?%!!!%%!?%%!%!%%?!%!%!?!%%!?%%%?%%!!!%!%%?%%%%!!!%%!%?!%%%!????%!!!!%!??!!!%%%!%?%%%%!!!?%%%!!!!!%!!%%?!%!?!!%!?!%%!!!!??%%!?%!!%!!%?%!!??!%%?!%!%%%%%?%%%!%%!%%%!??!%%%!!!?!?!??!!!??!%!%%?%%%!%!!!!?%??!%%!!%%%%%!%!%?!!?%%%%!%%?%%!?%%?%%%?%%!%!%%%%!!%!!%!???%%%!?%%%%%?%?!%!%%!!%?%!%%!%?!%%%??%!!?%%!%%%%??%%%?!!!%?!!%?!!%?!???!%%!!%?%%?!!!%%!!!!%%%%%%%%!!%!!?!%%!!??%!%!%!%%%%%%%?%%%!%?%?%%%%%!%%!?%%%!!%%?%%?!!!%%%%%!!%!%?%%%!!!?!?!!%%%%%%%%%%!%%!?%!!%!%!%%%%%%%%%%%%!%!%!!!%%%!!!%!%%%!!??%%!%!?%%!?!!?%!!%%!%%!%!?!%?%%%!%%!!%!!!%!%%%?%!!%!%?%%!??%!!!%%%%%!%!%%%?%!%??%%%!!!!%%??%%!!%!%%%!?%%%%%!?%!%%%!%%??!%%%!!!%?%!%!%%%!!%%%!!!!%%!%!%?!!%%!%%%%!%%!!!!??!%!%?!!%!!!!%?%%%%!!%!%%%?!%%!%!!?%%%!%%%?!?%!%?%%!!%%%!%!%!!%!!%%!%!!%%%%!!!?%%%!!%!?%%!!!%%%???%%!%?!%!!%%%%%!?%%?%%%?%%%%%!%%!%?!%%%%!!%?!%%!%?!?%!%%%?!%%%?%%%%!!%!!%%%%!%%%%%!!%%%%%%!!%!%!%%!!!%%!?!%?%!!!!%%%%%%?%%%%%?%%%!%%?%%!??!?!%%!%%%!%?%?%??!!?%!!%%%%!?%%?!%?%%%%%%!%%%%%!%!%?!!%%!!%%!%%??%!%%%%%%!%!%!%%??%%?%?!!!%!!%!!?!!%%?%!%%%%!%???!!!%%?%%?%!%!%!!?!%!%%!?%%%%%%?!%%?%?!%%!!!!%%%%?%%%!%!%%%%%!%%%!!%%!%%!?%%?%!%%%%%%!%!%%%!%!!%%!!%%!%!!!!!%%%%%%!%%!!!%!?%!%%!%%%%%!?%!%!%%!!%??%%%%%%!%!%?%?!%?!!?!%!?%!!?%%!%!%!!!!?%%%%?!%?!!?%%%!?%?%%!?!!!!!!!?!%?!?!???%%%!%?%%%%%%%%!%%!!?!!%%?!%!!%!%?!?%%!!%%!?%%%!%%%!!!%%%%%%!%%?%!!!!!%!!!%%?%!%%!!%%?%!!%%%!!%%%!%!?%%%%%%%?%!%%!!!%%%%?%!%%!!!?%%%!!%!%?%%!?!%%?!?%?%!%%%!??%?!%%%!??!%!%?%%!%%%!%?!?%?%%%%!%?%%!%!!?%%%%!!%%%%%%%?%!%!!%!?!!%!!%%%!%%!??%%%%%%%!%!%!%?!%?!?%!%!%!?!!!%%%!!%%?!%%!!%%!?%!!%!??!%!%!%?!%!?%%!%%!%!!?%!!%!%!%%!%%!?%!%%!%%%%%%?%%%%!!%!??%%!!!??%!?!%?%%%!!%!%%!%!%!!%%%!%%%%%%!!?%!!!!%?%!!?%!!%!%!%%%%%!%!%?%!!%!%%%%?%!??!%!!!!%!%!%%!!%!%%%!%%??%!%%%!%%!%%%!%%%!!??%?!%%%!!%?!!%%%?%?%!%%?!%%!%%%!%!%%!!!!?!%%%!?%!!%!?!?%!?!%??%!%?%%%%%%%?%??%%?!!%!%%!!%%!?!%!?%%%!%%%%%%%%%%??%!%%?%%!%%%%?%!%%%%%!!%!!!%%%!%!%?%??%!!%%%??!%%%%%%%!?%%%!%!%?%%%!%!?%%%!?!%%!!%?%!%!%%%!%%?%%!%?!%%!%??%%%?!!%%%%%%%%%%!?!%?%!!!%!%%%%%%?!%!%!!!!??!!!!%!?!!%%%?%!??!%%?%%%%!%!!%%!!%%%?!%!%%!%%%%%%%%%%?!!!??!%!!!%?%%%%%%%%%%%!?%?%?%!!%%??%?%!%!!!!%!!%!%!!%%?!!%!%?!!?%%!%?%%%!!?!%%%!%%?!%!!%!%!!%%%%%?%%!!?%!%%%?%%%!!%%!%%%%!!%%%%?!?!!%!%%%!%%%%?%?!%?%!?%!!%%!!%!!!!%!!%!!?%%!!%%!!!!%%?!%!%%!!%!%%!!%!?!%!%%!%%%%%%%?%?!?!%!%!%%!?%?%%%%!?!%%!!!%!%!!!%!!!!!?!!?%%?!??%!?%!?!%%%%!!%%%!!%!%%%!%?%!%!%!%%%!!?%!%%!!?%!!%%!??!%%!%%%?%%!!%!!%%!!%?%!%!%!!!?%!%!!%!%?%!!%!?%!%!%?!%!%!!!%?!%%%?%!%?%!%%!%!%!!%%%%??%%%%%?%%%%%?%%!%%?%%??!?%%%!%?!%!%?%!!!!%!!%%?%?%%!%%%!%?%!?!%%%??!%%?%?%!!!?%%%!%!!%!?%!%%%?%%%%%%??%!%%%%!!!!!!%!!%!%!!%%%%%%!%?%!??%%??!%!!!%%%!%?%%%%%%%!%!??%!!%!!%?%%!?%?%!!?%!%!%!!?%!!!!%%%!%!!%%%%%?%?!%?!%%%%?!!!!?%%%%!??!?%?%%%%?%!%?%!!%%%!?%%%%!%%%%%%%?%!?%!%!%%!!%?%%!%???%!%%%%%%?!!%!!%!%!%%%!!!%%%?%!!%?!?%%%%!%!%%!%!%!!!%!%%%%!!?!%!%%!?%%!!%%!%%%%?%%!!%!%?!%!%!!!%%!%%%!!%!?!%%%%%%!?!??%?!!!?%?%!!???%%?!%!%!!?%%%!%?!?%%!%%%!%!%!%%%%!!%?%%!%!%!%!%!!%%!??%%%!%%?%%!!%%%??%?%!%!!%??!!!!?!?%!?!%!%%?%%%%%%!!%%?%!%!!%%%%?%!%%%%!!!?%!!%!%%?%%!!?%!%%?!!?%?%!%%?!%!%!%?%!%%!!?%%?!%%%!%?%?!%%%%?%!!!!%!%??!!%?!?%?%!!???%!!!!%?%!!%%!%?%??!!!%??!!!%%%%!%%%!%!%%!%%%%%?!%%%?!!%%!!%%%??!%%!!%%%%%!!?!%!%!%%%%!%!!%!!?%%!%%%!%!%!%%%%%%%!%!%%%?!!%!?%?%%?%!%%%%!%%!%%%?!%%?%%!%%%!%!!?%%%%?%%%%%!%%?%%%?%%%?%!!!%%!!?%?%!%%!!!?!%??%!!?!!%%%%%%??%%??%!%!%%!?!%?%%%!%%%%%!!??!!%??!%%!%!!%??%!!?%!!%%%%!%?%!!%?!%!?%%!%%??%%%%%!%%%%??!?!%!!?!%!!%%%%%!???!%%%!!%!?!!%%%%!%!?!%!?%%%%%!%%%%?%?!%%%%%%!%?!%??!%%!?%!%!!%?%!!!!%%?%!!!%%!%!!%?!!%!%?%!%%?%!!%%!%!!%!?!?%%%%!!!!%%?%%%%!!%%!!!%!%%?!%%%%?%?%%%%?%%%?%?!%!%!%%!%?%!%?%%!!!%!!!%%!%??%!!!?%?%?!!!%?%%%!%!%%!%!%!%!?%%%%%%%%%%%!?!%%%!%%%%%%!!!%%%!%%%%%!%%?%!%!!?%!%%?%%%!!!?%!%!%?!?%%!?!!%%%?!!?%!?%%!?%!%!%%%%!?%%!%?%!!%!%%!%%%%%!!%%%%%%?%??!!%!%?%%!!%%%!!!!%?%!!!??%%%?%%!???%%?%%%!!%%!%!%!!!!%%!%?%%!%%!%!%!%%!!?!%%?!%!%!%%%!!%?%?!%!%!%%%!!%%?%%%%!!!!!%?!%%!%!%%%!%%!?%%?%!!?%%?!%%%%%!!!%!?!%%!???!?%!%%%?%%%!%!?%?%!!!!%!%%!!%!!%%%%!?!%?%!%!%%%%!%%?%!%?!%%!%%!!%%?!%?!?%!?%%%?%!%%!%!?%!%%%?!!?!%!?!?%%%%%%%%!%?!%?!%%!!%%?%!%!!%%%%?%%!%!%!%%%%!?!?!%!%!!%%!!%!!%%%?!%?!%%!!%%?!%??%!%??!%!!!%!%?%%!%%%%!!?%!!!!%?!%!%!%%%!!!%?%?%?%!%!%!%?%%%!%!?%%%%!%%!!!%%%%%?!%!!%?%%%%!!%!%!%!%%???%!%!%%%!?%%?%!!!%?%?%%!%%%?%?!%??!%!%%%?!!!!%?%%?%%%!?%!%!%?!%!%%%?%!%?!%%%%%%%%?!!!?%%!%%!!!!%!!%%%%%%!%%?!%%%%!?!%!!!%!%?!?%!%%%!%%?%!%!%%%%!%%%?!!%?%%!%%!!%!?%?%%%%%%%?%%?%!%!%%%!%%%!!%%!%!?%%!!!???!!!%!%%!?%!!!%?!!%!!%!!%%??%%%!%!!?!%%%%!%?%?%%%!?!!%%!%!!!%%!!!?%%%!%?%%%%%!!?%%!?!%!!%!%!!!%%%%!?%%??%%%%%!!%!?%%!!%??!%!%!!??%%?!!%?!%%%%!%%%%%%!!?!%?%!?!!%!!!!%%!%!%%!!%!%%??%%?!!%??%%%?%!%%!%%%!%!%%!?%?!%%!??%!%%%!!??%%!?%!%%%%!?!!%%%%!?!%!%!%%??%?????%!%?%%%!!%?%!!!?%?%%!!%!%%%?!?%?!?%%!%%%%%!%!%%%%?!!%%?%%%%%%!!%!?!!%%%%%%!%!!!%??%!!!?!%%?!%!%%!?%%??!!%!%%?!!%%%%%%%%!%!!%%%%%!!%?%%%%%%?%?!?!%!?%?!!!%??!!%?!%!?%!!???!!%%?%%!!?%?%%%!?%%!!!!%!!!!!!%%%!%?!?%?%%!%%!%?!%!%!?!%!%%%!%%%%?!!%!%%%!??%%!??%%!%!?!%!?%?%!!%!!%%!?%%%%%%!%%???!%?%!!%!%%!!!!??%!%!%%!!%%!%%!!??!%????%!?%%?%%%%!%?%%!%%%%%?!??%!%%%!%!%!!!!?%%!%%!%%?!%!!%%!%%%!%%%%!!?%%?%%%%!!!??%!?!%!!%!!%!?!%!?%%%%%!%%%!??!%%%%%%?%%?%%!?%!!%%%???%%??!!?%?!%!%!?%%??%%?%!%%%!%%%%!!%!%%?!?%%%!?!??%%%%%%%!!%%%%%!!!!!?!?!?%%%%!%!?%%%%!%%%!%?!%!%!%!?%%?!%%!%%%!%%!%%!!!!%!%!%%!%!!%%%%??!?!!?%!!%!%!??%!%%%!???%!!!!%%%!!?!?%!%%!%%%%%!%!%%!%!%!!!!%!%%%!%%!!!??%!??%!!%%%!%%!!!%!!%%!%%%??%!%%%%?!?!%!?%!%?%!!%%%%%%%!%?!?%%%%!!?!%%!%!%%?%%%!%%?!%!%??%%!!!%%%!%!!%!%?%!%!!!!!%%%%!?!%!!%?%?%%!!%%?%?%%%%%!%!%!!%%!%%?%%%%%%!%%?!%%!!!%%%%!%%!!%%!!??%%%?!?%%%%%!%!??!%%%%%%!%%%%%%!!%??%%?!%%%%!%?!!%!%!%?!%!!?%%%!%%!%!%!?%!%%%%!?%%%!%!%!%%?%!!!!%%!%!%%%%%?%?%!?!%!%!%!?%%!%%!%%?!!%!!!!%%?%%?%!?!%!%??%!!%!?!!!!%!!%!!!%%?%%%!%!!!%%%!%%!!%%!!!!%?!%%%%%!!%!%%?!%!%%?!!%!%?%%!!%%%%!!?%%%?%%%%!%!%??%!!!!%!%%%?%!%!%!%!%!%%?%?%%%?%!!%%%%%%!!%%!!%%!!!%!?%!?%%%!%!!?!??%?%%?%%!%%!?!!?%!!!%!?%!!%!!!?!?!!%!!?!%!%%?%%%?%!!%%%%?!?!%%%%%??%%%%?%!!!%%?!!?%%%!%!%!%%%!!!!%%?!?%?%%?%?!!!!!?%%%!%!%%%?%%!%%%!%!%!%?%%%!?%%%%!!%!%!%%!%?%%!!!%%??!%%%?!!!!!%!%!!!%%!!%!%!%!%!%%%%%!%%!%%!%%!?%%!%%!%!!%!!!%%%%?%%%!?!!!%!%%!%%!!%%%?!%!?%%!?!!?!%!?%%%?!%%!!%%%%!?%!%%%????%!%%%!%!%%%%!%!?%!%%%%%%%%%%%%%%%!!%%%!%%!!%!!%%!%!?!!?%!%%!%!!%?!%!%%%!%%%?%!!%!!%%%%!%!%%%!%!!?%?%%!?%%%?%??!!!?!!!!?%?%?!%!?!!!!!%!!!!!%?%!%?%!?!%!%??%!!%!??%%??%%%%%!??%%%%%!%%%!%%%!%%?%!?%%%%?!%%%%%!%??%!!?%!!%!%!??%%%!?%%%!?%?!%%%%%!!?%%%%%%%%!?%%%%!!?%%!!%%%!!%!%?%!?!%%%!!%?%?!!!%?%%%%?%?!?%??!%%%%!%%%??%!%%%!%!%%?%%!!%%!!%!%!?%%%!%??%!!%?!!%!%!%%?%?%%%?%!%??%%%!!%%%!!%%?!!%!%!%%%%!%?%?%%?%%%!!!!%%!%!!%%%%%%%?%%!%%%%!?%%!%!!!!!%?%!!!%%!!!?!%%!%%!%%!%%!?!%%%!%%%!?!?%?!%!?%?%%%%!%%?!%?!!%%!!%%%%%%?!%!!%%!%%!%%%%%%!%?%%%!!%?%!?!%%%!%%%%%!%%!%%%!!%!!!!%%!%?!!!!!!!!?!%%%!!%!?!%!%%?!%!?%%%%%!%%%%!?%!!%%!%?%!%?!%%%?!!%!!!!%%?!???%%%!%%!%!!!?!%!?%%!%!!%%%!%!%!!%!%!!!!!%%%?%%%%%%%!%!%!%??!???!%!!?!?%%!%?%%%??%%%%%%%%%!!%%?%%%?%?!%?%%%!!%!!!!?%%%!%%!!?%!%?%?!!%!!%!!!%%%%!??!!%%%%%%!?!%%%!?!?!!??%!?%!?!%?%!!!!%!%!%%!%%!!!!%%!!!%!!%?%%!%?%%%!!?%%!!%%?%%!!%%?%%%%!%%%?%!!%!%%%%%!?!!!%??%!%%!!%!!%!%!!?%!?%%!!??!%%??%%!%%!?%%%%!%%!??!%%%%!?%!!?%%!!!%%?!%%%%%!%?%!%!%!%%!!??%!%%?%%!%%!%!%%%!%!%%%!????%?%!%!!!!%%!%!??%%!%!%%%?!%%!?%?%%!!?%??%!%%%!%%!%!%%%%%?!%%%%?%%!?!%%%?%%!%!!%%!?!%!!!%%%%!!%!?!%?%?!%%%?!%!%%??%%!!!!%%%?%%!%%?!!?!?%!%!?%%%%%%%!??%%!%%!%%?!!%%%%!?%%%!%%%!%%?%%%!%%%%?!?!%%%%!?%!!!!!%%!?%?!?%!!%!??!!%%%?%%!%%?%?%%%!%!!%%%%%!%!?!!%%?%??%%?%%?%%%%?!!?%%!%%%%??%!%%!!?%%%%!%%%%?%!!!%%%%!?!!!??%%%%??%!%!?%!!%%%?%%%!%%?%%?%%%%?!!!%%%%!?%%?%!%!%%!%!%??%%%!%!%%%%!?%%%%!!%%%%?!!!?%!??!%%%!%?%?%!!!%?%!%?!%!%??!%%!%!!%%%%%?%?!?!%%%%%%!!%%?!!%%%?!%%%%!%!%?!%?%!?!?!%%%%!!!%%%?%%!!?%%%!?%%!%!%%?!%%?!%%%%%%%%?%!!%!!!!??!%!!!!?%!%%!%%!?!%?%??%?%!%%!%%?%%??%%?%??!%%%!!!%%!!%!%?!%%!!%?!%!!%%!!%%!%!%%%!!!!?%!%%!?!%?%!!!%%%!??%!%%!%?!!!!%%!!%!%%?!!?!%!?%%?%%?!%%!%!%%%%%?%!%!%!%%%%%%%%%%%%%%??!%!!%%%!%!?%?!!!%%!%%%%!%%!%%?%%%%!%!%%%%%?%!!?!%%?!%!%%?%%!%!!!!!!!!%%%%%%%%!%!!!?%%?%?!%!%?%!!%%!?%%%!%!%?!!?%%%%%!%%!?%?%%?!?!?!%?%!??%!%%?%%%!!!%%!%%!!!!%%%%!?!%!!%!%!%!!%??!%!%!??!?%%!!%??%%!?!%%!%%%!%%%%!??%?%%?%%%%%%!%?%!!!?%!?!!!!%%%!?%!?%!?%!%??%!!?%%?!!!%!%%!%%!?%%!?!!!!!?!!!%?!%?%%!!%!%%!%%!!%!!!%%%!%!!%!%%?%?%?!%%!!%!!!%%!!%!%%!%!%!!!%%!%!?%!%!!!!!!?%%%%!%!?%%!!!!!%!%!%%?%?%%%??!!!!!%%%?!%%?!?%!?%%%!%%%??%!%%!!?!%%!%?!%%%!%!!????%%!??%%%!%!!!%%!??!?!?%!!%%??!%!%!%%%%!!!!!?!%?!?!!!!!%%%!?!%%?%?%%%!!!?!%%!!%??%%!%!%%??%!!!%%?%!%!!%%%%%!%%%%%%??%%!%!!%?!!%!!%%?%!!!%%%%!%%!%%%!%??!!!%!!%%?!%%!?%!?%!%?!%%!!!%!%!%%%%%%%%%!%%!?%%%!%%%!!??%%?%!?!%!!!%%!!%%?!!%%%%%%%%%!%!%%%%!%!?!%%%%!%%!!%!?%!%?%%!!%%!%!!%!%?!?%?!%%%!!%%!%!%!?!%!%???%%%%!%!%%%%!?%%%!%%%%!!%!!!!%!!%!%%?!!%%!!%%!?%%%%%?%?%%?!?!?!%!!?!!!%%%%%!%%%%%!%!!?%%!%!%%??%%%!%!?!%!%%?%%!%!%%%%!%%!!%%!?!%!%%?%!%!%!!%%%!%?%%%!!%?%%!?%%!!?%%!%?%%%%%?%%%!%!!!!?!?%!!%!%%!%!!%!%%%?!!!%?%%!%?%%!%%%%%?%??%%!%??%!%!%%%!!%?%!%??%!!??%%???%!%!%%%%%%!%%%%%!!%%%!%%%!!!?!%?!!%%!%!!!!?!!%!%%%%?%!%%%?!?!%!!%?!%!%??%%!?%%!!%!%!%???!%%%%!!%%!%!%%%%%!%%!%%%%?!%!%!%%?%%?!%!!%!%?!%%%%!%%%%%%?%%!%?%%??%!%%%%%!!?!!%%!?%%?%%%!%!?!!???%!%%!%%%%%%!!%!!%%?%??!%!%?%!!%!%%??!!%%?!?!%?!%%%!%!!???%!%?!!%!%?%!%%!?%%!%%!!%?%?%?!%%!%%!?!!%!!!!!%!!%%%!!!%?%!!!!%!%!%!%%%!?!?%%!%!!?%?!%%%%%%%%!%%%?%%!!!?%!%%?%!%!%!%%!%!?%%!?%%%%!!%%%%%%!%%!%%%%%??!%%%!%%?!%%!%%%%!%%%%%?%%%!!?!%%?!%%%%!!??!!?%%%?%!%!%%%%%!?!!%!%%!!%!!%%!%%?%!%?%%?!%%%!!!?%!!%?!%%%?%?%?%?!!%%?%!!%?!!%%!!?%??%%%%%%!!!%!!!%?!%!!%%%!?!!%?%%!!!!%!%?!?%%?!!!%%%%!!%%!?!%%%??%%%%%!%?%?!!!%%??%%?%%%%?!!%?%!%%!%!!!%%%!?%%%%?%%?%%%%!!??!%%%%%?%?%!?%%%%!%??%%!%%?%!!%?%%?%%%%%%!!%!%!%%%%!%!?!%%%%?!!%?%%%%%%%%%%%?%%!%!%!%!!%%%%%?%%%??!!?!?%!!%?%%%%!%%%%??%%%%%!%!%%?!%!!%?%%!!%!%%%!%!!%%!%%%%%%%!%%?%!%%!%%%%%?%%%%?!!%%!%%%!!%%!??!!!!!!%%??!!%?%%!!!!?!%%%%%!!?!!%%%!%?%?%%%%%!?!!%!%!%?%!!!%?%!?%%!?%!%%!%!!%%?!%%%%%%!%%?!%%!%%!???%?!!!!%%%%?!%!?!!%%%%%%%!%%?!!%%!%%%%!%!%%!%!!%!%!%!%%%!?!%!?!%%%%%%!!%?!?!!%!%!%??%%%%%!%%!?%?%%!!!%%%!??!%%!!%!?%%!?%!%%%%%%!%%?%%%%?!??!%%%%%%?%%!!%%%!!!!%?%???!%%%%%%!!%?%!?%%%%%%%!%!??%%%?!%%?%!%%%%%%!%!!%!%%?%%%?!%?%?!?!!%!!%%%!%%%!?%%!!!?!!%%?%%?%%?%%!!!!%%?%!???%%%%%!%!!%!%?%%!!%?%?%%%%%%%!?%%%%%?%%!!!!!%!%!%!?%%!%%!%%?%%!%%?!!!?%!?!!!!%%%%?%%%%%?%%%%%!%%!%!!!%!%!!%%%!?%%%!?!?%%%!%!%?%%%%%%%%!%%!%!%!%%??%!?!!?%%?%!?%%%!?%!%??%?????%?!!!%%%%%%%!!%%%%?%?!%!%!!!%%!?!!%%!%%?%??%!!!%!?!%%%%%%%!%?!%!%!%%%%%%%%!?!??!!%!?!%!!?!!!!!!!%!%!??%?%%!%%!%%!%%%%?%%%!?%%%%?%%%!?%%%%??!%?%!%!%%?!%?%!%?!%!??!!%%%%%?%%%%%???%!!%%%?%%???!!!!%%!%!!%%!%%?%?!%!%%?%?%?!?!?!%?!%%%%?!%%?!%!%!?%!%?%%%%%!%!%%!?!%%%!?%%??!%%?!%!?!!%%!%%%!!!!%%%%%!?%!!%%%!!%!!%!%%?%%%!!!?!??!?!%?!%%!!%?%!%???%!%%!!%%?%!%%?%%%!!!%!?!%!%%!!%%!!!!%!%%!!!?!%%%%!%%%%%%!?%!%%?%%!%???!%%!%%!?%%?%%%%?!%?%%!%%%??%!%!%%%%%%%!!%%%?!%%%%!%%!?%%%%%%%%%!!%%%!%%!!%!??!%%%?!!%%!?%?!!!%!!?!%%%!%!%%%%%%!%%%%!%?%%!%%%%%!!!!%?!?%?%%%!??!%%!%%?%%!!?%!%%!%%!!!%!%?!%!?%!%!%%?%?%%!%!!%%%%!!%!?%%%%!??%%%?!%?%!!!%%%%!%!%%%%!?%%!!!!!%%!%!!%?!%?%!!!!!??%!?!%%!!%?%%!!%%%%%%?!%%?%%!!!?!!%%!%?%%%!%?%!!%%%%?!!%%!??!%%%?%%%%??%%?!%%%??%%!!%%!!%%%%%!%!%%%%!!!%!!%!?%!!!%%?%%%!!?!!%!%%!??%?%%%?%%%%%%%!!%!%%?!!?!!%%?%!%%?!!%?!?!!%%%?%%%%%%!%!!!%!%%%!!%!!?%%%%?%%%%%!%!!%!!?!%%%?!!%?!?%%!!?%!!%?%%?!%%!!?!%!!!%%%%!!%!%%%%%?!!%%%%??%!?%%?%%%?%!%!%%!?!!%%!!!?%!?!?%%%!%%?!?%!!!%%!%??%!!?%!%!!?%!!!%??%??!?%??%!!%%!!!%%!%!?%!%!!?%%!%%!!!!%!?%!%%%%!%!%!%%%!%%!%??%%?%%%%%?%%!!!?%!!!%%!%!!?!!!%%%?%??!%!!%!%!%%%%%%!%%!!??%%!?%!?%!%?!!!%?%?%?%!%!?%?%%%%!%?%%?!!!%%!!%!!%!!%%%!!%%!%?%?!%!!%??%!!!?!???!%%%!%%%%!%!%!%!%?%%%?!%!!%%%%%!!!%%%!?%!%%%!%!!%!%%?!!!!%?!%%!%!%!%%?!?!!!%!%???%%%%!%!!??!%!!??%!%!%%%%%%%%%?%%%%!?%%!!!%%?!?!!%!%!!!!?%!%?%%%%!%%%?%!?%!%%%%!%%?%?%%!!%%%!%%%!%???%%%!!!%%!!%%!!%!%%!?!!%!%%??%%%!%%%%?!!!%%%?%%%%%%!!%?%%%?%?!%!%!!%%%%?!!!%%%%?!!%%??%%%!%%!?%!%!?%?!%!%?%%!%%%%%%!%?%%%!%%!%%?%?!!?%%!?%%%?%%%?%%??%%!!!!??!%%%!!%%%%!?%%!?!%!%!?%!%%!%%%%????%??!%!!!!%%?%?!!!%?%%?!%!!?%%?%%!%!%%%!%%!%!?!?%%%!%!%%!%%%%%%%?%%!?%%?!%!!!%!%!%%!%!!!?%%%%!!%!%?%?%?%!!%!!%!!%%%%!%%%!%%?%!%?!%?!%!%%%%?%%!%?%?!!?%?%!!!!%%?%%!!%%!%!%!%%%%%?%%!%!!!?!%!%%%!%%%%!??!!%%!!?!?!%!%%%%?!%%%!%?!%!?!!!!%?%!%!%?!?%!%?%%!!!%%%%%!%%?%%%?!%!%%??%%%%%%?%%!%?%!!%!%!%%%%!%!?!?%%%%%?%%%!%%%?%%%%!%%%!%%%%??%%%??%%%%%%!!%!%!%?%!%%?%%%%%%%!?!%%?!%!%%%!%%%!%%!???!%%!!!%?!%%?%?!?%!%??!%%%?%%%%%!!%%?%%%!%?%%???%%?!??%?!%%!?%%%%?%?!%?%%%%!!%?%%%!!%%%%!?%%?%!%%%%%%%!???%%!!!?%!??%!%!%!?%!%%!?%?%%!!%%%!%%%%!%?%!%%?!!!!%?%%%%%%?!!%!?%%?%?%%%?!??!!%%?!?!!?!%!%%!!%%%?%%!%!%%%!!?%%!!!%%!%!%%!%!!!!%!!!!!%?%%?!%!!!%!%!%%%!!%!%?%!%??!!%!?!%%?%!?!!?!?!!%%%%%?!%!%!??!!!%!!%%!%!%%%%!%%%%??!!%!!!!%!!!!?%?%!?%!!!%%?%%%%%%!!?%?%%!%%%!!!%%%%!%%%??!%%%?%!%%%!!%%?%%!%%!%%!!%?%?%%!%!!%!%%!!%!%!!%!%%?%!%%%%%?%!%!%%%%!%%%%%!%!%%%!%!%?!??!!?%!?!!%%!%%!!!!%!%!?%?!%%!%?!!!?!%%?%%!%!%!%%!!%!?!%%%!!%!%%?!%?%%!%!?!%!!%%%%%!%%%?%%%%%%!!%%%!!!?%%!?%%!%!%%!%%?!?%%?%%%!?%%%?!%!!%!!!!!!!%!%!!!%?%??!%?%??!%%%%%!%?%%%%!%%??%??%%%%!!%%!%%%?!%?%!!%%?%%??%!%%??%%%%?%%!!%%!?!!!%%%%%%%%%%%!%!%%!!%!%%?%!!!%%!!%%!%!%%%!!%!%?!!%%%%%%!!!%!%%!!!%%?%%%%%?%!%!?%%%%%!%!!!%?!%%%!%%%?%?%%%!!!!%!!%!%%%%%%%%!??%%!!!%%%%%!%?%%%!!!?%%!!%?!!!%!!!!%?!%?!!!!%%!%!?!%?%%?%!%!%??!%!%%%%?%%!!?%%%%!!!!%??%%%?%!%!%???%%?!%%%%?!?%!%%!%%!%%%%%!!%%%??!!!%!!%!%%?!%!!%%%!%%%!!%%%!%!%??!!%?%!!?!%!%%%???%?!%%%!!%%?%!!%?%%%%%?!?%!%!%???%%%!!!%!?%%%?!!!%!%%%?%?%!%!?%%%!%!%!?!?%!%!%!%%%!%!%%!%?%!%!%%!!?%%%!%!!!%!!!!%!!!%!!%%%%%!%!%%%!%%!%!%%%%%%??%?!!%%!%%%%!%?!!!!%!%%%!%%?%!%%%%??%%%!%!%!!%%!%%%?%%!!%!%%!%?%%%?%!!!!%%%%%%%?!%!%!!!%?!!!!%%!!?!%%%!?!%%!%%?%!%?%!?%!!%%%%!!?%!%%%!%%!%?%!%%%!!%!%%%%!%%!%%?%%?%%%%%%%%!!%!%?%%%!!%!%%?%!%%!?!!%!!!%?!!!!!!%%!%?!!!!!!%%%%!?%%%%!%!!!%%?!??%%%%?!%!%??%???%%%!%%!!?%?%%%?!%%!!!%!!!!%!%%%!%%%%%%%%!%%?%?%%!%!%!%%%?%!?%!%!!%!!!!%!%%?%%!?%%!?%%%???!!%%%!?%%!%%%!??%!!%%%%%%?%%%?%%%%%!%%%%%!%!%%%!%%!%?%?%%!!%%%%!%%%?%%%!!?!!!%%%!!!%%%!%!%%%!!%%%!%?%%%?!%%%%!%%!%!??%??%?!!!?!!?%%!%!!!%%%!!!!!%!%?!%%!?%%!%%?%%%!!??%%!%%%%%%!!%%%!?!!!%%!?!!?%?!%!!%!!%!%%%%!%!!?%%%?!%%!%?%!?!%!!%!!!%%!%%%%!%%!%%%%!??!?%%%!!%%%%!%%%%!!%%%%!%?%!%!!!?%!%?!%!%%%%%?%!!%%!%!?%%%%%%%%%!?%!%!%?!?%%%%%!%%!!%!!%%!!!%%??!!!!!?!!%!%!!!?!!%%!!%%!%%%!!%%%%%?%%!!%%%?????!!%%%!?!%?!!?%?%?%!%%%%%!%?!??!?%%%!%!!!!%?!%!%?%%%%%?%!%!%!!%%?%%%%%%??!%?!?!!%%?%!%%%%!?%%?%!!?%?!%!%%%%%%!!%!!?%%!!%!%%%??!?%!%?%?%%?%!%%%%!%?%%%%!%%?%?!%!!%%%%!%??!?%%%!%?%%%%%%!!%%%!?%%%%?!%%!!%?%!!%%%!%%%%%%%%!%%%!%!%?%%%%%?!!%!!%%!??!??%%!%%%%%?%!%%%!%!!!?%!!!??%!%%%%!%!!%%!%%%!!%!%%%!%!!!%!%??!%!%???!?!%?!!!!%%%!!?!!%%!%%%%%?!!!%%!?%%?%%%?%!%%!!!!%!!%!!!%%%!!?!?%%!!%%%%!!?%?%%%!!!!%!%%!?%%!!%?%!%!%%%%!%?%?!!%%%%%%%!!%?%%!?%!!%!%%!%%%?%!!%%%?%%%!%?%!!%%%%!%%???%?%!!%%%!%%!?%%%!%%%?!%%%!!%?!!!?!!%%?%!!!!!%!%%%%?????%??!%?!!?%!?%?%!%?!%!!!%%%%%?%%%%!%%?%???%%%?%!!%!%?%%%??!!!!%!%!!?%%!%?%?!%%!!%!!%!!%%?%%%!%%%!%?%!!!?%!%?!%!%%%!?%%%%%%%%!!!?!!!!%%%%%!%%!!%%??%!%%?!!%!!%!!%!!!%%%%%%!%!%%?%%%??!%%!%%%?%%?%!%%?%!!%%!%!%%%%%?%%%!%!%!%%!%%%!%%!???%?%!!??%!%%%%!!!%%%%%?!!?!%%%%?!%!?%%%%%%%%%%??%!%%%!%!?%!%%?%%%%%%?!%?!%!%???!!%%%!!!!%!!!%!%%%%!!???%%%!!%!%%!%%%!!!!%%%!!?%%%?!%%!??!%%!%!!!%%!%%%!?!!?%%!%%?%?%!%!%%%!?!!%%!?%!?%%!%%%%%!%%%!!?%!?!%!?!%%!%!%!!%!%%%%!!!??%??%?%%!%!!%!%!%!?%!%%%!%?%!%%?!%%!?!%%!!?%?%%%!%%!%%%%?!%?%!%!!%?!!!%!?!!?%%%!!?!%%!?%%%!?%%!%%%%!%%?!%?%%%%!%%%%%!?%?%!?%!%%%%!%!!%!%%%%?!!!%!!%%%!!%!??%!??%%%%%%?%!!!?%!?!%!?!%?%%!%%%!%%%%%!%!!!%%%!%%!%%!?!%!?%!%!%%!%%??%%%%%%%%?!%%!%!%!??%!!%%!%%%%%!%%%!%%%%?%%?%!!%!?!%??!%?!%%%!%%!??!!?%!%%%%!?%%%!%?!%!%%!%%!%%%%?!%%%?!!!%%!!%!?%!%%%?%%%?%%?%!%%%%%!!%?!%%!%%!%%%!%!%!?%%!%!%%!!%?!%%?%!?!%?%!!!?!??%%%!?%!%?!!!%!%!!!%!?%?%%!%!%?%%?%%!!%%?%%%!!!!!!%%!!%%%!!?!?!!%%!?!!??%%%!%%!?%%!!%?!!!%!!?!?%%%?%%!%!!!%%?!!?%%!!%%!%%%!%?%%?%%%%%?%!?!%!?!!!%!!!!!%%%%?%%%!%?!%!%?!%!%?%%!?%?%%%%!?%%%%!!!?!%%%%!????%%?%%%!%%%!!%%!!%?%%%%!?!%!!!!%%%?%%%%?!!!!?%%%%!%!!!%%!%??%%?%?!%%!!%?%%!!!!!!%%!%?%?%%%!%!%?%%?%!%!%??!!!!%%%!%?%!!%%!!%%%%?%!!?%!?!?%?!?!%%%%!!?%?!%!%%!?!!%!%%%%?%%?!%!!%%!%%%!%!!!!!%%%!%?!!!%?!%?%!!!?%%?%%?%%!!%%?????%%%??%%!!%?!?%!?!%%??%!%!!!!%!%!?%%!!!?%?%!%?%!%%!!%!!%??%!%!%!%?!%!!%!!?%!!%%%%%!%!%?%?!%?!%!%!!%%!%%%%!%!!%?%!%%!%%%!%%%!?!!%!!%%%!%%?%!%%%!%?%!%%!!!?!%?%%%%%!%?!%?!%%!%%!?!%!%%!%!%!%!%!??%?!!%!!%%%!!%%!%?%!!%%!%!%!%%???!%!%%%!!?%!?!%!%?!%%%%!!!%%?%?%!%%%?!%%??!%%!%?%?%!!!?%%!%%!!!%%!%%%?!%!%!!%?!%!!%%?%!%!!??%!!?%%%%??!!!%%%%%!!?%?%%!%%%!!!%%%%%%%%!!%!!!!%!%%!%!%%?!?!%!%%%?!?!!%%?!%?%%%%!%?!?%%%!%?%%%%!!%!%!%!%%?!!%!?!!?%!?!%?!%!%%%%%%??%!?!!%!%!%?%?%?%%!!%%?%?%%!!%!!%%!!?!!!%%!%!!%%%!!%?%!%%?%!!!%?!?!%%!?!!??!%%!%%!!%?%%%?%?!?!!!!!!!!%?!%%!!%!%!%!!??%!%!%!%%?!?!!%%%%!%?%%%!!%?!!%?!%?%!%%%%!??%%%!%%%!%%%%%%%?!?%%!%!%?!?%!%%%!??%%!%!%?%!!!%%%!!%%%%%!%?!!!%%!?%%%!%%%%?!%%?%?!???%?%%??%%!%!!%%%!!%!%%!?%?!%%!!!%%!!%!%?!%%?!?%%%!%?!!!!%%%?%%%%!!?%!!%!!%%!!?%%%???%%!%%%%!?!??%%%%!!?%%!%!?!?%%%??%%%?!%!?!!%%!?%%%%%!%!%!?%??%?%?!%!?!!!%!%%!!!!%?!%!%!?%%%?!%%%!!%%?!%%%%!%%%%%!!%%!?!!%%%%!%!%!%!!!%!%!%?%!%%%%%%%!?!??!?%?%!%%?%%%%!%%%%??!!%!!%%%%%%%!%?%?%%!%%!%!?!%?%%!??!!%?!!%%?%%!%!%!%%?%%%!!%%%%%%!%!%?!%!%%!!!%!?%%%%?%%%?%!!!%%!%%!?%%%%%?!!!!%%%!%%%%!%!%%?%%!%?%?!%%%!%!%!!%!?!?%!%?%?%%?!?!?%%?!%?!%%%!%%!%%!%%%!!%%??!%%??%%?!%!%%%??!!?%%%%?%%?!!!!!%%!!!%%%!%%%??%!!%!?!!!%%?%?%!!%!?%%%!!?%!%%!%!!!!%%%%%%%!!?!??!%%%%!!??!!%%??%!%%%%%%???%%%?!!%!%!%%%%%%!%%!%%!%!?%!%%%%!%%!!!!%%?%!?%%%%%%%%%!%!!%?!%??%!!%%!!?!?%?%%%%%%%?!%!!?!%%%%%%?%%%%!%%?!%!%%!%!%!%!!%!%!?%%%%!!!!?!!!%%%%?!%!!%%%?%!?%!%?!?!?!!%%%!?!%?%!%%%!%%%!?%!?!!%!%?%!!!%%?!%%%%%%!!%%%??%%%??%%%%%%%!%%%!%%!%?!%%?%?!!%%%!%%%?%%!?%!%?%?%%!!%!!%!!%%!??%!%?%!%%%%%%!%!%%!%!!!%%?%!!!?%?%%%!?%%%!?!!!!??!%%%!%!?%%%!%!??!!%!!!!%?%!%%%!!%%%%!!%?!?%!%!%%%%%%?!!%%%%!%%%!!%%??!%%%!%%?!?!%?%!!%!%?!?%%%!%!%%%!%!!%!%!!%!!!%!%!%!%!%%!%%%%%!!!%?!?!%%?%?%%?%?%?%?!?%!!%%%%!%!%!%%%!%%%?!!%!%!%%%%%%%%%!%?%!%!?%!!!!!!%%%%!!?%?!%!!?!%!?%%%!%!%!?%!?%%%?%%!!!%!?%!!%?!?!!%!%%?!!%%?!!?!?%!%%!?%%%%%!%!%!%%%??!?%!!!!%%!?!?%?%?%%%%%?%%%%%%!!%%%%!!?%%%!%!%!?!%!!!%%!?%!%%%!%%%%!?!!%%!!?%%%!?%!?%%%%?!!%%!!?%%%%!!%%!!%?%?%%%?!%!!%%%!%?%!!!!!%%%?!!%%%!!!%!%!%?!%%!!!%%%!%%%%!!?%%!!%!%!!%%%!%%%%%!!!!!!%!%%?%!!!%%%%%???!%?!%!%%!!%!%%!!?!%%!%!%%?%?%%%%!%%%%?!%%?!??!%?!%?%?!%%!!?%%!%%?%??!%%%%!?%!%!%!!%%%!%%?%%%%!!%%%%?%%%?%!%%?!!!%?%%%%%%%%!!!%!%%!!%!%!%!%!%!??%?!!!!%!%?!%!!!!%!?%%%?!%%!!!!!!?%?%!%!%!!?!!?%!!??!?%%%?!!?%?%%%%!!!%%!!?%!%%%%%!%%%!%%%%%%!%%%!%!??%??%%%?!!%!%!?%%%!!%%%?%%%!%%!??!%!%%!!%!%%!!%!%%%!%%!!!?!!?!!!!?!!%?!?%%%!%%%??%%!%%%?!!!%!!!!!?%!!%%!!!%%!%%%!!!%%%?!!?%!%%?%?%%%%!?!!%!%!?%%!%!?%%!!!%%%%?!%%%%%%%!!%%%!%%?!?%!%%%!!%%%%%%!%%%%%%!!%?%?%!%!!%?%%%%%!?!%?%%!%!%%!!!!??%?%%%?!%%??%%?%!!%%?!%%!%!?!!!%%%%%%%%%%%%%%!%!%%?!!%?%%?!!?%%%?%%%!%%!!?%!?!!!?%!%!%!!%!?!%!?!?%%!!??%!%%%!%!%?!%!!%%%%%!?%!!!%?%%?!%!%?%?%?!!!!%!?%!?%!?!??%%!!%!!??%!!?%!??%!%!!!%%%!%%%!!!!%!%?!%!!%%!?%?%%%%!!%%%!%!??%%!%%%!!%%!%!%!%%%!!%%!%%%%%%%%!%!?!!%%!%!%%?%!%?!%!!%!!?%%%%??%!%!%?%%%!!?%!!?%?%%%???%%%%?%!!%?%%%%%!!!!!%%%??%%?%%%%!!!!%%%??%!%!?!?%%%%!!%%!?!!%!%!%!%%!%%!%?!%%?%%%!%!%!%%!?%!?%?%!%!!%!!!%%?!!%?!!?!%%%%!?%!%!%%!!!!%!?!%!!!%%%?!!?%?!?!!%!%!?!!%%%%%%?%%%!!!%%!!?%!%!!!%?%%!%?????%!!!!!!!%%!%%%!%%%!!%%%!!%!?%!%%%%?%%%!%??!%!?%%!%%!%?!!!%%%%?%%%%%%!%%!%%%?!%%%!!?%%%!?%%!?!%%%%%!%!%%!%!?!!!!!!%%!!!!!?%?!%!?!!!????%!%??%?%%!?%%%%!!%!?!%%%%%%%!%!!%!!%%?!?!?%!%%!!!?%%%!%%??!%!!!%%%!%!!%!?%%!!%!%%%!?%!?%%!?!%!!!!!!%!?%?!!!%?!%?%%%?%!%%%!!%!%%%%?%!%%?!!!%%!?%!%%????%!!%%!%%!%%%%!%%%%%!%!!!%?%%??!%??%%!%%??!%%%%!%%%%%!!%%%!%%%?!%!%?%%!!???!%?%%%?!?%!?%%%!!!%%!?!%!?!%%!!!!%!%%%%%??!!%!%?%%%!!?%!%!?%%!!???!%?!?!!!%!%!%%?%!!%%!?%!?%%??%!%%%%%%%%%!!!!?%!!!!!%%%%!!%%!%%!%??%%%%?!%%!??!!!!%%%%%!%%%%!?%%!%%!?%!?!!!!!%!!%!%%?!%%%!%??%%%%!%!!?%%%?%?!!???%%!%%!??!%!%!%%%%?!?%!%%%%%?!%%?!%%!!!%%?%?!%!%!%%?%%!!%!%!!?!!!%?%%%!!!???!!%!%!%!%%%%!?!!!!%?%?%%%!!%!?%%!!%%%%%%!!%%!!!!%!%%%!?!?%?%%!!!%!%%%%!%?%%!!!%??!?!%!%!%%?%%!??%!%!%%!%%%%%%%!!%!!!!%%!%%%!?!%!%?!%%!%%%%%%!%%%%%%!!?!?!!!%%%!%%??!%???!!%%?!%?!%?%%%%%%?%!%%%%!!%?!%!%!%%!!!!!%!%?%%?!?%%!?!!%%!!!!%%%%%?!%%!!%%?%%??%%%?!!%!!%!?%%!%%%%%%!?%%!%!!!?!%!?!%!%%!!%!??!%!!?!!!%%%%%!!!!!!%%!%!%%!%%!!??!%%%%%!!!%!%%?%%!%%!%?!!%!%%%%%%%%%!?!!%%?%%?!%%!%%!!%!%%%!?%?%%%%%%?!?%%%!%%%!!!%%!%%!!%%%?%!??!?!%%!%%!%?%%!%%??!?!%!!!%%!%?!!!%!%!%%%?!%%%%%%?!?%%%%!%%?%?%!?!%%?!!!!?%%!%!%%%%%%%?!!%!%?%%?%%%%%%%??%?!?!%%?!!!%%%%%%!%?%%%%?%!!?!%%%?%!!%%!!%!!%!%?!%!%%%%%%%%!?!?!!!%%!!%%?%%%!!%!!%????%!%%!!?!%%%%!?!?!!!!!%%%!!??!?%!%%!%%%%%%%?!%%!!!?%%!!%!?%!%%!%%??%?!%???!!!!?!%%%?%!?!%?%?!!!!!%!!!?!!!%%?!?%%!!?%!!?%??!%%!%%%!%?%%?%%%!%!%!!??%!!%%?!%%?!!%!?!%?!!%!!!?!%%%??%!?%%%!%?%!%%??%!?%?%?%??!!%%%?%%%!%!!!?!!?%%%??!!!%?!%!%!%%%%%!%%?%!%!%%%!%%?!%%?%%%%!%%?!!?%?%!%!?%%!!%!%%%!?%%%%%%%%%!!!!!?%%!%!?!%%?!!%!%%!%?%!%%?!?%?!?%!%??%!%!%%%%!!%!%!%!!%%?!!?%%???!%!!!!!??!?%?%?!%%!!%%%!%%!!%%%!%?!!!?%%%%%%!!%!%!!??%!??%!!!%!%!?%%?%%%?!%%?!!%??%?%!!%!!%%!%!!?%%!!!%?%!?!%!!%%?%!!!??!?!??%!%%!!%%!%!!%%%?!!?%%%%%%%%%!?%!%%%%!%%%!!%?!??!!%%%%%%%!%!%!%!%%!!!!!!!%%?!!?!%%%!!!!?%!%!!%%%%%%?!?%!?%!!!!!??%%!!%??%%%?%!%!%!!%%%?%?!%%?%?%%%!%!!!%%!%!%%!%%?%%!%?!!%%%%?%%%!!%!%?%?!%!!%!%%??%%!!!?%!?%%%%?!?%!%!%%?%%!%?!!%!!%%?%%??%!?%%?!!%!!%??%%!%%%!?%!?!%?%?%%?%%??!?%!!!!!%%!%%!%%%%?!%%??%%%!%!!!%%%%?!?%!?!%%?!%%?%??%?!%%!%%!?%%%%?%%%!%?%%%%!%?!!%%!!%%%!%!%!%!%!!%%%???!%??!!?%%%!%%%!%%?!%!%%?%%!!%!!?!!%!%%!%%!%%!!%!?%%?%%%%!%?%%%%%%%!%?%%%%%%%%!%%%%%%%!%!%%!!?%?%??!%%%!!!%%?!?!%%!?%%!%?!?%!?%!!??!%!?%!%%!?%%%!!%?%!!%%!%!!%!??%%!!%%%%!!%?%!%%%?!%%!!!!?!%%%!?%?!!%%!?%!%!!%%%%%%%!!!%?%%%!%!?!%%?%%??%!!?!%!%!%?%%%%??%%%%?!%%%%%%!?%!?!!!??%%?%%%!%!%%!!!!%?%!%%?!%%?%%%%?%%!!!%%%%%!%!%!%%%%%?%!?%!%?%%!!%?%!!%%%%!?%!!!%!%?%%?%%%!%%%!%%%!%%%%!?%!%!%!%!?%!%%!?!%?!%!!??!%%?!%%%?!!!%%%%?%??!!!!%%?%%!%!?%%%%%?%?%?!%%?%%%!?%??%%%!%%%%!?%!%%!!!%%!%?!%%?!!!!!%!!%!?%%%%%!%?!?%!?!%%!!%%%%!!%%!%!!%%?!%?%%!??%!!??%%%!?%!!%?%?%!!%!?!%!!%!?%%!%%%?%%%%%!?%%%!!%?%%!!!!%%%%!%%%!%!%%?%%!?%%%!%%!!%%!%%%!%?!%?!%%%!%!%!?%%%%?!%%!%??!!%%!%?%!%??!%%%?%??%!!?!%%%?%?!%%?%?!%?!!%%%%!%!?%%%%?!!%!%!%?%?%!%%%%!%%!%%%!!!%%!%!%!?%!!?%??!%!%%!!!%%!!%%!!%%!??!%%%!!?!%?%%%%?%!?!?!%%%!?!%%????%!%!%??%!%%!!!%!?!!?%?%!?!!%%%?%%!%%???!!%%%!%!%?!?%!%?%!!!%%%%!%!?%!!??!?!!%%%%%%!!%!?!%%?%!!!%!%?%%!???%%%%%!%?%%!!!!!!%!!%!%%!!%%%??%%%%%%%!%?%%%%%!%%!%!?%!!!%!%!?%!%?!%%!%!!%%?%?%!?!?!!?%?!!%!%!!%!%%%!%%!%%?!%%%%!!%%%%??%%%%%!!!%%?!%%!?%%%?!%%%?%?!%!%!%%%%!!%%%%%?%%??%!%!???!%!!!%%%!?%!%%%!%!%%%%%%!%!%!%%?!!?!%!%%!%%%!!%!?%%%!!!%%%?!%%%!%%%!!!!!!%??!%!%%!%!%?%%!!%%!%%!!?%?%!!!?%%!%%%%?!%!??!!%%%%!!%?%?%%?%?!%%!%?%%!%%%%??%%%?%!%%%%??!%%%%%?%%?%%!%%?%!!?!%!!?%%%!%%!%?%!%%!%%!!%%!%%%%!%%???%%%!%%%%%??!%?%%?%%%%%%!!?%?%%%%%?%%%%%!%%%%?!%!%%!%%%!??!?!%%!%%!%!%!?%?!%!!%?!%!?%!!!%?%!!?!%?!%%!%%!?%!%%%%!!%%?%!!%%!??%%!%%?!%!%?!!?!%%%%!!%%%?%%?!%?%!!!?%%%!%!!!%%%%!!!?%%%!%!!%!%%?%%%%!%?!%%%%%!?%%!%%?!!!!!%!!%!%!?!!?%!%?%%?!!%%!!!%!!!%%?!!%%!%!%!%%!%?!%?!!%%!!?!%%?!%?!%%%%%%%%!%%!%%!%%?%!?%!%%%%%%!???!!%%!!!?%!%%%%%%!%%!!!%%%%%!%%?%!%!!%!!!%%!!?%%%%!!%%?%!?%%%!%!%?!???!%?!%?%%!??%%?%!!%%!%!!%!%!%%!%%%?%%?!!!%!?!%%!%?%%!%%%?%%%%!!%%%%!%!!%!%!%%!%!%!!??!!%%?%!%!%%!%%!%%!??!%%%?%?!%!%!!!!%%!!!%%!?!!!%!%?%!%%?%%!%!?%!%!%%?%%!!!??%!??%!!%%!!%%?%%%!%!!%!%%%%!%!?%%%%%!?!?!%?%%!%!??%!%%!!!!!%%?%!!?!%!%%%%%!!!?%%!?%!%%%!%%!?!!%!??!%!%!!??%!%%!%%!%%!%??%!!!!!%??%%!%!%!%!!!!%?%!%%?%!%!?!%!!%!!!?%%?!?!%%?%!%%%!%!!!%%!%%!%!!!%??%?!%!%?%%%!??%!%?%?!%%%%?%%%!%!%!%??!%%!!!?%?%!?!%?%%!%?!!%%%!%!%%?%%!%!?!!%??!?%?!%%%%%%?%!%?%!%%?%%%?%!!%!?%%%%!!%%!%%%%!%!!??%%!%!!!%!%%?!%%!!%%!!%!?!%%%%%!!%%!?!%%%%!%%%!%%!%?%%!%%!!!%!!!%!!%!!%!%%!%%?!!%!%?%%%%??%%!?%?!%%%%%!%?%%%!%%%?!%!%%!!%!?%!?%%%%!!%%%!%!%%%%%!%%%!%!!?%?!!!%%?%%?!%%%%%!%?!%!%?%%!%!%!?!!%!!?%%?!!%%!%%?%%?%%%%?%?%%!%!!%%%%%%%%%%!%?!?%!%%%!!%!%%%!%!%!?%?%%!!!%%!%%%%%?%!%%!!%%%%%!!!%!!!?%!?%!?%!%!!%%!?!!%%!!%!%%?%!%?!!!%%%%!%!?%?%%%%?!%!%!!%%%%!!?%%!?!%%!%%%%%%%!!%!!?!!%!%!%?%?%!%%!%%!%%!%?!%%%?%%%?!!%!!!?%%!%?%%!%%!!%??%??%?%?!%%%!%%%%%??!%%!!?!%%%%?!%??!!!!%%!%?%!!%%%%!?%!!%??%!%%?!%??%%??!%%%?!???!!?!!%%%!!%%%?%%!%%%%!!!!%%!%!?!!!!!%%%%!%%!%?%%%%%%%?%%!!%!!!%?%?%?!!%!??!!%%!!%!%%%%%!%%%%%?!%!!%%!%%!!%%%?%?!%!%%!%%!!%?!!!%%%!!?%!%?!!!!!!!?%%!???%?!%!%%!%!%?!?!%!?!%?!%%!!!%%!%??%!!?%%!%??%%%!!%??%%?!%%%!%%!?%%!?!!%%%!?!!%%!%%?%??!!!!!!%%??%!!%%!!%??!%%!%?%%%%%!%%%!!?%!%!%%%!%?!%!!%!%%%!?%?%?%!%!%!?!!??!%%%!!%%%%?%%%%%?!%%!%?!?%!%?!!%%%%%%%??%!?!%!%!??%%%?!!!?%!%%!%!!!%!!%%?%%%!!!%!%%%?!!!?%%?%%?%?%!?%%%!!%%!!%%%?%%%?%%?%!%%!%%?%!%!?!!%?%%%%!%!%%!%!!%%!%?%!?%%?%?!%%!%%%?%%?!%?!%!%?!!%%%!%%%?%!%%?%!!%!%%%!%%%%?%%!!%!?!?%!!%%%%%!%%%%%%%!!%%%%%%!%%?%?%%!!!%!!?%?%%!%%!?!?%%%!%!%%?%!%%!%!?%!%%%%??!!%%!!?%%%?!!!!!%!%%!!%%%%!?%!%!?!?%!?%%%%%!!!%!?%%!?%!%?%%%%!!%!?%!?!%!?!!%%!%!%%!?!!!%%%%%!%??%%!??!%!?!!!%%?!!%?!%%!!!%%!?%!!!!%%?%%?%!%!!%%!??!%?!??%%%!%!%!%%??!?%!?!%%!%!%?%!%%%%%!%%!?%?%!!?%!!!%!%!!?!%!%?!?!%%!%%!%%!!%?!!%!%%!!%!??%%%%%%!%%!!%?%%?%%!!%?!??!%%%%!?!?%%%%?!%!!!!!%%!!?%%?%%?%!%%!!!!%%?%?%%!%%!%!%%!%??%!%!%?!??%%%!!!!?%!!!!??!%%!%%!!!!!?!%!%%!%%%?%%%??%!%%%?%%!%%!%%%!?!!!%!!%!%%!%%!%?%!%%!!%%!!%!?%?%%%%%%%!!!%%!%!?%%!!!%!?%!!%%%%!!!!?%!!!%%!!%!!!?!%%!%%?!%%%?%%!%!%!%%%%!%%?%!%!?%!!!?!!%?%!%!%%%??%!!%!!%%%?%%!!?%%!!%?!%%%?!%%%%%!!%%%%!%%%?%!!!%?!%%%?%%%!!%!??%!%!%!!!%!?%%!%!!?!?!%!?%!?%%%?%!%!!!!!%%%!!!%?%%!!%%!%?!%?%%?!%!%!%%!!!!!%!?%!!!!%%!!?!%!!!%!?%!!??%%%%!%!!?!!!?!%%%!%?!%?!%%!!?%%%%!%!%!%!!%%%!%??!!?%%%%%%%?%%!!%?!!!!%%%%%?!?%%%%%!%%?%?!!%%?!?!!!%%!!%%!%%%!!??!!%%%!!%!!!%%%%!?%%%%!%!%??!!?%%%%%%%%%!??%%?%%%%!%?!!%?%!?!%?%!%!%!%!!%%?!%%%!?!%!?%%!%%%!?%%%!%%%!!!%%%?%%%%!%?%%!!!%%%%!!!%%!!?%%!??%%!!%%%!!%%!%???%?%!!%!%?!%!!?%?%%!%!%!!??!!!%!!%!%%??%!?!%%!%%%%%!!%?%%!%%%%!%%%?%%%?%!!%!%%%%%!!%?%!%!%%%!%%?!%!!%%%%%%%%%?%%%!%?%!!%!%!%%!%%%%%%!%%?!?%%%%%%?!%!%%!%%!%%%!%!!?%%%%!!!%%?!!?!%??%!?%?%!%?!%%%%%!!%%!?%!%!%%%!?%%!!%!?!?%%%%!%?!!!%%%%%%!%%?!!%%!!!%%%%%%%%%???%%?%%%!!!%!%?!%!!%?%!!!%!?%%%%?%%!%%!!!%%!!?!%%%!%!!%%%!%?%!%%?!?%%?!%!%%!!?!%??!!!!!!%%%%!%%!!!%%?%!%!!%%%%?%%%!%?%???%%??%%!%!%%%%!%!!?%?%!?%%!?%!%%%!%%?%?%!!%%%?%%%%%%%%%?%?%%%?%!?!%!%%%%%?!%!!!%!%??%%%%!%!!!%?!!%%%%%!?%?%!%%%%%%?%%?!%?!%?!%!!?%!%%%!!!%%%%!!!!?!!%%?!%?%%!!!%%%%%%!!!%%!%?%%%%%??%!!%??%!%%!!!!%!!!%!%%%%!??%!!?%%!?%???%%?!%!%%!?%%%%!!!%%%!%?%?!%%%%!?%%%%%!??%%?!%%?%!!!%%%%%%!%%!%%!!%%!?%!%!%?!?%?%?%!%!!%%%!?!%%%!%%%?!!!!%%%%%??!!%%%%%!%!!%%%%%%%??%!%%!%?!%%%%%%%!%%!!%!!?%!%%!!!%%%%?!!%?!!!?%%%%%%?!%%?!%%%%!!%!!!%!%?!%??!%%?%%?!!!%!!%%?%!%%%%%?%%!%%!%?!!!%??%!!%%%!%%%!?%?%?!%%%!%%?%?!%!!%!%?%!!%?!%%%!%%!?!!?%!%!%%!%%?%%%%%%%!%%%?%!%%%!??%!?%%!%!?%!!!!!%!%%%!%!%%%!!!%%%?%!?!!!%%!%%%!%!!!!!%!!%?%!%%%%%%??!??%?!?!!!!%%%!%%!%?!%!?%%%%%%!%!%!%%%%%!!!!%%?%?%%?%!!!!%%!!!%?!%?!%!%%!???!!%%??%!!?!!?%!%!%!?%%%!%%%!%?!%!?%%?!?!%!%?%!!%!%?%!%?%%%!?%?%%%!!%!?!%%%%%!%?!%%!?!%%?%%%?!%%%%%!!!!!!%!%?%%%%!?!?!%!%%%!!%?!%%!!?!?!%!%%%??%!%?!!?%%%%%?%!!%%%?%%!?%!%!!%?%%!%%%?%!!?!?!%%!?%%!?!%?!!%??%%%%?!%!??!%%%!!!%!!?!!!??%%%%!%%!?%?!%??%%%!%!!?%?!!%%%!!?!%!%!!%%!%%!!%!%%%%%!%%%%%!%?!!?%%%%%?%?!%%%%%!%?%%%%?%%%%!%!%?!%!!!%!%%!%%!!%!%!%%!!%?!?%?%!%!%%!%!!!?!%%%?!%!??!%?%!%!!%%??%?%%!?%?%%%!!%%??%%?%?%%?%?!%%!!%!?!%%!!%%!!%%!!%!!%?%!%!%%%%!%%%!%%%%%?%?%%%%?%%%?!!!!%!%!!%%?%!%!?%%%!?!?%?%!%!%!!%!?%!%!%!!%%?!%!%!%!!!!?%!%%%%?%!?!%?!?%%%!!!%%%!?%%!?!!%%!%!!??%!%!??%?%%!?!%!%%?%!?!%%%%!%!%%%?%!!!!?%%%?!?%?!???%%%%%!%%!!?%!%!%%%?%%%%%%!!!%!??%%%!%%%!%%%%%?%!!%%!%%!!%%%??!%%%%!!%%%%!%!?%%%%!?%!!!!%%%%!%%%!%%!?%%!%%%?%!%%!%?%!?!!%%?%!%%!%!%%%%!%!?%%!%?%%%!!!!!!!%!%!?%%%%%%%?!%%%%%%%%%!%!!%!%%!!%%%%!!??%?!%?!%%!!%%!%?%%!??%!%??%!!%%!%%%!!??%%?%?%%!!%%?%%?%?!%!!?%?%!%%!?%%?!??!?!%%%%%!!%%!!!!%!!?%%%!!%!%%!%!%?%!%%%?!?%?!%!!%%!%!%%%%%%%!!!?%!!%%%?!%%!%!%%%!!!!!?!%%?%%%?!%??%%?!!%!%!!!%%%!%!%%!%!!?%%?%%?!%!!%%!!!%%??%%?%%!!!%?%%?%!%%%%!%?!%%!!%%%!?!?%%!%%!%%%!%%%%%!!!%%%!!%%%%%?!%%!%?!%%%?!!!%!%%!?!?!??%!%%!!%!%?%!!?!!%%%!%%%!%!!%!?%%%!!%%%%%%%!%%?%%%%%%?%%!%%%?%!%%?%%?!%!!!!!%%%?!%%%!%!%!%!?%%%%!?%%!!%!%%!%!%?%%?%!%!!?%!!!%%%!???!?!%%?!%%%?%%%!?!%!?!!?%!%!%%!%?!?%!%%%%%%!%!?!?%!?%%!%!!!%!?%%%%!%%?!!!%??%!%!%%%!%%!!%%!!!%%!!%%!??!!%%!?!!%%%%%?!!%?!?%!!%!%?%%?%%!%%%!?!?!!%!!%%%%?!!!%!%%%??%!%!!?!%!!!!?!%%%!%%!%%%!!%%!%!%%!%?!%%%!%!!%?%!%?%%?%%%!!%%%!!!%!%?%!%?!%!?%!%!?%!%%?!!?!%!?%!%!%%%?%?%%%!%%!%?%%%!%!?%!?%!!%%!?%!!?%%!!?!?%%??%%!%%%%!%!%%%%?!%!%%?!!!!%%%%%!!%%%!!?%%%!!!!?%!?%%??!%%%!!%%%%?%%!%%?%?%%!%!!!%?%%!???!???!%%%!!!%%!%!%!%?!!%!%!!%!%!%!%!!!%%!!%%!!!%%%??!%%?!%!%%!%!!%%!%%!%%?%?%%%!!?%%%?%%?%!%%%%!%%%!?%%!!!!%!%?!%!%%!!?!!%?!%%?%!%%!!!%?%!%!!%!%!%?%%!%?!%!%%%!?!!!%%!?%%!?%!?!%!%%%%?%%???%%%%%%%?%%%!%%?%!!%%%%%!?!!%?%!!%%%!%%!!%%!!%?%?!!%%!%!%%!!%%?%!!!%!%%!?%%%!?!?%%??!?%!%%!!%?!%%!!?%%%?%??%!%!??!%!%!!%??!!?!!%?!%!!%%%%%%?%%!!??%%%%%%!?%?!?!??!%!%%?!!%?!?!%!%!?%!%%%%!!??%!%!%%!!%%!!!%!%?%!??!!!?%%%?!%!%%!!%%!!!!%!%%%!%??!%%!%%%%!%!%!!%??!%!%!!!?!%%!!%!%?!!!!%!%!??!!%%%%%!???!!%!!%?%%%%%!!%%%???!%!%!!!%%!%!!%%%!%!%!!%%%%%?!%%%%%%?!%?!%!%?%!%!!?!%%?%%?%%!%%!%%!!!%%?%!?%?!!?%%?%%%!??%%?!!!%%?%%!!!??!?!!%!%%%??!?!?%!!%%%%!!%!%!?!%%!%%!%???%%%%%!!%!%!%!%%??!%?%%%%!%!%%!!!%!%!%%%?!%%!%!%%??%!!!!%?!%!!!?%?%??!%!!%?%!%%%?!%!!!%?%%!!!?%!!!%%!!%%%%%!?!?!%?!!!!%%????%!!%!%?%%?!?!%!%%%%%%%%!%!!%%?%%%!%%%%!?!??%%?%?!%!%!%%!%%!%?%!%!%!%%%%!%%!!%%%!%%%?%%!!%??%%?%!%%!!!%!%!%%?%!%%%!!%!%%%%%!??%%%%!!%%!%!?!%?%%!%??!!%!%%?%%?%!%!%%%!%?%%%%??%%%%!%%?%%%%%%??%%%%%!!%!%?%%%%?%?!%%!%%!!?%%%%!%%!!?!%%?%??%!?%!%%%!?%%!%!!%%??%%%!%?%%!??%%!%%!%%!%%%!!!?%%%%!%?%%%!%%%%?!%!?%??%%%%%%!!%%!?%!!!!%?!%!%%!!%%!%!%%??!??%%!!%%!%!%!!%!%!??!!%!%!%%???%%!%%!!!!?%!%%%?!%!!%!%%!!%%??%%%!%%%%%!!!%%%%%%??%!?!!?%%?%%!!%??%!?!%!%!%?%!%?!%!!!%%%!!!!!!%%!%!!?%%%%%!%?!!%!%%?!!%%??%!!!%%!?!%?%%!%??%%!%%%!?%%!%!%%%!!??%%!%?!%%!?%%?%!%%%%%!!%%!!%!%%%%!%!%?%%?%%%!!%%!?%%!!!!%%!!%?%%%%%%%?%%?!%!%!%%%%?!%!%!%?%%%?%!???%%!%!!?!!?%????!!?%!!%%%%%%%!%%!%%%!%%%%%!%!%%!%!?%?%!!%!!!?!%%%%!%%%!!!%%!%!%%?%?!!!%%?%!%!%!%!%?!%?!!%%!%%%%?%%?!%!%%?!%%%%!%%%%!?!%!%!%%%!%%%%%%%?%!!%!%?%??%!%%?!%!?%!?%!?%%!!%!%!!!%%%?%%%%%%%%%?%%%!%!%?!!%!!%?%!!%%!%?%!!!%%!!???%%%%%%?%!!?!!!!!%?!%!?%%!%%%%%?%%%%!!%%?%%!%%!!?%%!!%%!%?%%!!!%%%!%%?%!?%%!%%%%%?!%!%?!%%!%!%?!!%%!%%%!%%??%%%!%%%?%%!!%%%%%%%%!!!!%%!!%%!%%%%!%%%!!%%!?!%!%%%%!!%%%%%??!%%%%???%!%%?%%!%%%!%%!%%%%%!!!?%%%%!!%%%%%?%%%!!!!!%!%%%?%!%?!?%!%?%?%%%!!?%?!??!%%%!!!!%%!!%%!%%??%%!%%!%%!%%%%!%%!%%%?!%%%%%%%!%?%%%!%!%%%%%%%%%%?!!!?%!?%%!!%%%?%%%!%!!!!%??%%?!!!!%%%!!!%!!!!!!%%!!?%!!!!%?%?!!?%!!%%%%?!%%!!!!%!?%!%%?%%%?!!?!%%!!!?!!!?!?!%??%%??%%%%%?!%%%!%%%%!!!?!%!%%%%?%%%!!!%%!!!%%%!%?!%%%%%!?%?!%%!!%%!!?!!%%!!!?!?!%%%!%%?!%%??%%!?%!%%%?!?%!!?%%%%!?!%!?!!%%?!%??!%%!!!??%!!%%!!%%!%%?%!%%?%!%%!%%%?!%!%??!!%??%!?!%%%?%%%!%%%%%??%!%%!!?%%%!%%%!!!%%?%?!%!%%?!%%!!!?%!!%%!%%%%!!!%%!!%%!!%%!?!!%!!!%!!?!%%!%!?%%!%%%!%?%!!?%%%%!%!!!?%!%%%%%%%?!!?%!%%!!!%!!%??!?%%%%%?%!%%%%%?%%%%%%!!?%%!%!!%?%%%??!%%%!!%%!%%%%?%!!%%?!!?%%!%%%%!%!%!?%?%?%%!?%!%%?!%%%!?%%%!??%%!%%!!%!!!!%!%!%?%%%?!%%!!%!%%%%!%?!!!?!%!!%%%%%!!?%%%?%?!?%%%%??%??%%%%!!?!%%?%!?!!!%!%!%%?%%?!!%?%%!%!%%!%%!!!%%%%%%!%%%?!%?%!!%%%?%%%%?!%!!?!!!?!%!!?!%%!?!???%%!!%%%!!??%%%?!%!%!%%!%!%%%!!%%!!!?%%%%%%%!?%!!!%%%%%%%%%!!!%!%%%!?!%%!!%!%%?%!!!!%!%?%?!%?!?%%?%!%!%%!%??!!!!%%??%%!%!!%!%%%!!%!!!%!!%%?!%%!!?%!%%!!%!!%!!%%!%!!!??!%?%!?%%%?!%?%!!%%!%!%%!%%!%%%%!%!?%?%%%!!!!!!%%%%%!?!%%%%?!%%%%!!%%%!%%%%%!%!%?!?%!!%%!%%??%?%%!%%?!%!%!%!%!%%!!%%%!%%%!!!?%%?%%%%%%%??%%?%!%!%!%%%%!!%!?%!%!!%%?%?%??!%%%%%??!!%!%%?!%%%%%%%%%%%!%%?%!%!%!!!?!??%%?%!?!%!%%%%%%%%%%?%%?%%%%!%!%%%%%%!?%%%%!%%%?%%%?%?%%%%!%%!%%%!%!?!%%!!!!%!%!??!%%!!!?%%%!%!?%%%!%%?!!%!!%?%%?%???%??%%%!%%!%%?!!%!%%%!?%%%!%%%%!%%%??%%%%%%!%%?%!???%%?%?!%%%!%!?!!%%%%!%?%%%!%?%%%%!%!?%%%!%%!%!!!?%?%?!!!?%%!%%%?%!??%!!!!!!%%!%%!%%%!!%!?%?%%!!%!?%%%%!!!!???%%?%%!%%%??%!!%!%!!%?!%!%%%???%%%!?%%%!%??!!!!%!!%!%%%%?!%%%?%!?!!!!!!%!%%%%%%%%%??%!%!!%!!?%%%%%?%%%!!?%!%%!%?!%%?%!!%%%!!%%%!%?%!!!!!!%!%!%!%!!!%?!%%?!!%%?%!%??%!%%!%%%%%!%%!%%%%%%?%%%!!!%%%%!!%!%!!%%%!%!%!%%%%%%!!!!%!%%!!???%!??!%!?!%!!?!!?%%!%%%%%%??!%%!!%%!!!%!!%!%%!?%%!%?!%%?%%!%?!!%?%%!!%!%%?%!%%%%!?%?!%!%!!?%%%!?!%%%?%%!%!%%?!%?!?%?!!%!%!!?%%%%!%%%%%%!?%%%%!%!%!%%?!!!?%%%%!!%!%!%%%%?%%!%%%%?!!%%!?!%%?!!%!!%!!%%!%%%!%!!!%%!!?%!%%%?%?%%?%!%%!%%!!%%%!%%!%%%%%!%%%!%%%%%%%%%!%?%?%!%%!!%%?!?%!!!%%%?!%?%%%!!%%!%%%%%%!??!%%!%!%%!%%%%!!!%?!%?!%!%!!!!%%%?!?%%%%%%%%%%?%%%!%!%!%!%!!!%!??!!!!%!!%!%!%!!%?!!!?%%!?!?%!?%!?%!%!?%!%%%%?%%!%!%!!!%!!%%!!%%%%??%!%%%!?%!%%%??!%%%?%?%!%%?!?%%%%%%?!%!%?%%%?%%%?!%%?!!%%%%%%!?%%%%!?%?!!%?!%%%!%!%?%%!%%%!%%%%%%%!%%%%!%%!?%%%?%%!!!%??!%!!%?!!!%%%%!%!!!%?%%!%%!%%!!%?%?!%%%%%%%%%%?!%!!!%%!%?%!%%!%!%??!???%?!!!%%!!!%!%%%%%%!%%!%??!!?%%!?%%%%%%%%%%%?!?!%%%!??%!?%!%%!!!%?!%%?!%?%%!?!%%!!!%%??%?%?%%%%!%!?!!?%%%!!?%??!%?%!%!%!?%%?%!%%??!%!!%%%%%%%%%?%?%?%%?%%??!%%!!%%!%%%!%%!%?!%!%?%%!!!??%%!!%?%%%%%?%?!?%??%?!%?!%%!%%%!%%%%%?!?!%!?%!%!?%!%%%%!%!%??%%!!%?%?%!!!!!%!%%!?%!%%%%%!%?%%%!!??!%!!%?%%!!%%!!%%?!!!!%!?!!%!%%!!?%%!%!%?!!!!%%!%%!%%%!??!%%!!%!!%!%!!!%%!?!%%!!?%!%?%!?!%%%!!%!!!%!%%!%%%!%?%%%?%!!??!%!%!%%?%!%%!!!%?!!%%?%%!%!%!%%?!!!%?%%%!?%%%%%?%%!%%%!!%%%!?!%%!!!%!%?!!%!!!%?%!!%!%%%%!?%!%?!?!%%!%!%%!!%!!%%?%!!%%%!%%?!!%!!%%%%%%%%%%%?!%!%%%%%!!%!!%%!!!!%!?!?!%%%!%?%%?!%??!%%%!%?!!!%%!%!%%%%%!%!%!!%%?%%!?%!!%%?%?%%!!%%!%?%%%!?!%%!?!%%%%%%!%!!!%?%%%%!!!!!!%%%%!%%!!%%%?%!!!%!!?!%%??!%%%!%!%!!%!?%!%?!%?!%%?%?%!%!%%!!%%%%?!!%%%%?!!!%!??%!%%!%%%!%%?!!%!?!%!%?!%%!?%%%!%!!?%%!%?%%?!%?%!!!%%%!?%%%?!%%%!%%!%%%%%%!!?!%%%!%%%???!?!!%!?%%%%?%%!!%!%%%%%!?%!!??%?%!!!%!!!%?!%%!?%!!?%!?%?%!!!%%!%%%%!%%%%?!?%%!??!%!!!!?%!%%?!%%%?!%!%!!%%%%!!%?!!!!%%!!%%%!!?!%%!!?%%%!%%!?!%?%!%%%%!!!!?%%!!%?!!?%%%%%?%%!!%?!?%!%!!%!?!%%%%!?!%%%%%!?%?!%!?%%?!%%!!%%%%%%?%??!!!?!%!%%!!!%%!%%!!%!!%%%%%!!!!%%!%%?%%!?!%%%!%!%%!!?%!%?!%!%%%??%!%?!!!%!!?!%%!!!?%!%!%%%%%%!!%%%%%!!%%?%!?%!%%%%%?%%?!%?%%!%!%?%!?!!?%%!??%?!%!!?%!%%%%%!!!%%!!?%%%!%?%??%%?%!%%%?!!%%!%%?%%%%!%!%%!?%%??!!%?%%!?!?%!%!!!?%%%%%%!%!!%%?%?%%%%?%%%%!%%%%?%?!!????!%%?!%!%%%%??%!!?!%!?%???!%!%%%%%%%?%!!%!!!%?%%!!%%%??!%%%%!!%%!%%??%%%%!!%%%?%%%?!%%%%?%%%%!%!!!!???%!%!!%!%!%!%%!!%!%!%%%%%?!!%!?%?%%%%?%%%?%!%!!!?!%%%%%%!!!?%%!%?%%?%%?!%?%!%%!%%%!%%!%?!?!%?%%%!%?!%%!%!?%%?!!%?%!!!%%!%%%%%!%%?%%!??!%?!!%%%?%!?%%?%!?!!%!!%%?%%%!%?!%%%%!!?%%%!%%%%!?%!?%%%%%??!?%%?!%%??%!%!%?!?%%%!%%%!%!%%!%%%%%%%%?%!%!%%!%?%?%%%%!!%!!%%%%%?!??%%%!??!!%%%%?%?%%?%!%%!!%!%!!!!???%?!!?%%?%?!?!%!%?!?!%%%%%%%!%?!%!!%?%!%!%%%%%!!!%%%!?%%!!?%??%!!?%!?!!!%!%%%%%?%!?%!%%%%!%!%!!!%?%!!%!%%!%!?!!??!%!?!!%%?%??%!%%%??%%%%%%%%%!%???!%%!!!%%?!?%!%?!%?!!%%!!!%!%%%!%!!%!%?%?%%%%%%?!%?%%?%?!??%!?!%!??!?%%%%?!%%%!!%?!%%!%%!!%%%!%%?%%??!%?!%!%?%!!?!!%?!%!%?!%!!?%%!%%%!%!?%!%%!%!%%!%!?%!!%%%%%?!!%!?!!?%?!!%%!%?!%?%!!?%!%%!%??!%%%%%!!%!%%%!%%!%%%%!%?%%?!%!!%!!?!%%%???%%!%%!!%?!!!!%?%?%%!!%%!!?%%%%%%%!!?%%%%%%!?!%%!%!%!?!!%!!%?!!%!%%!?!?%%%!%!%?%%!%%!%!?%!%!%%!??%?!!!%%%%%%%%!%!%??!???!%%%!%%%!!!!%!?!??%!%%%%?%!!%?%!%%!?%%%!%%!%%%%%%%?!!!!!%%%!%??%%%%%%???%?!!%%%!!%%%?%!?%!%?!%%%!%!?%!!?!?%!!%?!!?%!%%?!!!%%!!%%!!!!%%%!%!!%%%??%%%%?!%??%!!!%%!?%%!?!!%?%%%%%?%%%%?%!%?%!?!??%%%%%%??%!!!!??!%%?!???%%!?!!%%!!%!%%?!!?%!????%!%!%%?!?%%%%%%%?!?!%%%%!%!%%!%%!%!?%!%?!!!%!%!??!??!!!%?%%%?%!%?%%!!%!%!%!%%%!%!%?%!?!%!%%%!%!?%!%%!?%%?%!%?%%!!%!%!?%%%%!!?%%%%%!%!?!!?!!?%?%!%%!%%!!%?!!%!!!!!%!%??%%??%%%!!%!%?%?%%%%%!!??%!%!?%?%%%%%%%%?!%%!%%%%!?%!!%!?%!!!!?!%%%!%%%%%?%%!!%%??%!%!%%!!!%%?%?!!!!%%%%%%%!%%%%%!!?%%?%??!%%??%%%%!!%%?%?!%?%?!?%!!%%%!%%!%%!!%!%%%%!%?!%%!%!!!%%?!?%?%!?%%?%!?%!?%%%!%%%!!%!?!%%%%!%%!?!?%!!%%!?!!%%!%??!%%%!!%!!!%!??!!??%!%?%?!%?!!%%?%%%??%!!!%%%%??!%%!%?%!%%!!?%!!!!!!%?%?!??%%%?!?%?%%%?%!%!%%%%!!%%%%%%%%%%%%!%!!!?!%!%%%%?%%!?!%%?%!!%?%%%!%!%?%%?!%%%%!!%%%%?!%%%%!!?!%!%!!!%!!!?!%%%?%!%!!?%??!!!%?%!!!%?!%!??!!!%%%%%?%?%%%!!%%%!?%!!!%?!?%?!?!%!%%%%%%%%!%%%!%!%%%%!%%%!%?%%%%%?%!%!%??!??%?!??%%!%%!%!%!%%%!?!%?%%%!?!%%%%!%!!%!%%!!%%%?!%!%!??!!!!??%!%!%%%!!%%%%%%?!?%%!?%!!!?%%%!!!%!!??%%%?%%!!%!%?%?%%!?!!%%?!?!%%?%%%%%%!??%!!!!!%%%%%%%!!%%?%?%%%!%%%??%%?%%!?%%!%!!%%%?%%?%!!!%!%!!!%!!%%??!?%%%?!%!?%%!!!%!!%%%%!?%%?%?%?!?!?!%%%!%%%%!%?!??%?%!?%%%%%%!???%!?%%%%?%%%?%%%%!%!%%%??%!!%%%%?%%%?%??!%!!%!%%%%!%!%!!!!%%%%%!%%!!%!!?!?%?!%%?!%%%?!%!%??%%%%%??%%%?!!%%!!%%%%%%!??%%%!!!%%%?%!%?!!%%%!!%?%%?%?%%%%!%%!%%%?%%%?%%%?%%!!?%%!!!%?%!%%%!!%!%%??%%!!%%?!%%%%?%!!%%!!!%%%%!%%?!?!!?%%%%%?!?!?!?!%%%!%%%!%%%%?%?!%%!%??!%!%%%%!%%!%%%?!!!!?%?!%%%!!??%!??!%??%!?!%!!%!!!%?!!!%%!!!%%%%%!?%%%?!%%%%%?%!!%%%%%!%!!%%?%?!%!!?%%!!?!%%%!!%!%%%%!%%%%%!%%??!!%%?!!%%%%??!%%!!%%?%%!!?%!!!!%%?%%!!!%!%%%??%!!%!!%%%%!%?%!!??!%!%!?%%%!?%%!%!!!%%!?%%!%!?%%%!!!%!%!%!??!%!%%%%!%!%%!%%%?!%!!%%!%!!?!%!!!!!%%%%%%!%%%%???%%!?%%%%!%!%%%!?!%%%!%%!!!!!?!?%%%??!??%!!!%%!%!!!%%!%!%!%%!%!%!%!?%?!?%%!!!?!%%?!!%!%?%!%??!%%!%!%?!!%%%%?!!%%%%!!%!%!%!?%?!%%%%%!???!!%%%!!?%%%?!?%!!%%%?%!%%%%%?!!%%%%%%%?%%%?%?!!%%%%%%!!%!%%?!!%?%!?%%%%?!%?!!!%?!%%%%?%?%?%%%!%?%%?!??!!%!??%!%%%%%%!!%!!?%%%%%?%%%!%%?!?%%?%!%%!%!!%%%%%%%%%?!%%%!?%%?%??!%%%%!!%??%%%%!!%??%!%!!%%!%!!?!%!?%%%?%!!?!%%%!!%%!!!%%!?%%%%%%%!%%?!!!%%%%!%%?%%!%!?!%%?!!%%!!!?!%%!%%%?%!!!!!%%?%!%!%%!%!%!%%!%%%%%!!!%!?%?!%?!%?%%%!%!!%%%%?!?%!%%!!!!?%%%%!?%%%?%!??!%?%??%!%%!%!!%!%!!%!?!!%%?!!%%%%!???!?%%!%!??%%%?!%%%%%!!!!%%?!?%%?%!%!?!!%?!%?%%!?%%%?%!!%!!%%!%??%!%%?%!%%?%?!!!%!!???!!%?!??!?!%%%%?%!%%?%%%%?%%%%?!!!?!?%!!%!!%?%%%%?!!%!?%%%!?!%!!!?!%%%%%!!!!!?%?!!%%%!%!%%%!%?%%%%!%%!?%!%%!%%??!?%!?%%!!!%!?!%%%%%%??!%!?%%!%?%%%%%!?%%!!?%!%%%!%?!%%?%?%!!%!%%!%%%%?%%%%!%!%!!%%?%%%!!%%?%%%!!!?%%%%%!!!%%%!%%%!%!%!!%!??!%%%??!%!!!!%%?!?!!!!%?%%%?!!%!%%!%!%??%!!?!%!%%%%%!!%%%!%%%%!!?!???%!!%!%%?%%%!%%%%!%!%%%%%?%%%!?%!?!%!%%!!!!%!!%%%%!%!%!!!?%%?!%%%%%!%?%!?!?!!%%%?!!%!%?%%!%%!!!?!?%!!!!%?!%%%?%%%%!!?%%%?!%%?!%???!%!%!%%%%%?%??!?!%!?!%?!%?!!%??!!?%??%!%%%!%%?!%!!!%%%!%%!%?%%!!!%%??%%%%%?%!%?%%%%!!???%%%%%%%%%%%%%%!?%%%?!!!!%!%!!??%!!%!!%!?!%!?%!%!%%%%!%%%%%!%%%!%?%%%%%%%!%?%%%!%!%%%!!??!%!!%?%%%%%%?!%%!??!??!!!?!%%%!!!%%??!???!!%!%%!%%!?!%?%%%??%!%%%%?!%%%!!%?!???%?%%!!%%!%!!%!!%!!%%!!!!%!%!!%!!%?%%!!!%%%!?%?%!%!%!%%%%%%%%%!%%!!%?!%%!???!!!%%???!%%!!%%???%%%!!%!!%?%!%%%!%%%???%%%%!?!%%!?%%!%?!!%!!%%??!!?%?%%!%%%%%%%%%%%%%%%?!!%!??%!!%!%%%%!%????%%!??!%!!%??%%%%%!!!%!?%%?!??%!??!%%%?!%%%%!?%?!!%%%!!%%!%%!%%%%!?%?%!%%!!%!!%%%%%!!%!%%%%!??%%%!!!?%!%%%%%?%!%!%!?!!%%%!%!!!%%%%!!?!%!?%%%%?%!%!!?%%%?!%%%%?%%!%?%?!!%%%%?%!%!!!%%!!%!!!?%%%%%?!??!!%!!%??!%??%%!!%%!!%%%!???%%!!!!%?!%!!!?%%%?%%%%!%%!?%!%%!%!%%?!!%?%%%%%%%%%%%!%?%%!?!!%%%%?!!?%%%!%%??%!%!?%%%?%%!?%?%!?%%%%?%%%%%%!?!%!?%%%%?!??%?!%!!!%?%!!?%!%%?%?%?%?%%!%!?%!!%%%!!%%%!!?!?!%!!!?!??%!%%%!!?!!%?%%%!?!%!??%%!%%%%%%%!%%?!!%??%%!%%!!!!?%!!!!%%?!%%%!%%?%%%!?%?%%%%!%!%?!%%!%%%%!%%?%%%!!%!%%!!%!!!%!%!?%!%%?!%!%?%!!%?%?!%?%%%?%%!?%!%%%%%!?!%%%!%%!%!!%%%%%%!!!%!!%%!!%%%!%!%!!%!?!%%%!%%?!!?%%!%%%%%!%%%?%!%!?%%?!%!!!%%!%%!!%%%%%!%%%???!%?%%%%%!?!!%!%!%%%%%%%%!%!?%%%!%%%!!%!!%??!?%?%%!!%%%!?%!%!%%!%%%%!%%!?%%!%?%??!%!!%!??!!%%?%%%!!!%%!!!%%%!%%%?%!%%!%%!??%%!%%%!!!%%!!%%!%!%%!!!?%!%%%?!%%%!%%!!%!%%%%!%?%!!!?%!!%%%!!%%%?%%!%!!%%%%!%%%%????!!!%!?!!%?!%%?!!%%%%%?%%%%%!%!%%%%%%!!!!%%%%!!?%%??%?%%!?%!?%%%?%%?%?%!!!!%!%!?%%!?!?%%%%!!%!!%%%%!%!??%%?%%%?%%%%%?%%%!!????!??%%%%%%%!%!%!%%!!%??%%!%!!%%!%%%?!?%%!%%!?%??!!%!?!%%%?%!%%%?!?%!?%!!%%?%?%%%%!%!!%%!%!!%%%?!%%%%%!!%??%!!%%%!%%!?!%%!!!!!%??%%%!?!%%%?!%%%%!!?%?%!!??%%?!!!?%%%%!!%!!%!!%%!!%%!!?!!%%%?%%%!%!??!%%%%%%%??!%!!?%%!%!!!!!%%?%!!!%%%!!!%%!!%%!?!%%?!%!%??!%%%%!!!?%%%%%%%%%%%!%!%?%%%!%%%%?!?!!!%!%!?!%%?%!%!!???%?!%%??!!!!%%%%!%%%!%%?%!%%%!%??!%!%%%%!!!!%!!!%%!%%%!!?%!!%!%!?%!%%%!%%%?!!!%%!!!!!%%%%%!???!!%!%%!!!?%%!!%%%%%??????%!!!!!!!%%%%%%%%%%!?%?%!?!%!%%%!?%%%%%!%!?%!!%!%!!?!%%!!?%%%?!!?%%%%%%?%%%%%!?!%%%%!%%%?%!%%?!%%%%??!!%%%%%?!%?!!%%?%%%?%!%%%%%!!%?%%!%%%??!%%%%!??%!%%!%!?!%%%%?%!?%%%%!!%%%%%!??%?%%%%%!!!%?%!!!!!%%!!%%?%%%?%%??%%%%%%?!%!%?!%!!%!!?!%%%%%%%?%%!!%%%%?!%%!?%%%!?!%??!!%%!%%!%%%???!%!%%!%!??%!%?%%%!%!%!!%!!!!??!!!!%??!?%?!!%?%!%%!!!!!%%!%%%!!?%%%!%%%?%!!!!%?%!!%!%%?%%!%%%?!%%%%?%!%%%%%!%!!!?%??!%!!%%!%%!%%!%%%!%!!%%!!!!!?%!!?%??%!%!%!%%%!!?!!!!!?%%%%!?%%!%%!??!%%%!%!%!%!!!%?!!?!%!%!!%%%%%%%?!%!!%!%%!?%!%%!%%!!%?!%?!??!!%?%%%%%%!%!%!!%%?%%!%!!%!%%!%%??%!!%?!!%!%%%!%%!!%!!!%?%%%%%%!%%%?!%%!!%?!%%%!%?!%!%!??%!%%!!%%!%%%%%%?%?%%!!!%%?!%!?%!%%%%%?!%%?%!!!%%!%!?%?!%!?%!%!%?!%?!!%!%?%!%%??%%!%%%%?!!%??!?%!%!!!%%%??!%%%%%%!%%%%?%!%%%!%%!!%!%%??%!%!!%%!%!!!!%%%%%!!?%%!%!%%!%%%%!%%??!?!%%%%?%!!%%?!?%!%!%!%!!%%!!%??%%!%%%%!!%%!?%%!%%!?%%!%%!?!!%%%?%!%%!%%!%!!?!%?!!%!!!%%!!!?!%%%%?!?!%!%%!%?!?!!??%%!!%%!%%?!?%%%%%%%!!%!%!!%??%%%!!%?%!%%%%%%!!%%%%%!%%?!%!?%%?%?!!%%!!%%%!!!?%?!!%!%!?!%!%!%!%%%%%!%!?!!%%!%%??!%%!%!%%!%%%%%%?%%!%!!%%!%%%?%%%%!%%%%!??%!%?%?%?!%!!!!?!%%%!!%!!%!%%%%%%?%%?%%??!!%!%%!??!%%!%%!%%?!??%!%!%%!?!%%%?%!%%%%?!!%!?!!?%!!%?!%%%%?!%%!%!?%!!!!!%!!%!?%?!%!%?%%%?!?!!%!%%!!%?%!!%??!!?!?%%%!!?%!%!??%!!!?%%!!%%!%?%%%?!?!!!%%%!!!%!%!%!!%%%%%!!?%%%?%??!!%%?%??%!!%%!%%!!!!!%!%%?%%!?!%%!!%%?%?!%%!!!%!%!!%?%%!!%%%!%%!??!%!??!%?%!??!%!?!!?!!?%%%%!%!!??!%%?%%!%%%!%%!!%%!!?%!%%%%?!%!%?!%!?!?%%!!%!!%??%!%!%!!!%!!!%!?!%!%!%!?%%!?%!!!!%%%%%%!%!%!%%%%%!!!%!%%!?!!%%!!!!!%!%!!%%!??%%%%!?%!%!?!%?%?!!%%%!!?%%!%%%%!!!!%!%!%!%??%%%?!!?!?%%!%?%%%%%%!!%?%%%!%%%%%%%%!!%?!!%!!!%!%!%??!?!%?%%?!%%!!%%!???%?!%!!%!%!%!?%?%?!%%!%?%%%%??!%%%!%%%%!?%%!%%%!?%?!!%?!?!!!%!%%%%%%%!!%?!!%!%%%!%!%%%!!!!?%%%!%%%?!!%%!!%!!%!%%%%%!!%%!%%%!%?%%%%?%%!?%%!!!?%!%%!?%%!%%??%!?%?!%??%%!%?%!%%!%!%!!%!%?%%!!!?!%%%%%%!%!?!!!?%%!!%!%??!%%?!%?!%%!%!%!%?%%%%?%!%%!%!!!!??!%%!%!?%!%%!!%!%%?!?%?%?!%%%?%!!%?%%??%%%%?%%%%%%%%?!!%!!%%!!?%%?%%!%%?!!?!!!%%!!!%%!%%?!%%?!%%?%%%%%%%%?%??%??!%!!!!%%%!!!%%%%!%%%!?%?!?%!!!?!!?%?%%!!%%%%!?!!!%!!%%%?%!!%%%?%%!!!!!%%%!%?%?%?!?!%!?!%%?%?%!??!%!?!%%%%!?!%%%?%%%!!!%?%%?!%!%!??!!!%%!%?%%%%%?%!%!?%!!??!!%%!%!?%?%?!!!%?%!%%!?!%?%!?!!!!%?%%%%?!!%?%!!%!%%?!%%%!%%%?%!!!?%%%?!%?%!%?%!%%??%!%!%%!?!!%?%%!?%!!%%!????%%%%%%%?%??%%!%%%?!!!%%%!??!%%?%%!!%%%%??!!%%%!%!!%!!%?%!%%%!!?%??%!!!%%%?!%?%%%!??%%!%!!!!!!%!%%%!%!!%%!!%%%%%%%%%!!%!%?%%!%%?%%%%%?%%!!!!!%%!%%%%%!!%!!!%%?!!!?!!!!%!!%!!%!%!%!!!%%%%%!!??%%%%!?!!%!%%%%!!!!%%!???%%%%%%%!%?!%%!%???!%%%?!%?%!%%%%%!%%!!??%!?!%?%%!!%%!%%%!%%!%%!!!!%??!%!!%!%%%!%%%%%%!%%%%!!%!!?!%?%!%!%%!%!!!%!%%!!%%%%%!%%!%%%!%%!%%%?%!%%!%!%!%%!?!%???!!%?!%%!!!%?%!%%!%!?%!%%!%%?!!%%!%%?!!!!%?%%%?%%%?%?%!?!%%%%%!!!?!%%?%!!%!%%%%%%%?!!!%?%!?%%%!%!%!!!%!%%%%!??!%%%!!%%!%!%%?!%%?!!!%!%?!!%%%!%!!!!?!!%%??!!%!%!%!!%%?%%%!%?!?%%%!?%?!%%%%?%%!%%%%%%!%%?%%%%!%%!%%%%!!!!%?%!%%!?%%%!%%!!%%!%!!%!!%%%%?%%%%!??%!!!!!!!!%%!%!?%%%%!?%!?!%?!!!%%!%?%?%?%%!!?!!%!?%%%?!!!%!??%!!?%%??%%%?%!%!?!?%%%!%%!%%%%!%!?!!!!!%%%%%%!?!!%%?%%%?!!%%?!%%?%%%%!!!!!!???!%?%!!%?!!?%!!!%%%?!?!!!??%%%!%%??%??!?%%!%!!%%%?%!?!!?%%?!!!%%%?%?%!%%%%?!%%?!?%%%%?%!!%!%%!!%?%!%!%%%%!%%%%?%!!??%%%!%??%%%?%!!!!%%!!%!?%!%!?%?%%%!%!!!!?!%?%?%!!!%%%%%%!%!%!?!%!!!?%!%!%!!?!%!%%!!%%!!%!!!!?%%!!!%%!%%!?%?%!!!%%!!%!?%!%!!!%%%!?%%!%??!?!%!?%%%%%??%%?%!%!%!%%%??!%%?%?%!%%!%?!!?%?%!%%!?%!%?%?!!%%%?!%!!!!?%%?%!!%!!%%!!%%!%!!%?%?%%%!?%!%?!!%%!%!%%%??!!%!%?%%!?%%!!!%%?%!!%%!!?%%%!%%%!???!%!!!%%%%%%!%?%!%!%!!!%%!%!%?!!%%?%!?%%?!%???!!!%!%?!!!%%!%%??%!%!%!!?!!%%!!!!%%!%?!?%!%?!!%?%!!?%?!!!!?%!!%!!%%?!%!%%!??!!%!%%%!%%%%%!!%%!!??!!?!%?!%%?!%!%?%%?%!!!!?!%?%?%%%%?!!%%%%%!%?%%!%!%?!!!%%%%!%%!%!%%?%%?!%!!!!!!%%%%%%!%???!?!%%%!!%!!%%%%!?!%!%!%%%%!?%?!!!?%%!!%%!%?%!%!?!!!%?!!!%?!?%%!%!!!%%%?%%%!?%%%%?!!%%!%%%%?!!%%!!%%%%!!?%?%%%%?%?!%?!%!?!%!%%!!??!%%%!!!%!%%!%!!??!%!%%!!%%!?%!%!?%??%%!!%%%!%!!%??%%!%%%%%!!%%?%%%!?%?%%%!!%!%!!%%%!%?%!??!%%!%!%!!%!!?%!%%!%!!!?%!%%%?%%%!!!%%%?%%?%%!!%!?!%?%%%!%?!!?%!!%%%!%!%?!%!%%%!%!?%!%!!!%!?%%%!!!%!!%%%!!%!?%%!!!!!?%%!???!%?%%!%?%%%?%?!!%%%%%!!!%!%%!%?%%%%!!%!%%%%%?!%%%%%!?%%?!%%!%%%%!%%??%%?%%!%?!!!!%%%?!%%%!!!%!%%%!%?!%!?!%?!%!%%%%?%%!%%?%?!%?!%%!%%!!!%%%%?%!%???%%%!?!?%%%!!%%!!%????%!%%!?%%%!!%!%!%?%%!%%%%!%%!!%!!!!!%!%%??%%??%!!?%%!%%%%%!!!?!%%%%%?!?%?%!%%%!!!?%%!%%!!%?!%%%%%?%%%!%%%?!?%%%?%%%!%?!%!!%%!!!%!!!%%%%%!%%!%%!??%!!!!?!?%?%%!%%?!!%??%!??%!?%%%%?%!?%!!%???%!!%%%%!%%%%%?!??%%%!??!%?%%?!%%?%!%???%%%%?!?!%!!%%!%!!%%!%!!%?%%%?%%?%%?!?%!!%!?%!%?%!!!?%%%!?%!%%%!%%!%!%%%??!%!%%%%!%!!%!%%!%!??%%%?%!!!!?%!?%%?!!%%!!!%!%??!??%%!!%%%!%!!%!%%!%%!!%%%%%??%?%%%%?%%!%%?%%!%!?%%%%?%!?!%?!%%%?%?%!%!?!?!!%?%%!%%!?!?%%%!!!?%?!!!%!%!!%%?%!!!!?!!%%!%??!%!%%!%!?%??!?%%?!%!??%!?%%%%%?%%?%%%%?%%!%!%%!%%%%!%%!%%!!!%%%%?!!!%%%?%!%!!%!!!%%%!!?!%%%%?!%%%!%%!%!!%%!?!%?!!!%%%!?!!!?!!%!%%!!!%?!!?!%!%!%%?!!%!!%?!%%%?%??%%!%%!%%?!!?!?%!?!!!%%%?%?%??%??%%!%%%??%!!?!?%%!%!!!!%?%!%!??%??%%!%!%!?%!!?!!%?!%%%!%%!%%%%?%!!??%%%%%%!%%%?%?%?%%!%?%%!%%%%%!!!?%%%!!!%!%%%!%?!%%!%%%!%!!!%?%!?%%?!%%%%!%%%??%%%%!?!%%?%!%?!?%??%!?!!%!?%%%?%%%%?%!%%!?!%%!???%!%%!%!%%!%!?%??%?!%%%!%%%!%!%!!%!!!!!%%%?%?%%!?%?%%%%%%%%%!?!!%%!%%%!??!??!%?!%?%!!??!%%!!!!%%%%!??%!!%%%%!!?%%!%!%!%?%%?!%!%?!%!%%?%%!%?!????!%%?!%!%%!!!!?%%%%!%!%%%??!?%%?!!%%!%!%%%%%%?!?%%%%?%?!?!??%?!!%?!!%?!!!%%%!!?!%!!!?%!%%%%%?%!%%!%!%%%?%!??!!?!!%%!!!%%??!%?%??%%??!%!%?%%!%!%!%%%%%!!%%!%?%?%!%!!!!?!?%%!%%!%!%!!%!!!%!!%%?!%%%%%!%!??!!%?%?%!%?!%!?%!?%!?%!!%!%%!%?!%!%%?%?!!!?!%!!%%!%%!!%!!%!%!%%%%%?!!!!%?!!%%%?!!?%%%!!%%!%%%?%!??%!?!%?%%!!!!?!?%%%!!%!%%%?!!!%%!!%%?!%?%!!?%%?!%!%?%!%!%%!!%%%?%%%%%%!%?%!%%%%!?%!?%%%%%?!?%?!%%!%%%%%%%%?!?!%!%!!%%!!?!%?!%??%%%%!%%?!!?%%?!!%!%!%!?%??%%?!!%%%??!%!%%%%%?%%%%%?%%!!%%?!!%?%?!!!%%%%?%!%!!%!%!!%!??%?!?%%%!%%!%!%?!??%!!%?%!!%!%%%%%!!!!?%!%!!!%%%%?%!!?%%%%?!!%%%%!%??!?%%?!%%%!%!!%%!%%%!??!?%???%%%%%!!%%%%!!%%%!%!!%%!!%!%%!?%?!%%%!%%%!%%??!!%%??!!%!%!%%%%!?%%%%!%%%!?%%%%%??%???!!!%%!%%!%!%!%%%!%%!%!?!%%?%!!%%!%%!%%!%!?!%!%!!%%!%?%?%!?%!??%%!%!%!!%%!%%!!%%%!!!%%%??%%%?%?%!%%%!%%!%%?%%%!%?%%!%%!%%!%?!%!%!%!%%!!%!%!?!%%%!%%%%!%??%?%?%!!!%!%%???!%!!!!?!?%!%!!!%%!%!?!!!?%!!%%!%!%!%%!!!%%%%?%!!%!%%%!??%%?%!?%%%%!?%%?%%!%%!!%!%%%%%!!%?%%%%!%%%!!%!%%!!!!%!!%%%!!%!%!!%!%%%!%%?%!?%%!?!%%?!!%!!!?!%!!%%!?%%!!%%%%!!!!%?%%%%%%!!!%%!!???%%%%!?!%?!%%!%%%!%%%%?!%%?%%!%?!%???!?%%?%!%%%?%!%!!%%%%!%?!!?!%?!%!%%!%%%%%%%?%!!%!%!%%??%?%%%%%!!!!???%??!%?!!!%??%!%%!!%?%%%%?%!!%?%!?%!!!!!?%%!%%%%%!%?%%%%%%!%?%%%!%%%?!%%%%!!?%%%%?!%?!!%!%%%%%%!%?%!!??%?!%%!?%%!!!?!?!?%%?%%?%%%?%%%?%!%!%?%???%%%!!%!%%%%%%!%%%!?!%%%%???!%?%?%%?!!%!!?!%!!%!!%%%%%%%%%!!!?%?%!?%%%%%%%!!%%!!%%%!%%?%%%!!!%??!?%%!%%%!!%%%??!%!%%!%?!%%%%%!!?!!!!!?%%?%%%%%%!%%?!%%%?!%%!%%%?!%!%?%%!?!%?%!%?!%!%!%!!%!!%!%?!%!%%%%%%?!%!!%%!!?%%??%%%!!%!??%%%%?%%?%%!%!%?!!!%!!?%%%%%!?!%?%?%%?%?%!!!??!%%%%!!!??!!??%%!!!%!??%%?%%%%%%!%!%!%!??%%!!!??!!!!%!!!!!%?%!?%?!%%!%%!%!%%!!!?%!?!%!%?%!%!!%%%%!%%!!%!%?!%?%!%!!%%%%%%%!?%!??%!%!%%?%%?%%!%!!%%!!%%?%!?%%!!?%??%%!%!%%??!%%!!%?!%%!!%?%%%!?!!%%%%%%!?%!!%%??%!%%%?%!!?%!%%!?%!%!!?!?!!%?%!!!%%%!?%%%?!?%!%%!?!!%%%?%%%%%%!!?!!!!%%%%%%?%%%%%%%!%?!%%%%%!%?!?%%?!%!%%!%!%?%%!%%%%%!!%%%!%!%%%!%%%%!!%!%%?%?%!%%!!!??!?%!!%%?%!!!%%%!%!%%%%%%!%!%%!%%!%%!!%?%%%???%?%!%%!%!!%%?!!%%%!%!%!?%%?!%??!!%%%%%!%?%?!?%?!?%%?%%?!%%?!%!!!%%!!%!%!%!?%!!%%?!%!%!?!%%%%%%%%!%%%%%%!?%%%?!%%%!%!!!%%!?!!?!?!%!!%!??!%?!%!%?!%%!%%!!!%%%?%%%!%%!?%%!%??!%!?%?%?%?%%!%%%?%%%%%%!?%%%%?!%%!!!?!%%??%!!%!%%!!%%!%??%!%%%!?%!%!%!%!!%%%!?%%%%!!%%!!%!%%?%%%%%?%?%!?!!?%!!?!!%%%?!?%%%?%!!?%!!!!!?%!!!!%!!%?%%!%!%%?%!?!!?%?!%%!%?!!%%%%%!%%%%!??!!%!%%?%!!%%%%%?%%!!!?%%?!%?%%?!?%!!%!%!?!%?!!!%!!!%%!!!!%%!!!%%!!!%%?!!!!%%!!?!%%?!%%?%%!!%%?%!%%%?%!??%%%!!?%!%%%%!%!%!%%%??%%!?%??!?%!!%!?!!%?!?%%!!?!?%!!!%!%!%%%?%%%%!???!%?!!!!%!!!!%!!!!!%%!!%!%%%?!?%??%!%?%%!%%%%!%!?!%%%%%%!%!!???!!%!!%!%%?!%%%%%!?!%%%%?%??!!?%!%!%!!?%?!?!!!!!%??%%!?%?%%!!%!%%%!%%%%?!!%!!%!%%%!%?!%!%!?!%%!?%%!%!!?%%%%!??%%!?%%%!!?!%!%%%%%%%!!?!%!!!!!!%%%%!!?%?!?%%%%!%%!!%%%%!%!%!!%!?!%%!%!!!%!%%%%%%%!?%%%%%?%?%?%!%%%??%%?%%%?!?!!!%%%!%%%%?!%!%!!?!!%!!%%?%%%!?%%%?%%!%%%%!!%!!%!?%%%%%?%!%!%%?%%%%%%!!%!?!!%%!%%?%%%%?%%!%???%%!!?!!%%!!%%!%!%%%!?%!%%!!%%%?%?%%!?%%!?!!%%!!!%!%!!!%%%%?%%!%%%%!!!!?%%!%!%!!%!!?!?%%!%%%%%?!%?%?%%%%%%!??%!%%!%!?%!%%!%?!?%%%!%!%%%?%!%%!%%%%%%%!%%%%%%%%?!?%!%%%%%%%?%!?%!?!?%!!%%%%%%!!!!!!%%?%?%!?%??!%%%?%%%!%%!!%%%%%??%%%?%%%%!%!!?!!?%!!!!!!!!!%%%%%%%%!%!??%%!?%%?!?%%%%%?!%!!%%!%%!%%%?%%!!!%?!!?%%%%!%%%?!!!%%!%%!!%%%%%!!%%%%%!!%%%%?!!!%!!%!%%!%!%!!!!%%!%!!%?%!%!?%%%%%%??!%?%?%%%%!%?!%!!?!?%%%!%%%?%%%%%!%%!!%%%%!%%?!!%%?%%!?!%%!%%!%%?%!%%?%%%%%%?%?!%%!%?!!???%!?!%?!%%%??!%%!%!%!?%%%!!%%?%!!?!??!%!!%!??%?!!%%%%??%!%?%?%?!%!%%?%%%!!%!%%%!??%%??%?!%%!%!%?!!!%!?!%%!?%?!%%!?!??!!%%%!?!!?%%?!%!%%!!?%%!!%!%%%!?%!!%?%%%!!%?%%!%%!%!%?!?%!%%!?!%!!!%!!?%%%%%!%%%??!%!!?%%!%!??%%!%!%%!?%!%!!!%!!%%%%%%?%!%%%?!%%!%!%?!%%%%!!%%!%!%%!?%!%%!?%%%%!!!!%!?%??!?%%!??!!%!!%!%??%%!%!?%?%!???%!!!%%!!%%!!!%!??%%!%%?!!!%!%!?%!???%?%?%!%%%%%!?%!%%!!%%???!%%!!?%%!%!%!!%?!%!!?%!%!%%%%%!%!%!%%!??!!!!%?!?%!%%!%!?%%%%!%?%%%?!?!%%%%!%%!%%%%!%%%%%!!%!%%??%%%?!%!!?%!!!?!%%?%?!%!%!?!%!?%!%%?%!%!!%%%!%%%%%?!%!!???!!%%!%%!%%!!!%!!??!%!!%%!!%%!%!%%!!%!!%!%%%%?%??%%!!%!?!?!%!%%%!%!%?!!!%!%!?%?%%?!!!?!%%!%!%%?%?%%%%!%%!!%%!%!%?!!!!%!!%!%?%%%%?%!?!%%%%!%%%%!%%%?%%%!%%!%%!?!!!%%?!%%%%%!?%%!!?%%%%%%%%!!%%%!!?!%?%%%!%!%%!!%?%!?!%!%%!%%%!!%%?!%!%%%!%!!!!?!!%?%!%?%%?%!%!!%%??!%?%%%%%?%!%!!%!!?!?%!%!!%%%%%!%%?%%%?%!!!!%%?%%!!!%!!!!%%!%!!%?!%!!%%!%!!%?!!%%??%%!%?!?%%%!%!%?%%%%!%%%?%%%%!%!!%!??%%%%!??%%!!%?!!%!??%?%%%!%%!%?%?!!%%!!?%%%?%??%!%!%!!!%%%%%!%!%!%%!!%%%%%%!%%?%?!%!%%??!?%%%?%%!!!%%?!?%!%%!!%%?!%%%!%!%?!%!%??%%%!!%%!!%?%?%%%%?!%%?%!!!%%!?%?!%?%?!??%?!?%%%%%!%?!!?!%!!!!%%!%!?%%!%%!%!%?!!%%%!%%!!!%%!%!?%?!%%%?!%!%!%!%%!%!%!?!%%?!!%%!%%%%!%??!!%?%%?!%!!??!%!%%!%!!!%%?%%!!!!?%!%%%%%%%!!%%%%%!%%!%%!!%?%%%!%?%%!!??%!%!%%!?%%?!%!?!!%%%%!!?%%?!%%?%??%!!?!%!%?%%%?!!!!%?%!!!%!%%!!%%%?%!%!!!%!%!%??!%!%?%?%!%%?%!%%%%?%%??!?%%??!?!?%!%!!!?%?%!%%%%!?%!!?%%%%%!%!%?%!%%%%%%!%!!??%%!!%??%?%%%?!%?%!!?%?%!%%!!%%?%%!!%!%!%!%!!%?%%%%?!%%%?%!??%%%%?%!%%!?!%%%%%!%!%!%!%!%?!%!%?%!%%%%!!?%%!%!!?!!%?!%!%??!!!!!%!%?%!?%?!%?!!!%%%%%!!?%%%%!?%?!!?%%%%%%%!!%!%%?%%!%?!!??%%%%%%?%??%!?!%!!%%%%%!%%?%%%%??%!%%?!%%!%%!!!%!?!?!?%!!%%%%%!%%!%!!%?%!%%%!!?%%%!?%%!?%%?%!%?%%??!%%!!?%%%!?!%%?!%%%?!!!!!%%%%%%!%!%!%%%%%%%!%!?%!?%%%%%%%%!!!!%!%%%%!!?!!?%%!%!!%!!!%%%?!%?%%%?%%!%%%!%%%?%%%?%%?%%%%%!!!%%?%%%%!%%%??!%%%%?%%!?%%%%?%%!%?!%?!%?%!%?%!?!%!%%!?%%%%!%!!%%!!!?!!!!%%%%!%%!%!!%%!%%!?%%!?%?%?%%!!%!?!?%%!!%?!!%%%%%!%%%%!%?%?!%%%%?%!!%!%!%?%?!%%!!%%!%%%%!!!!%%%%!%!!%%%%%%!!??%%%%?!%!!%!%!!!%?!%!%%%%?%%%%%?!!?!%!%%%?%%%!%!%!!!?%!!%%!%!?%%%%!!%!%?%%%!!%%!!%!%%?!%!?%%%!%%%!?%!%?!!?!%?%?%!!%%%%%?%%!%!%!?!!!%!%%%?!%%!%%%%!%!!?%%%!!??!!%!%!?!%%%%!??%!%?%%%%!%?%%%%%!%!%%%%!!?%!%!%?!!?!!%%!!%!!%%?%!%!%?%%?%%%?%%%!%?!!!?!%?!%!!%??%!!%?!!%!%!!%!%??!%%?!%??%?%%%%?!%%!?!!!%%!%%%%?%%?%%?!!?!!?%%%?%%?%%%!!?%%!%%%%!?!?!!%%!?%%?!%%!!%!!%%!?!%!%!%!%!%?!%?!%!?!?!?%!%?%!%?%%%!%%!!!!!%?%?%?!%!!%%?%%?!!!?%%%!%%%%%%%?%!%%%!%%%!%!%!%%%%%?%!??%%%?!!%%%!%!%!?%?%!!%%?!!%!!?!!%%%%!%%!?%%?%!%!%%?%%%!%%!%%?!%?%!!%%%%%??!%!!%?%%!%%!!!%%?%?%?!!%!!!%!?!%%?%%%%!%%!!%?!%%!?!%!%!%%%!%%%?!!%%?!!?%!%%%%!%%!!!%%?%!?!?%%!%?%!%?%%?!%%%%!!??!%%!%?%%??!%%%!!%!!%%!%%%!!%!%%%!!!!!!%?!!!%?%%?%!%%%%!%!%!%%%!!%%%%!?%!%%%%%?%%?%?!!?%?!!!!%%!!%??!%!!%%?!?%!?%%!??%%%%%!%%%%%%?!%!%?%??!%%%!%?%?%%!%%!!%?!%%!%%?!!%!?!!!%%!%%%!??!%%%!?%!!!?!%!%%??%?%%%!%%??!%%!%!!%?%%!?%?%!%?!!%!!%!%!%%%??%?%!%%%%!%%%%!%!?%%!!%!%?%%%!?%%%!!%!!!%!!!!%?%%?!!%!%%!!%?!%??!!%???%%!!%!!%!%%?%?%%%!%!?%%%!%!!!!%%%?%!%%%!!?!?%%!%?%%!%%%%!?%!%%!!?!%%%?%%%%%%%!%!??%!%?%!%!%!%%!%!%%%!%%%?%??!%!?!%!%%?%!!%%%!%%!%%%?%!%!%%?%%!?%!%%!%!!%%%%!%!%!%!!?%%%!!%%??%%%%??!%!??%%!!?%!%?%!%%%%!%%?!?%?!%?%?%%!%%!%!!%!%!??%%%%!%%!?!!!%%%!?%%??%??!%%!!?%!?!?!%%!%%!!%!!!%%!%?%!%%%%%!%!%!%%%%!!%!!%?%!%%!%%%!?!%!%?!!!%%!%%%%!!%?%!%!%%?%!%%??!%%!!%%!!%?!!%%%!!%!%??%%%%!!?!?!???%%??%%%%!%%%!!!!%!%!%!!%!?!%%%%%!%!%%%%!%%%!!%!!%%?%%%??!%%%%%!!!%%!%%%%%!!%!!?!%!!??!%?!!?%%%!?!%%%%!!%%!!%!%?!%%!%??%%%%%%!?%!!?!%!!%!?!%%%%!%%!!%!%%?%%!!?%?%%!?%%%%%!?%?!!%!!!%%%%!!%%%?%%!?%!?%%!%%!?!%%%%?%!?%!%!%!%%!%!!?%%%!%!%%?!%!!!%%!!%?%?%?%?%%%!%!%%%!%%%%%%%?%!?%!!!%!!%%%?%%%%!!%%%%!%?!%%??%!?!%?!%!!?%!!%%!%%%!%%!%?%%!%??%%%?!%!!%%%?%%%%%%%!%!!%%%%%?!!%%!!!%%!%!%%!!?!%%%!%??!%!!!%!!%%!%?%%%%%!?!%!!?%%%%%?%%%!%!?!%%?%%%?!%!%%!%%%?!!!%!!%%%!?!!%!!!%?%!!%??%!!%!%%?%?!%%%%%%%%!%%?!!%!?%%!!???%%%%!?%%%%%%%!!%!%%?!%%?%%!%%%%!%%?%!%!!!?!!!!%?!%%%?%?!%!!!!!!!%%!%%%%%!!%%!???%!!!?!!%%%%%%?%%!!?!!!!%%%%%%%%!%%%?!%%%!?!%%%%%!?!%%!%%%!%%!!%!!%%%%?%!!?%!%%!%%!%!?!?%%!!%?%%!%%!%%%%!?!%%%!???!%?%!???%!%%%%%!?%%%%%%!?!%!%!%%%!%!!!%%!?%!!!!%%%!%!?%!%!?!!%%%%!!?%?%%!%%!%!!%%%!??%%%??%%?%!%%!?%%%%%%%%%?%%%%%!?%?!%!!%!%%%%%%!%%%!!?!!%!!??!?%!?!?!%%%%!!?!!??%?%%!?%!!%%%?%!%%!!!?!%!!!!%%%?!%!!!?!!?%%%!!!%!?%!%!%%%!%??!%%!%!!?%%%%%!%%%!?%%%%%%?%%%!%%%!%%!%%?%%!%?!?%%?!%!%!!%%%!%%%%%!%%%%%!%!!!%%%%!%??%%!?!%!%%%!!!!!%%%%%%%!?!!%%??%%!%%%?%%%?%!?!%%%!%!?%%%!%%%%!%!%%%!!%?%%%!!%!%%%!%!!%%%%!!!!%%%!!%%%%%%%!%!%?%!%%%!%?%%%!%?%?%%%!%%%%%%%%%%?%!%?%%%!!?%!%%%?!!!%!%?%%!!%%%%!?%%%%!%%%%%%%%%%!%%%!%!!???%!%%%!%%!%!!%!%!%%%?!!%?!%%%!%!%???!%%??!!!!?%%%%?%%%!?!%%!?!!%!%!%%%?%%%%%!!????%%%%%%%!?%%%%!%%%!!%%?%!?%?!%%%!%%?!%%!%!!%%%!%%!!!?!?%%!?%%!?%?%??%!%%%%!!!%%%??%%%!%!!%!!?%%%?%%!%!?%?%%%?%??%%!%!%!!%%%%!??!%?%!%%!%!%%??%?%%???!?!%?!%!%?!%!!%%%!!%%%?%%%%!!%%%!%%%%%!?%!%?!!%%?!%!%%%%%%!%%!!?%?!?!?%!!%?%?!!%%?%%!?%!%%?%!!?%%!%!?!!!%%%!%%%%!%%%%!!%!!!!%!%%%?%?%?!!!%!%%%!?!%!%!%!!%!?!?%%?!!?!%!!!??!%!?!?%!%!!?%!%!?%%?%!%!%?%?%%%?!?!?%!%%!%%%%!!?%?%%?!%%!??%!!?%%%%%?%%%%!%!%!?%%?%%?%!!%%%%%%!%!%%!%%%!%%%!!%?!!%%!???!%%%?!!?%!?!%!!!!!?%!%%%!%%%%%%%!!?%!!!!%%%%%%??%!%!?%%?!!!!%%!%%!?%!%!!?%%????!%!!!?!%!?%?%%%?!?%!%!???%%%!??!%?!%%%!%!!!!%%??%?%%?!%%!%?!!%%%%!!!!%?%!!!!%!%!!!!??%?%%%%%%%%%%!%?!?%!!!!%%!?%!?!!%!%!%!%!!%!?!!?%%?%%%%!%?!??!%%%!!%?!%??!?%%?!!%%!!%!!!!!!?!?!%%%%%?%%%%!???%!!!?%!!%?%?!%%%?%%!?!!!!%!?!?%!!%%%!%?!!%%%!?%%%!%%%%%%%%%!?!%!%%%!?%%%!%???%%%!%!!%?%%%%??%%?!!%!%%%!%!?%!%%!!%%!?!!!%!%%!?%!%!%!!!%%?%%%??%!!?%%%%?!?%!%%!?!!!%!!%%!?%??%!%%%%!!%!!!??%?%!%!!%%!%%!%!!!?%%!??%!%%!%%!!%%%!%?!!%?!%!!!%!?!!%?%%!%%!%%!?!?%!!%%%%%%%?%%%%!%%?%%!?%!%!%%%%?%%%!?!??!%!?%%!!!!%%!%??%%%%%%%%%?!%%%%%!!?%%??!%%!!%!%?%!%!%%?%!!%!!!!%%?!!?%%%!?%!!%!!!%%%!!!%!%?%!%!!!%%%%%?%%%!%!!!%!!%!?!!!!?%%%?!!%!?%%%%%%%%%%%%%%!!!%!!!?!!%!?%!?%!!%!%%%%%%%?%!%%!%%%!!?%%%?!!%%!%?!?!%??%%!%%%%%%%%%?%!?%%!!!%%%!!?%?%%?!!%%%%?%?%?%%%!!%!!%?!%%%%!%?!!%%%!?%%!%!%%?%!%!%%?%!!%%%%!%%%%%?%!!%?%!!????%!%!%?!%!?%!%!!%%%?!%%?!!%%?%?%!%%!%?!%%%!%!%%!%%!?!?!!%%%%%!%%?%!?!?!!%%%%%%?%!%%%?%!%%???!!%??!%%%%!?%?%%%?%%!?%%!!??%!%?!!%%%!!%!%??%!!?%!!!%%%?!%!%%%%%!!!!!!!!%%!%!!%?!%%%!%!!%??!%!%%?%!??!%!?!?!%??%%%?!!!?%!??%%%%%%%%?%%!!?%!?%??%?%%%!!!%%?!%!%%!!%!?%!%??%%%!!%%!%!%%?%!!?%%%?%%?%%%%%%%!!%%!%!!%%%!!%%!%%?%%%%%!%%!%?%?!!!%!?%?%%!%%?!!!%!%!%!!!%%?!%%%!!??%!%?!??%%%!?%%!%?%??!%!%!!!%%%%%?!!%%??!%!%%%%?!%%%!%%!%!?!%?%?!!%!%?%?!!?!%%!!!!%!%%%!%??!%%%%%%!%%!!?%!%?!!!%%!%!%?!%%??!%%!!!%!%!%?!!%!!%%?%%%?%!%!?%!?!!!!?!%?!?%!?%?%%%%%!%!%!%%%%?%%!!%!%!%!?%?!%!%?!%?!!%%%!%!!%?%!!!%%%%!!%!%%!%%%%%%!?!!%%%%%%!%%%%%?!%%%%%?%!%??!%!%%!%%%!!%%?%%%%!%?!%%!%%!!!%%%%%????!%%!!%!!%?%!?%%?%!%%%%!%?!%!%!?%%%%%%!%!%%%!%%%!!!%%?%%!%%%!?%!%!???!%!%%!%%?%%%%!!?%!!%%!!!%?!%%?!%!%%%%?!%!?%!%!%%%%!!?!%???!%%??!!!!?%!!%!%!%!%!!!!!!%%%!%%%%%%%%!!%!?%%%??%%!%?%%%!?%!!%%%%!%%?%!?%%!!!%!%%!%%%%!?!%?%%!!%!%?%%?%%?%???%?!!?!%%%%?%%%!!%!!?%!%%?%!!%%%%!%%%%!?%%%!?%?%!?!?!%%%%%%%!%%!!%?%%!%%%%%%%!%%%%!%%%!%%!!%%!%!%%%?!!?%%!!%?%%%%?%!%%!%%%!!!?%!?%%%!%!!?!%!%%?!?!%%%!%%!%%%%%%??%%!%%?!%?%?!?%?%!%?%%%!!?%%?%?!!%%?!%%!%%%!%%%%%!!!%%%%%%%%!!%??%!!!?%!?%%%!!%%%?%%%!%%!%!%!%?%!!%%%?%%%%!?%%?!!%%!%?!!%?%%!%%%%!%?%?!!%!%%?%!??%!%?%%?!%%%%!?!!%%%?%!!%%!!?%??!%!%!%%!%%%!!%!%????%%%%%!%!!%%%!%%%%%%%%!!%??%!?%!%!%%!?%?!%??!?%!?%%%?!!%!????!!!%%!!!%!%%%%!%!%%!!%%!%%%%%%%%%?!%%!!%!%?%%!%%?%%%%%!%!%!%!%%!%!%%%%!?%%%??!%!!?!?%%%!%?!%%%??!%?!!?!%!!%%!%%!??%!!!%%!!!!%!?%%%!!%%%%%%%%!?%?%%%?%%!%%%%%%!%!!%?!!!!?%!!%!???%?%%!%%!!%!%!?%%%%?%?!%!?%%%%%%?!!%%%?%!%%??%!%%!%!%%%%!?%%%%%?%%%!%!!%??!%%!!%%%%%??!!?%??!%%!%!%!%?%%!!%%%!%?%!!!%%!!%%!?%!?%!%!%%!%!??%%?%%%!??%%%!%%%%%%%!!?%%%%!!!!?%%?%%%%%?%%%%?!!%?!%%?!!!!%%%!?%!%%!%%?%!%%?!%%!!!!!%!!!!!?%%%?%!%%%%%?!%!%?%!!!!%!%!!%?%?!%?!!%!%%??!!%%!%%!?%??%!?!%%!%!!!%?!%?!%%!%?%!!%!%%!%!!?%?%%%!%%?%!%%%!!%%%!?%!%%!%!%!%%?!%??!%%%!%?%%%%!!%?%%!%!!%%?%?%%%%%!!%!%?!%!%%%%%%%!!?%?!!%%%?%%%%%%!%??%%!%%!%%!?%%%!%!%!%?!!%%!%%!!!%%!?%%%!%%?%!?!?%%!!!!%%!!!%%%%%!%!!!!%!%%?%!%!!%!%?!%!!!%!?!%%%??!?%!%!?%%%%???%%?%!!?!%%?%!!!%!!??!%?%?%%%%!!%%?%%%%!%%%!%!!%%%%!%?%%%%%!%%%?%!??%%%%!?%!!!!%!%%%%??%???!%%%%!%%!%%!%!!%?%%%%!%!!?!%?!%!%!!%!!!%%!???%%?!%?%?%%!%!%%?%%%?%!%%%?!%%%!%%!%?%%??%?%!%?%!%%%??!%?!!?%%%!%%??%%?!%!%%!!%?%???%%!!%!!!!%%!%%!%?!!%?%%?%%!%%%%!!!%%!!%!!%%%%%%?!%?%!%!%?!?!%%%!!%?%%?!!!?!!%%%!!?!?!!!%%!%?%%%%?!%%!%!?!?%%!!????%?%%!%%??%!??%!%%%!%?%!%?%!%?%%%%%!%!%%%%!%!?%%%?%%!??!!%!!!%?%!%?!%%!%%%!?%?!%%%!%!!!?%!%%%%%?%??%?%%%?%!%?%!%%%!%%!!?%%%!!%!%%!!%%%?!%?!%!%!?%??%%%%!!?%%%%%%%%?!!%%%!!?%%%!%??!%%%??%%!%?%?!?!!%%?%%%!??%?%%%!%%?!%%%%?!!!?%%%!%?!%%!%%%%%%%%!!?!%%%?%%%?%!%%!!%%!%%!!%%%!%%%%%?%?%!?!!%%!!%%!?%!%%!!!%%%!!%%!%!%%%%%!?!!?%%%%%!!!!!%%?%%?!!%%%%!%%%%%!%%?%!%%!??%?!%!!%!%%%%?%?%%!%?!!?%%%?!%!%?!%%%%%%!!!!%%%%%%%!%!!%??%?!!!%!%!??!!%%!%%!!!%?%%?!!%%%%!%%%?!%?!%?!!?%%%?%%!%!%%?%!%!?%%%!%?!%%?%!!%%%%%!%%!%?!?!?!!!!%%%!%%%!!%%!%%?!%%?!%??%%%%%?%?%%%??!%%!%!!%?%!%?!%%%%%%%!!?%!%%!%%%%%!%%?!%%%%%%!!??%!%!%%!%%!!%%%!?!!?%%%?!%%?!%!!!%%%!%%%%%%%%??%!%%%%!%!%!%!%!!!%%%%!?!%%!!!!%!?%%%%%!!%%!%%%?%!%?!%!!?%!?!%%!%!!%%%%!!%%%%!%%%?!%%!!!!%%!??%!%%?%%!?!!%!%%%!!!!%!%%!!%!%%!?!?%!%?!!%?%%%%%%%?%%%%%%%%!!!?!%!!%%!!!!!!!?%!%%%?%%?!?%%!!%!!%%!%?%%?%?!!%%?%?!!%%?%!!%!!%?!?!%%%?!%?%!%!%%!%%%?!!?%?%%%!%!!!!%%%%!%%?!%?!%??%!!%%%%%%!%?%!!%!?%!%%!%!?%!?!?%%%%!!?%%!%%%%%?!!%%%%%!!!!!%?%????!!%!!%!?!%!%?!%?%?%%!?%%!%%?%%%%%%?%!%%%??%%?%!%!%!?!%%!!%%%%%%?!!%%!!%?%??!!!!?%?!?!!%!%!!%%!%%???!%!%%?%%!%%!!!!%%?!%%!!%%?%?!%!%%!!%%!%???!?%!!%?%!!%!%!?!!!!%?%!%?%%!!%!%!%%?%%!!?!%%!?!!!%?%%!%%!!%%!%!%%!!!%!%%??!!???!?!%%!!%??%!%%%?%%%?!%%!%%%%!!%%!%!%%%!%!%%%?!?!%!!%%%!%%?%%%!!!!%?%!%?!!?%%%%?%%!?%%?!%%%%!%!?!!%%!!%?%!%%?!%!%%%?%??!%!!!%!%?%!%!?%%%??%!!!%!?!%%!?!%%!%%!%!!?!%%%?%!%%%!%!%!%%?%!!!!%!%%%!%!%!?!!!%%!!%%!!!!!%%%!%!%!!%%?!!%%%%!%!?!!%%%!?!%%!%%%!%%%!%!?%!!%!!%!%%%%%!%%!%%?%%%!%?%%?%!%%!!!!!!%%%!%?!!!?%%!!%%!!?%%%%%!!%%!!%%!%%%??%%?!%%!!%?%!%?!?%%?!!!%%!%!?%%%!?!?%%%%%!?%!?!%!%!!%%%%%%?!%!%!%!%!%%%%?%!%??%%%%%!!!!%%?%%!%%%!%%?%!%%!%%!%?%%%%!!%?%!%%!%%!!?%!%!!%%%!%!?%%%!!%%%!?%!%!!?!!%%!!%%??!%%?%%?%%!!?!!%%!?%?!!%%!%!!!!%%%?%?%?!%?!!%????%%%%?!??%!!%%%!?%%%!%!%%!%%???%?!?%%?!?%%!%%%!%??!!!!%%%!?!!?!%%%!!!?%?%!!%!%%!!!!!?%%!!%%%!%?!?!%?!%?!!%?!?!!?%?!!!?!!%%%!!%!?%!%!%!?%%?%%%?!%%?%%?!%%!%%%?!??!%?%!%!%?!%?%%%!%?!%!!%%%%!%%!?%%!%!!%!!!?%??%%%%%%%%?!%?!!%!?%%%%?!?%?!!%%!%?!%?!!%!!!?!%%%%??!!?!%%%!%!!?%%%!!%%%?!!%%%!?%?%%?%%?%!%%!%%!%!?!!!!!!%!?%%??!%%%?%%!??%!%%%!%%%!%%!!!%%%%%?%%?!?!!%%!%??!%!%%%!%%%!%%%%%?!%!%%%%?!%!?%%%%%%%!%!!!%%%!????!%%!!%%%%!?%%!%!%!%!!!?%?%!%%!!!!%%%%!%?%!!!%!?!!!%%!%??%?!%?%!%%%%%!%%%%?%?!%!%!!!%!%!%%?!?%!%!%%%!%%%!!%!?%?%%??!%%%!!!%%%%%?%!%!?%%%%!!?%%!%%%?%%!%!%!!%%!%%%!%?!%!!%???!!%!%!!%!%%%%%?%!!%!%%?%!%?!%%%!%%??%%%%!!!%!%%%!!?%!!!???%!%!%%!%%!!!%!%!%?!%%%%!!!%!?%%%!?!!!%!%!%%%?!%%%!?%%!?!%!%?%!!?%%!%!!%!%%%!%!%?%%!%!%!%%!?%?%?!!?%%!??!%%!!?%!!%%%?!%?!%%?!%%??%??!%%?!%%!%%!!!%!%!%!%?%%!%?%!?%%%%?!??%!!%?%%%?%%???%!!!%!!%?!%%%%%!!?%%%!!!!?%!%!!!%!!!%%%!%%!!!%%%!!!%%%%%%?%!%%%%?!%%!?!%%%!%?%!!%!!!!!?!!%%?%??!!%!%%%!%?%?!%%?!%!?!!%!%!?%%???%%%!?!!%%!%%!%?!%?%?%%%?%%%!%?!??%?%!???%!!%%!?!%?%%%?%%%!!!!?%!!!%!%%%!%%%!%%!%%%?!?%?!%%%!%?%%?!?%%?!!%%?%!%%%??%!??%!!%%!!!?%%!!%!!?%%%!%%?%!%%?%%?%!?%%?!!!?!%%%!%?!!%!%!%%!%!!%!%!?!%%%%%!%%!?%!%%!%%%?!!!%?!??%?%%!%!??%!??%%!%%?%%!?!%%%!%!%%!%???%%?%%?!%%!!%%%%??%%?%%%!%!%%!!!%!!%?!%?!!!%%!?%????%%%%?!%%!%!!?!!%%%?!!!%%%!!!!?%%%%!%%%?!!!!%?!%%!!%%!!%%!!%%%%%%!?!?!%%?!!!!!???!!!%%%?!%%%?%?%!%?!%!%%?%%%%%%%%%!!??%!%%%%!!!?%%!%%?%%%?%!%!%%%!%?!%%!!!%%%%!?!??!%%??!?%%%%?%!%%%%%%?!%%!!!?!%!!%?%!!!%%%%!!!%%%!!?!%!%!!!?%%%?%%%%!%%?%%!?%%%!!%?%?%!!%!%%!?%?%!%%!!%%!%%%?!%%!?%?%!!%%%%%%%?%%%%%%%!%%%?!!%%?!%%%!%%%?%?!%%!%!%!!?%!%%%%?!%?!!%%%%%!!%!%%%?!!%!%!%%!!!!%!%?%!%%%%%%!%??%%!!%?%%!%%%?%%%%!??!?%!!?%%%%%!!!!!%%!??!%%!%!%%!!!!%???%!???%%!%!?!%?%%!!?!!%!%%%%!?%!!!%%%%!!%%%%!%!!!?%!??%!%!?!%%%%%%%!?!?!!%%%%!!%?!%%%?%%!%%!%!!?%%!%%%%%%?%%?%!!?%!%?%%!?!!??%!?%%!%%!%%!!!%!%%?%?!%!?%%%?!%%!?%%%?%%%%%%%%%%%!%??%%%!!!%%?!!%%%%!!?!%!!%!%!%!%!%%!%?!%%!?%%%?%!%%%!!%?%%!!!%!%%%?%?!!%%!%!%?!!%%%!?%%%!!!%%!%??%%%%!!%%%%!!%%%!!!!!%%%%%!%%%!%!%%%%%!%!!%%!%!!?%?!!%!!!??%!%%!%%!%%%!%%%%?!!%%%?!?%%!%%?!%!%!??%!%!%!%?%%%!%!%!%!%!?!!?%%?%!%?%%%%?%%%%%%!!!!%??%%!%!?%!%%%%?!!%%!%%%!??!?%!%!!!??!%%%%%%%!!!%!%%!%%!%!%%!!!!?%!!??!?%!!%?%?%!?!?!?%%%?!!%%!%!%!%%%??!!!?%!!!!!?%?!%%%%%!%%!!%!%?!?%%%%%!???!%?!%!%%!%%?%!!?%%%%%%?!%%%%%%%?!?%%???%%?!%%?!!!%%%%!??%%%?!%%%%?!%!%%!%?%%!?%?%%?%%%%%%%?%!%?%%%%%!%!%?%!%%??%!%!!!?%!%%%!%?%!!%%%?%%%%%??!%?%!%%?!%%!%?%!!%!%!%%!%?!%%%??%%!%?%%!%%%?%??%!!!!!%!!!%%%%!?%%!!%!%%%%%%%!%!%!!%?%?!!%?!%!?%%%?%%%!!!?!%%%!!%%!!!!%!!!!%!!!?%%!%!!%%!!%%%%!%?%!!%?!!%%??%?!%%?!%%%!%%!!!%!%?!?!%%%%%%%!!%??%?%%%%?%!?%!?%%!!!%%%%%%!?!%!!%%%%%%?!?%%?%%%!!%%?%?%%?%%%!%%?!??%%%??!!%%%%%??%%%%?!%%!!%%%??%%%?%%%%!!!!!%%!%%?!%%!!%?%!!!%%!%??%%%!?%%%??%!!!%!%?%!!?!!!%?%!%?!%!!%%%%%%%!!!%!%??%%!%!%?%?!%%%!%?%!?!%%%%?%%%%%!%%!!?%%!!%%%!%%!!%!%%%%!%?%?!!%!?%????!%%!!%%%!???%%%?!%?!%?%?!%%%%!%?!%?%%???%%!%%%!%??!%%!%?!?!%%%%??!%!%?%%%%%!!????!!!%!?%%%!%!?%?%!?!?!!?!?!%?!???%%!!!!!%?%%%%!!%!?%%%%!!%%%%?!??%%%%!?%%%?%%!!!!!%%%%%!%%?!%!!!%??%?!%%!?%!%!%%%?!?%!%%%?%%%!!!!%!!!%%%%%%%%%!%!!%%?%%!%%%%%!%?%?!!%!!%!!?!??!!%!!???!%%?!!%!!!%!%!%%%%!!?!!!%%%%%!!%%%!%%?!!!%%%?!??%%%%%%%%%?%%?%??!%%%!%%%%?!!!%?!!!%!%!%!%%!%%%%!!!?!!?%!%!!!%?%%!!??!!%?!!%%???%?%%%%%%??%!!!!%%!%!%%!?%%%!%%%!!%%%%!%%%%!%?!!!%?%?%!!!%%%%%%!%!?%%%%%?%?!!%%!??!!?%%!%!%?!%%!%!%!?%%%?%%!!%%%%%??!!%!!!%%%?%??%!%%!%!%%!!!?%?%%!?%%!%!?!%%%!%%!%?!!%!!%%?%%%!%%%??!!!%!!%%%!%%!%!%!!!!!!!%!!%!%%%%%!%%!!?!!%%!%%?!%!%%%%%!!%??%%!%!%%?!%!%!!%!%!?!%!?%!%%%%!%%%%%!%?!%%%!!!%%!?%?%%?%!%%%!%%???%%%?%!!%!!%?!!%!!?!%%!!%%%?!%!%!!!?%??!?%?%?%?!%?!%%!%%%!!!!%%%!%!%?%!%!%?%%%%%%%%!%%%%?!%%!%%?!%!?%?%%!!!?%?!!!!?%?!?%!!!%%!?%%!?%!!?%?!%%%%!%?!!%%!%%%?%?%!?!%!%%!%?%%?!%?%%%%?%%!%%%%??%%!!%%!%!?!%%!%!%!?%%?%!%%%?!!!!!%!!%!%?%%%!%%!%?!%%%!%?%%%%!%%%!?%!!%!%%!%%?%!%%!%?%!!%%!!%!!!%%!?!%%%!!!%%%!%%!!%%%!!?%!!!!!%%%!!!%%%!%!%?!%!%!!?%!%%%!%%!%!!%%!%!!%!%%%?!!!!%!?!%!%%%!%%%!%%%?%!!?!!!?!!%%%%!%%%%%!?!!!%!%%%?%!!%!%!!%!!%%!%%%%%%!!%?%!%%???%%%!!!%?%%!!!%!?%%!%%%%!%!!!!%%%%?!!!%?%%%%%??%%%!%%%%%%?%%%%%!%%!%%?%!%?!!?%%%%!%%!?!%%!!???%%?%%%%!?!!%%?%%%!!%%?%%!!???%!?%!!%!%%%!!!!%%?%!!?%%%%%%!!%%!%!!!%?%%?%%?!%!%!%?%!?!%%%!%%?%%%!??%?!%%?%%??!!?!!%!?%%?!!%%!%!?!!!!!%!?!%%%!%!!??!%%%!!!?%%?%%%!%%%!??%!???%%%?%?%%!%%!%!%?%!!!??!%%?!!!%%%%!%?%%%?%!%!!!%%%%?!!!!%%%%!!?%%!%%%!?%!%?%%%!?%!%!!!!%%%%%!?%%%!%%!!?%%%!!%!%%%%!!!?%%?%?%?%%!?%?%!!%!?%%%%%%%%%?%!?%?!%!??!%?%?%%??!??%!%%%%%%!!%?!%%%!?!%!%%!!%!%%?!%%!?!%%%!!%%?%!%%%%%%!%?%%%%%%%%%%%!?%%%!%!%%%?%???%%!%!?!%!%%%?%%!%%!%?%!!?%?!%!%?%%??%%!%%!%%%%?%%!%?%%!!%?%!%?%%%?%%%%!!%%!%!%%!!?%!%!!%%!?%%%!%?!%?%!?%!%%%%?!?!!!!!%%%?!?!%!%!?!%%%%!%%%?%!%!%%%%???%%%%!!?%!!!%%%%!!%?%!%?!%%!?%!%!!?!!?!!%%%?%!!%!?!%%%???%!%!?%!%%%%%%!!%?%%%?%?%!!%?!%%%%%?!%%%%%%%!!?!%%!%!%%?%!!!??!!?!?!!%!%!%!!%%!!?!!%!!!!%!!%%%%!%%%?%%%!!?!%!%%%%!%%%%%%!!?%%%!!!%%?!%%%%%%!!!?%!!!%%?!!!?!?%!%!?%%%%%%!!?%%%%!%!!!%!!?!!!%%!!!%%%%?%%%!%%!!?%?%%%!!?%!!?%%%%!!%?!%?!%!!!??%!!!!!!%?%%!%!?!%%!%%%!?%?%!?%%!!%%!?!!!?!%!!%%!%?%!%!%%%!!%?!%?%?!?%%%!%%!!%!!%!?%!%%%%!%%!?%%?%%%%!%?!%!%!!%!%!!%%%%%?%%%%%%!!!%!%%!!!!%?%?%%!%%!???%%!%%!?%!%!%!!%!?!%!%%!???!!?!%!!%%!%!%?!!?%%%%?%%%!%!%!?!%%!%!%!%?%%%%%%%%?%?!%%%%!%%%!%!?!!!!??%%%%!%?%!?%%%%!!!!??!%%?!%%%%%%!!!%%%?%%!?%%%!%%%!!%!%!!!!%%?%%%%!!!%%?%%%%%%%??%!%%?%?%!%!%?%%!%!%%!%!!?%%??!?%%%!%%!?!!?!%%!%?%%%%%%%?%%%%%!!!%!!%?%%!?!%%!!??!??%%%%?!??%%%%%!!%%%?%%%?%%!?!!%!!%%?%?%!!!%%%!!!%%%%%!%%?%?!?!?!!!%!?%!!%!%%%?!%%!?%%!!%?%%!%%%?%!%!!%!%!%!!%!!%%%?%!%%%!%%!%?%!!%%%!!!?%?%%?%!!%!!%%!%%%%!%!%%%%?%%%%%%!!!!%%%!%?%?%?%!!!!!%%%%%%!%!%%?%%%!%%!?%%%%%??%?%!%%%!!%!?%%%%?%%%%?!!%%!!%!!!%%%%!%%%%%!!%%%%%!!?%!%?%??!?!!!%%!????%?!?!!!%%%%%%%?!%!!?%%%%%!%%%!!%%%?%!%!?%%!!%?%!%%!!%!%%%?!%%%?!!!??%%%?!!?!!%!?!?!%!%%%!?%%!!%??%%!%!%%!%%%%%%!!!%%%%%%??%%!?!??%%???%!?%!%?!%!!%%%?%%%%%%!!%%%!%%?%%%%!?!??%!%!!%!%!!%??!%!%%%%%!!?!%%%!!%%%%?%??%?%%%?%%!%%%%!!?!??%!%%%%?%%!??%!%%?!!%%?%!%%?!%%%%%?%%?!%?!%%%%?%?%%??!?!%??!%?!%%%?%?!%!!!%%%%?!%!%!!?%?!?%%%!?%%!%!%%?%!%?!!%?%%!%!!%?%?!%!%%%%?%%?!%%%%%!%%%??!?!?%%%!%!%??%%%%!%%%%!%!??%%?!!!?!!%!%%!!!!!%%%%%?%!%?%%!!!%?!%!%%?!?%?%%%!!!%!!%%%%%!%!%%%!%%%!?!%?!!%!%%?%!!!%%%!!?!?!??%%%%!%%%!%?%%!!!!!?%!!!%!%?!%!%!?!%%!!%%?!?!!%%?%!!%!%%?!%%%%?%!%%%%!%?%!%%!%!%%!%%!?%!%%?%%%?%!!?!?%%%%%?!!%!!!!!!%%!?%%?%%!?%%?!%?!?!?!!%%%%%%!!!%??%!%?%?%?%%??!!%?%?%!%!%!?%!!%?!!%%%%%!!?!%!?!?!%!!!!!%%%%!%!?%!?!%%%%!%%?%!%%!!%?%%!?%%%%%?%%%?%%!%!%%!??%%%!!%!!%%%%%!!%%%%!%!!%!%!%%?!%%%!%!%!?%%!!%%%%?!%%%?%?!%%%%?%%!?%!!%!!!!%!!!?!%%%%%?%%!!?%%!!%?%%!!%!%%!%%?%!%!%%%!%%!%?%%%%%%%%!%%!!!??!!%!!!!%!%%%!!!%%!!!%%!%%%!%%?%!!!%?%%%!!%!!%%?!??!%%?%??!!%%%?%%%!%!!?%!%?!%%??%?!!!%?%%??%%!%!!?%%%%%?!?!%!!!!!%%%%?!%%!!%!%%?!!!!??!!?!%%?%!?%%%%!%%%!%%!%%%%?%!%%?%%%%!!!%%!%%%!%%%%?%%?!%%%%%??%!%?%%!%?%%!!%?%%%%%!!%!?%%%?!?!%%!%?!!%%!%!%!%?%!%??%%!!%!!?%%!%!%%!%%!%!%%%!!%?%%%!%%!%?!?%!!!%?!%%%%%!?%%%!!?%??%!%%%!??%!!?%!?!%?!%!?!%!%%!%!%!!%!!!%?%?%%%%!%!%!!%%!!%%%!!%%!%?!%?%%!%%%%!%%!%%!!!%%??%!%%%?%%!%?!?!%!%%%%%%!%%%%%%%!!%!%!!!!%%%%%%!!!!%!!%%%%%!%%!?!%%!%%%!%?!%!!%%?%%!!%!%%%%%?!!!%%?%%%?!!?%!%!!!%%%?%!%%!%%%!!%%!!!!!!%%%%?%%%%%?%%?%!!!!!!?!!!!?!%%%%!!??%?!%%%%%!?%%%%!%%%!!%??!%%!?%%!%!%!%%!%!%!!!%!?%!%?!!?%%%!!!%!!%!!%!%!!!!!!%??!!%!?%!%?%!?!%!!!%%%%?%%!%%?!!%%%%?%!?%?%%!?%%%!%%?!!%!%!%?%%!%%%!!%%%%!!!%%%%!%?%%!%??%%!%%%!%%%!%!%%!%?!%???!%%!%%%?%?%%%?%!!!?!?!%!!%%?%!!%%%?%!!!!!?%!!?%?%%!!%%%?!!??%?%!%%%%!%%%!?%%%%!%!!%%%%?%!!%%?%%???%!%%!%%%???%%%?%%!%%?%%!?%%%%%!%%?!%%!%%%!%%?!%?!!!%!%!%%?%?%%%!!%!!?%!%!%%!!%!%%!%!%%%!!%%%%!?%%%!%!%%!%%?%%!%%?%%%!!!?%!???%%!%!%%!%%!%%%!?!%!%!%%%!%!!!%!!!!?!!%!%%!?%%?!%!!%!!%?!%%%%%%?!%%%%!!?!%%%%!!??%%%??%!?%!%%!!?!%!%!!%%!%!!!!%?%%!%%%%%%?!%?!%!%?%!%?%??%?!%%?!%%!!?!%%!%%%%%%!%%%!!??!%%!!%!?%!%?%?!?!?%???%%%?!!%!%!%!%!!%?%!!?%%%!?!%%!%%%?%%%%!%!%%!!!?%%%%%!!%!%!?%!%!%!%!!%%%!%!%!!%%%!!!%%%!%%%%!%%%%!%!!?!?%??%%!?%??!%?!%%!!!!%??!!!?!%!!%%%%%!!%%!%?!??%%!?%%!%%%%%!!!!!%%%%%!!!!!%!??!!!%!?%%%%!!!%!%%%?!%%%%%%%!%!!!%%%!%%%?!?%%!%%%!%!%%%%!!?!?%%%%%!?!%%!%%%!!!?!%!!%??%%%?!%!%%%%?%!!%?%%%!%%!?%!%!?%%!?!%%!?%%!%%!!%%!?%%!%?%!!!%%!!%!%!?!%%%%!%!!%!!!%!%%%%!%?!!?%?!?%%!?%%%?!!%%???!!%!?!!!??!!%!%%!!!!!%%!%%%!!%%%%%!!%%%%%%?!!!%??!!?%%%%!%%%!%%%%%%%%!??%!!%?%!??!%%!!%????!!!%%%!%%%%?!!?!%%!%?%???%!%%!%%?!!%%%%!%??%%%%!%%!!!%!!!!%!%%%%!?!!?%?%%%%!%%%!%%!!?!%%?%!?%?%?%!!?%!!?%%!?%!!%!?%%%%%!!%?!%?%%?!!%!!!?%!%?!!!%?%!%!!!%%!!!%!?%!?!%%?%%?%%%!!!%!!!?%!??%%!!%!%!!?%!%%?%!%!!%!!%%%%!%!?%?!!%%%%?!!%!!!!%!!!!!?%%%?!%%!!!%%%!%%!%%!!?%!?%%!!??%%%!%!!%?%%%?!!%!%!!!%?!!%%!!%?%%!%%%%?!%!?!!?%%!!?%!!?!!%!%%!!%!%!?!?!%!%!%!!?%?!?%%?!!??%!?%?!?!%%?%%%%%?%%!!!!%%%?!!%!%!%%!!!%!%%%%!%%!?%%!%!%%!%%%?%%%%%%%%!%%?!!?%?!!%??%!?%%?!?!!%?%?!!?%!%?%%!%%%%?%!%?%%%%!!%%%!!%!!!%%%%%!!%%!%!%%?%?!%%!%!%!%!%%!%!?%%!%%?%%??%!%%!%%%%%%%%?%%?!!!!%!!%?!!!!!%%%%?%!%%%%%!!%%%%!!%%??%%%%!%%?%%%?!!%%%?%!!%%%%!!!%%%??%?%%?!!%%%!%!%!%!%%%?%%%%?%%!??!%%?%?!%%%?!??!%!%%!%?!!?!?!!%!!%%?%%!%!!%!%!%%!!%%%%%%%%%%%%!!!?!%!%%%%!%%!%%!%!%%%!?!%??!!%?%!!%%!%!%!%%!%?!??!?%!!%?!!?!%%!%%!!!%!%!!!%%%%!?!%!!%?%!!%%!!%%!%%!%??%!!%!%%!%%!!?%?%!%%?!%%?%!%!%!%!%%?%%?!%%%!!!%!!!?%%%!%?%%%%%!!%!%!%%%%%%!%%!!%%?!%%!%?%%?%!%%!%%!!%%%!?%%%?%?!%%!%%!???%%%%%!%%%%??!!?%%?%%!!%!%%%%%%!?%%!%%?!%!%!%%?%%%?%!!?%?%%!%!?%%!%%?%%!!!!%!!%%%%%%%!%!??!%%!%!!?%%%%?!?%%!?%%!%%??!!%!!?!!!!!!%%!!?!!!!%!%?%!%?%%!%??!?!%%?%!%??%?%!!!!!!?%%%%%!!%%%??!!!!!?%%!%!!?%!%!%?%%?!%!!%%!%%!%!%?%??!%%!?%?%%%%%!%!?!%%!%!!!%%%%%%?!%%%%!%!%%?!!!%!%!%!%%%%!%!%!?%!!?%%!%%%%%!%!!%!!!!%!!%%!?%?%?%%?%%?!!!%!%!%%?!%!!%!%!!!!%!%%%%%!?%!%!?%!%%%%!!%!?%!%?%!!%!!?%%!!%?%%?%!!!!%%%%%%!?!!!%!?!!%?!!%%%%%!!!%?%%!?%%?%%%%%%!%%%%!%!!%!!%?%%%?%%%%%!%%%%!%%%!%!%!%!%%%!!%%%%??!%?%!%%!%%%%!!?!%%%%!!%?%!%%%!!%%%!%%!!?%%!%!%!!!!!%%?%%%?!!%%%!%!!%%%%!!??%%%%!!!?%%%?%%!!%!!?!%!?%!!!!%!%%!!%?%??!!%%?%%!?!%!%%!%%%!!?!?%??%!?%!%!%%%%%!%%%%!%!?%?!%%%%?%!%?%!%!!%%%%%!?%!%?%?!!%?%%!%??%!%%%?%!!!%?!%%%!!?!?!!%!%??%!%!??!%%%%!%!%%%!?%!%!?!%!?!!!?%?%%%%!!?%!!!%%!%!?!!!%?%%??%?%!%%%!%%%!%!!%!?%%?%!!%%%%?%?%!%?%%?%??!!?%!%%!?%%!!%!%?!!?!%%!!%!!%!%!%!??%!%!!!%%%%!!%%%!%?%%!%!%%?!!?%!!!!%%!%!%!???!!%!!%!%%?!%%%%!%%%%!?!%%%?%%!?!%%!!!??%%%%%!!%!%%!?%%%?!??%%%?!!!!%!??%!!%%!!%?%!%%!%!%%%!%!!?%?%!%%%%%!!???!%!%!%!%!?!%%%%??%!%%%%%!!!?%%%%%%%??%!%%%!?!!!%?%!?%!%%%%%!!?%%%%!%!!!%!!%%!%%?%!!%%!%%%!%?!!%?%!%!!%?!%%%?%%!!?%%%%!!%?%!!!!?%!?%%???%%%%??%%%%%!!?%!%?%!%!!%%!!?%?!!?%%%!!%!?!%%!!?%%%!!%%!%%%!%%%!??!%?!!?!!!%!%?!%!%%!?!!?%%%%%!%?%!%%?!!!%!!!!%!%%!!!?%%!%%!!%%%!%?!!%?%%?%??%%!%%%%!%%%%???!!%%%%%!?!%!!!%%?%!?%!?%%!!%%!%!%!??%%??!!!%!!%%%%%%!%?%%!%%!?%%!%%!%%%%!%!!!%!??%!%%!?%%!!!??%!%!!%%?%%%!?%%!%%!%?%%!!!%!%%!%%?%!%%!!%?%%%%!!%%?!%!!%%!%??!%!?%!!%?!%!%%%%!!?!?!!!%!%%!%!%!%!%!%%?%%!%%?!%!%%?!?%!?!!!%%%!?!!%%%!!!%%!%!%%!%!%%!!!!?%%%!%%%!!!%%?%%!!!%!%%%%%!!!!%%!%%%%%%!?%?!%%%%%!%!!!%!%!%%!!!%%%%%%%?!%%%%!%%%!%!?%%%?%%!%%%%!%!%!%%??%!%??!%%%!%!%%%?!%!!%!%?%!!%%%%!!%%%!!?%?%%?!%!%!!%!?%!%%%!%%%??%?%%!??!%??%%??%%?%%%!?%%!%!%%?%!?%%%?%!!!!!?%?!?%%%%!?%%%%%!%%!!%?!!!?%%%%?!%%%%!??%!%!%%%%%??%?%%!%?%!%!!!!%%!??%?%%!%?!%%?!%!%!?!!%%?!?!!!%%!%%%!!%%!%!%%%??%%!%!%%?%!!!%??%!!%!!!!!??!?%%%%!!%%?!!!%!%%%%!??%%?!%?%%!%%%%%!?!!?!!!%??%!!%!%%%%%??%%%%%!!!%?%%!%!%%%!%%%%!!%!?%!%%%%!!!%?!?%!!%%!!%%%%%%!!%!!!%?%!!?%%%!%!%??!!?%%!!!!!%%%?!?%%!%%%!%%!!%%%%!%!!%?%!!!?%%%!%?%!%%%%%!!!%??%%%!!!%%!??%%%!!%%%%?%%!%%%??%%%%%?!%!!%!!!%%!%%%%%!!?%%!%?!%%%?%%%!%!%%%%!!%%!%%!%%!%%%?%!%%%!!%%!%!!!%%%!!!%%%%!!%%%%!%%%?%!!!!%!%!!%%?!!?!!!%%!%%!!%!!%!%!%%%%!%!!!?!%!?%%%!%%%!%!%!!%?!%!!%!%%??%%%!%!%!%!!?!!%?!?%%?%%!%%???!%!!%!!%%!!!!%%%!%%%!%%%!!%%?%%!!%!?%%%?!!%?%%!%!%?!!%!!!%!%!!%!??%?!!!%%%!%!!?%%%%!%!!%%%%?%%%%?%%%!%%!!!!!%!?!?%?!!%??%%!?!%%%%%!?!!%!!!%!%%%!%!!!%!!%?%%!%%%%!%!%%%%%%%%?!!?!%%%!%!!%%%?!%!?%!%%??!!?%%%%!!!?!?!%?%%?%?!%%!%%?!%!%!%!!!%%%??%%!%%!?!?%%?%%!%%!%!%?!%!!!?%!?%%!%!?%?%!%%%%?%!%%%!%%%!%%%%%!!%%??%%%?%%!?!%?%%!%!!!!!?!?%!%?!%!!!%?%!!!%%%%!%!?%?!!%?%?%!!%%%%!%?%%%%??%?%%?%!?%?%!?!!!%%%!%%%!%%!%%?!??!!!!%!%%%%%!!!?%%%!?%?%%%%%%!!%%?!!?!!?!%%!%%!%?%?%!%%%%!?%%%%%!%!!?%!%%%!?!?%??!%!%%!!!!?%%%%%?%!?%%!%%%!?%%%%!%%%%!%%%!%%%??!!?!%!%%?!?%!!??%%%!%!%%!%%%!%!!?%%%%%%%%!!!%%!%%!?%%%%?%%!%!%%?!!%?%%!%%!%!%%?%?!!!%?%?%%%!%!!!%!%%%%%%%%%%%!%%?!%%%%?%!!%%!%%!!!%!%!?%!?!?%!%%!?%%!%!%%?%!?%?%%%%%%!%%!%!%%%?!%%%?%??!!%%!%%%?%%%%%!!%!!!%!!%%?!%!%!!%!%%??%!!!%!??%%?%?!?!!%!?%!%%??!!%!!%!%!?!!%!%?%!%!%!!%!%!%?%!!%%!!%!%%%%%%%?%%%!%%%%!!%%%!%%!!%%!%%%??!%?%%!%?%%%!%?%%?%%!!%!?%%!!%%???%%!%%!?%!?%!?%!%%!!%%%%!%%!%%?!!??!?!?!!!%%%%?%!%!%??!%%!%%?%??%%%%%%%%%%%!!!%%%%%%!?!!%!!%%%%!!?%%%%!?%!?%%%%!%!%%%!%%%%%!!?%%!%%!%%%!%!!!!%%??!!!!!%?%!%!%%%%%%!%!%!!!?%%!%!?%!!?!?!?%?%!!%%?%!%%%!%!!?!!%%??%%!!%%!%%??%!%!%!?%!!%!%%?%%%%%%!!%?!%%!!!!!%%!?!!%!!!!%%%!!!%!%%%%!%%?%?%%!!!!!%!%%?%!%%%%%!%?%??!?!??!%%%!?%!%%!?%!%!%%%?!%!%%%%!%?!!!%?%??!!?!%%!%?%!?%!!!!%!%%!!????!%%%!!!!%!%%!%%%%!!%!?%?!?%?%%%?!%%%%%??%!%!%%!?%!%!%%%?%%%!%!??%?%%%%!!!!!%%%!!%!!?%%%?!!?!!%!%!!!%%?%?%%!!!%?!!%%!%%!%%!%!?!?!!%%%!%??!%%?%!%!%!!%!%%!%%%%!!%!!%%%!%%%%%%!%%!?!!%?%%%%%!%??!!?%!%%?%!!%!%%!!%%%!%?%%!?%!!?%!%!!!?%!?%!%?!!?%?%?!%?%!!%%%??%!%!??%!%?!!??!%!%!%!?%%%!%%!%%%%!%!%%%?%%?!%%%!%!!!!%!%!!%%!%!%!!%%%%%!%%%%%%%!!%!!!%%?%%?!%%%%!!%%!?!!%%%%?%?%%!%????!%?%%%?%!?%%??%%!%?!?!%%?%??%!!%!%!%%?%?%%%%?!!%!%!%%!?%!%%%%?!%?%??%?%%!%%%%%?!%%%!%?!%!?!!%%%!%!!%!?%!%?%?%!!!??%%%!%!?%!%!%!%%!%%!%%?!!?%%%%%?!!!%?!!%%!?%%?%%%%!%!!!%?%%%%%%%%!%%%%!%%!!%!!%%!!!?!%!!%%%?%%?!?%?%%%!!%%%%%%!%!!!%%%!%!!?%!!%%%%%%!%?!?!%%!??%!?!%??!%%!%%!%%%%%%%!%!?%?!%%?%!%%!%!!?!!%%%!?%!?%!%%%?%!!%??%!!%?%%%%%%!!!?%%!%!%?!!!%%%%!%%!!!?!%%!??!%%!?!!%!%%%?%?!!?!%!!!%?%?!?!%!!!!%%!!?%?%?%!%%?%%!%%%%%!%?%%%!%%%!%?!%%%%!%!!!!!%%!?%%%!%!!%%%%!!!%%!!?%?%!%%!%!!%!!%?!%%%%!!%%?%%!%%!%%!%??!!!?!%?%?%?!!%!%??%??%%%!!%%%%%!!!!!?%!%!?!%%%%!%%!%!%%!!%%!!%%!?!%!!%!!%!%!%%%?!?%%!%!%?!!%%!%%%!%%%%!!??%!%%%%??%%??%!%%!%%%%%%%!!%%?!!!%%?%%%!?%%!%?%%!%!!%!%%!???%%%?!%%%!%%%%!%!%%%?%%%%?%!%?%!%%%!%%!!?%%?%%??!%!?!%?%%!!%!?!%%!%%!%%%?%%%%!!%%!!!%%%!%%%!!!!!%%?%!%%%!!%%%?!%!!!!!%%%!%!!%!%%%%!!!!!?%%?%!%!?%?%!!!!%%%%!!!!%!!??!!%%%%%%!%%%%%%!?!!!?!%!!?%!?%?!%%%!!%!%%!!!!!%%??!!%%!%%%!!%%?!!!!!%%%?%!!?%%!%?!!%!!%%!!%!!!??%%%?%!!%?!!%!%%%!??%??!!??%%%%?!%%?!??%%!%!!!%%?%%%!%%%%!?%%!%%!!%!?%%%%!%?%??%!%!!%%%%!!%%%!?%%!%!?%??!!?!?%%!?!%%%?%%!?%!%?%%%%!!?%%!%%%%!!!%%%!%%%!%%?!!!%!%%!!%%%%?%???!!?!%!!!%!?%%%%!%%%%!%!!!%%!%?%%%!%%?%%?%!%!?%!!%%???!!?%%%%!!!%%!%%%%!?!%%??!%!%?%?%%!!%!%%!!!!!%!%%!%!!?!%!%%%%%!%%%!!%%%?%!%!%!!!%%%%%%!!?!?!%%!%!?%?!%!%%%%!%%%%%%!%?!%%??%%%%%%?!?!!%!!%!!!%?!%!%%?!???!!?%%!%%%%%?%??%!??!%%?!%?%?%!%!%!??!???%%!!!!!?!%!!%!!%%?%!%%%%%!!%%%!%!%%%?%%!%?%%!%%%%%??!!!%!%%!?%!!!!?!%!%%!%%!?%%?%!!?%%!%!!%%?!%%%%!%?!!?%?%?%%%?%!?%%%!%!%!%!?%%?%%!%%%?%%!??!?!?%!!%?!%?!%%!?%%%!!%!!!?!%%%%??!%%!%!%%!%%%!%!%%!!?%!%%%?!!!!!??!%!!%%!!!!!%?%!%!%%!?%%%%%%?!%%%%%%????%%%%!?!%?%!!%%!!?%?%%%%%%!%!%%%?%%%!!%!!?%%%!!!%??%%%%%%!?!??!%%!%?!%%%%%%%%%%%!%%??%%??%!%?!%%!?%!%?%%%%!%!!?%?%!?%%%!%!!%!??%?!!?%%!!?!%%!!??%!%%!%!!%!!%!%?%!?%?!%??%!%?%%??%%?%!%%!!%%!!!%%%?%%%!%!!!!?%%!!!??!???%%%!!!?%%!!%%%%!!!%%!%%?%!%!!!%%%%?%!?%??!!!%%%%!!?!%?%?%%!%%%%%%%?%%%%!!%%%!%!%%%!%!%%??%%%?!!%!!!?%%?!!!?%!%?!%%!?%!?%%!?%%%!?%?!?!!!??%!?%?%%?%%?%%%!%!%?%%!%%?!%%!%%%%!!%!%%%?%!!%%!!%%%!?%%??%!!!%%%%???%!!!%%!%%%?%?%!?%!%!!%%?%!%%!%%??!%?%%!?!%!!%%?%%%?!%%%!%!%%%%%%!!!%%%!!??!!!%%!!?%!?!%!!%%!?%%!%%%!!!!%%%%!%%%!%%!!?!%%?!%%!%%%!%%%!%!%%%?!%%%!?!!?%%%%%?!%!%%%%!%!%?!%%?%?%%%%?%%!%%%?%%?%%!!%?%%??!%!%?%%!?%?!%!%%%%!????%%!%!?!%!?%!!!??%%!%%%!%?%%?!!!%!%!%%%%%%%?!%%!?%!?%!!!!%?%%!%%%%%?!%!%!%?%?%?%%?%!%!!%?!!?%!!%%%%??%!?%%%!?%!%!?%%%%%?%%%!%%%!%%%%!%!!!%%!!!%!!!%%%%%%!!%%!%?!%%%%%%%%%%!?!!!!!!%%%%!%%%%!!!%%%!??!%!%%!%??%%!%%?%%%%!%?%%%%?!!%%?%!%%%!?!%!?%!!??%!%%??!?%%%?%%%%%?%%%%?%%%%%!!!%?!%%?%%%%%%!%!%!%%%?%?!%%!%!!!%%%%?!!%%??%!!??%%??!%%!%%%!!!%!%%%%!%%%!?%%!?!%%?%!?%%%%%!%%!%%%%%%%%%!!!!!%%%!%%%%!!%!%%%!%!%!%!%%?!!!%!?!%??%%%%!%!!%%%?%!!!%?%!?%%!%!??!!!%!!!%??%?!%%%!%!!!%?%%?%%?!%%%%!!%%?!%%%%%%?%?%%%!%%?!%%%%!%!%!?%?%!!???%%!!?!?!%!%%!!%%!%!%%%%%?%!%?!?!?!!%%!??!%%!%%%%?!?!!!%?!?!!%!%!%%?!%%!!!!!%??%??%%!!!!%%?!!%%%%%?%!!!!%%?!%%%?%%!!%%?!?!?%%!!%!!??%??!??%?!!%!%!%%%%%?%%%!%%%?%%!?%%!!!%!%?!%%!!?!%%%!!%!%%!!%!%%!%?%%%!%%?%%%!!?%!%%!%!!%!!%%%%??%!%%?!!??%%%%?!%?%%!?%!%?!%!%%!!?!%%!%%%%%%!%!!!??!%!?%%%?!%?%!!%??!%%%!!!?%!!%%?%%!%!%!%!%!%%%%%?%%?%%?!!%%%!%?!!%?%!%%!%!?%%%%%%?!%!!?!%?%!!?!!!%!!%?%%%!%!?%%%?%?%!!!%%!%%!!%%%%?%?%%%%%!%%!!!%%%!%?%%!!!%%!%%%%%!!%%%!?%%!%!?%%?%%%!?%!!%%!?%!??%%??%%!%!%!!?%!%%%%%?%%?%%!%%?%%!!!!?%!%%??!!!%%%%%!%!%!%!%%!%?%%%!!%!%%%?!!%!%%!!%!!!!!?%%!!%!%%!%!!!!!%!?%%%??%%?%%?%%!?%?%%%??%!%%!%%!%!%%?!!%%%%%%%?!%!%%%%!%%??!!!%!%?%%!!%%?!%%?!%!?%%!%%%!!%%%%?%!%%!??!!%?%%%!!!%!%!!!!%%?%%!!%%!%%?%%?%!%!!!%?%%%%%!%%%%?!!%!?!%!%?!?%%%!!?!%%?!?%%%%!?%%!%%%!%!!?!!%??!!%%?%?!%!!!%?!!%!%?!%%!!%!%%%?!!%%!!!?%?%!%%?!%%%!%%%%%!%??%!!?%%%?!?!%!%%%%!%%%!%%!%!?!%%!%%%%%?!?%%%!!!%%%!?%!%%!!!%!?%%%%!?%!?%!!%%%!%?%%!%%%%!!?%%!!!%%%!%!%!%!!?%!%%%!%%%%?!!!!%!%!%%!%%!%!!?%%%?!%?!!?%%%!?%%!%!!%%!%?%!?!!!?!!!%%!!%!!%%%!??%%%?!!%!!?%!!!%%!??%?%??!%%%%!%?%!!%%%!!!!?%!!%!%?!!%!!%!%%!%%!!!%!%%%?!?!%!%!%%%!?%??!%%%?%%!%%!!%%%?%%%!%?%!%%%??%%%%%%%!?!!%%!?!%!!%%?!??!%%%?%%!?!?%%?!!%!!%%%%%!!%%!!?%%!%!!?%%%?%!!!%!%!%%!?!%?%?%%%!%%!!!%%!!%!%%%!%?%%%!%!%!%??%%%!%!??%??%%!%%%!%%!%?!!%%!%%%%%%%!%?!!!!%!!%%?%%??%%%%?%%!%%!%?%%!%%%?%!%!%!?%%!%!?!???!%!%!%%?%%!!%%!%!%!!!!!!!!?!%%!!%%?%%?!?%%!%!!%?%!!%%%%%%!%!%%!%?!!%%!!!%%%!!%?!?%!%!!%?!%!!%%%!?%%%%??%%%?%!!?%%%%%%%%%!!!?!!!%%??!?%!???!%?!?%!!!%??%!%%%%%%%%%!%%!%?%!?!!?!%!%?%!%??!%!%!%!%!!%%!?!%?!%!%%%%!!%??!?!%!!%%?%%%%!%%%?%?!!%%?!!%%!?!%!!?!%??!%!%%!!%%!%%%?%??%%!%!%?%!!!?%%?%!!!%?!?%?%!!%%??%!!%?%%%%%!!!%%%%%!%!%%%%??!%%?!!%%!%!!%%%%!!?!!!%%!!%%%%!%%!%%%!%!%!%%!?%%%%!?%!%?!?!%!%%!?%!%%%!%!!?!%%%%!!?!%!!%!!?!!!%%!%?%!%%%?!%%?%%!%?!!!%!!!%%?!%%%!%!%%?%%!%%!%%%!%!!%!!%%%%!%%!??%!%!!?%%?%%?!%!!?%%!%!?%%%%%!!!!?!!%?!%%!!!!%%%?%!%?%%%!!!%?%%?%?!%%??%!%%!%?!%!%%%?%%%!?!%!!%%!%%%%!%??%!?!%%?!?%%%%%%%!%%%?!!%%?!!!%!?%%!!%!%%!!!!%?%?%!%%%%%!%!%%%!%??%%%!%??!?%!%%%%!!%%%!?%!%!%%%?%?%%?%%!!%%!!?%??!?!!%%%%!?%?%?!!%%%?!%!%!!!!!??!?%%!?%!!%!!%!?%%%!!%%!%%%%%!%?%!%%%%???%!%?%%!!%%!?!!%?%?%?%!%!?!!%%%?!%%!!!%?%?!!!%?%%%%!%%%!?%?%%!!?%!!!!%%?!%%%!%!!?!%??!%%%!%???%%!%!%%%!%%???!%%%%%%?%%%!!!!%!!?%!%%%%!%???%%!!%?%%%%!%%%%%?%%!!!!%!%%!%!?%?%!!%%!%!!?%%%%!????%?!%!?%!!%!!%?%%!%%!!%!%%??%?!%!!%%!%%!%%!%%!!%?%%?!%%%%%!!!%?%?%%?%?%?%!?%!?%?%%!!%??!%?%%!!??%?!%%%%%!!!!%%?!!%%%!?!%!!?%!?!!!%%%!!!!!%%%%%!%?%!%!!!!%%%!%?%%?!!%%!%%%%??%%?!%??%%!%!??%%?!%!%!!%%%%?%%?%!%%!%!!%!?%%%%%%%%!%%!%%!!%%%?%%!%??%!!??%!%!%!?%!%%%?%!!%?!!!!?!?!%%!%??%??!%!!!%%!!?%!%!%?%%!!%%?%%!??!%%%%%%!!!?%!!!%!!%%%?!%%!%%%!?%!%%%%%!%%!!%%!%%%%!%%!%%!%!?!%!%%?%!%!%!%!??!%%!!?!%%!%!%!?!%%??!%??%%%%%!%??!%%?%%?!?%%%%%!!%%%%%!?%??%?!%%?%!%!%!%!%%%%%%%%%!!??%?%%%!%!!%%?!!%!%?%%%!%%%!%%%???!?%%%%%%%!%%!%!%!!!%%%%!!!%!%!!%%%?!!%%!%%%!%?!%%!!!%%?%!!!%%%%%!?!%?!!%!%%%%%%!%?%?%%!%%%%%%?%?!!%%%!?%%%%!%!%?%%%%%!?%%!%!!!%!%%?!!!!%%!!%???%!%?!%%!%%%!%!%!%!%!!!%!!%!!%%%%%??%!%!%!!%%!!%?!%%%%?!!%!%!?!%%!%?%%!!%%!!!%!?%!%!%%%?%%%%??%%%%%%%%!!?!%!!%?!!!?!%!!%?!%%%!?%%?!%!?%?%?!!%%???!!%!!%!%%!%!%!!%%%%%%!%%!!!?!!?%%?!%??!!%%%!?%?%%%%%%?!!?%?%%!!%!?%%!!%!%?!!!%!%!%!%%%%??%!%!!%%!%%!%?%!!%!!!?%%%!%??%!%%%!?%?!%!%!!%!!%!%%!%%???%%?!%%!!%?%%%!%%%%!!!%??%%%%%?%%%!%?%%?%%%%!!%%%%%%%%!%%%!!%%??%%%??!%?!!%%?%??%%!?%!%%!!%%%!%?!%!!!%%!%%%%!%%%!!!%%!%!!!!%!%?!%!?%!!%!%%%%!%%%!!%!!%%%%%%?%%!%?%%?%%!?%%%%%%%!!%!%%!%!!%?%?%%%%%?%!%%?%%%%?%%!!%%?%!!?%!?!!%%%!!%!!%%?%%%?%!!!!!%??!?%?%?%%%!!!?%??%%!%%%%?%!%??!!!%!??!%?%%!%%%!?%%%%??%%%%%%%%%?!%?!?%%!%?%!!!%%%!%%%?%%?!%!!%?%?%!%%%%!!%%%?%?%%?!%?!%%!%%%!%%!%?%!!%??%?!??%%%!%?%%%%?%%%%%?!?%%!%!!%!%%!%!%!!%%!%??!%!!!!%!!!?!%!%%!%%!!!!!%?%!%%%??%?%%!!%%%?%%%%%%!?!?!%!?%%%%!%%!%%!!%?%!%%%%!%%%%??%%?!%?!?%!%?!%???!!!%%!!%!!%??%!??%!?%%%?%!?%%!%!!!%?!%%?%%%?!!!?%%%!!%%%%!%!%?!%!%%%!%?!%!%!%%%%%%%%%%!%%?%%?!%!?%!!!%!%%%%!!%%%!%!!!?%%!?%%!?%%!!%!!?%%%!!!%!%%!!%%?%%%%!??!?%!!!%?%!%%%%!??%!?%%!%%%?!%%!!%%!%?!?!!%%!%%!%%!%!%?%%!%!%%%!%%%%?%%%!?!!?!%??%!!!%%%%!!??%??%!%!%%%!%%!%???%%%%%%%!%%!?%??%%!%%!!%?%!%?!?!!!!%!!?%%!!%?%??%%%%%%%%!%?!%!%%?!!?!%?%%%!%%!!!%%!!%%!?!%%!%!!!?!%!%%%%!!!%!%!%!!!?%!!!!!!!%!!%!%%?%%?!?!%%%%%?!!%%!!%%!%%?%%%%%%??!%!!%%!%!%!!%!%%%!%%%?!!?!%!!!?%%%%?%%!!!!%!%??%%%%!%%!!!?!%%%%!%%%%%%!!%%!%%%!%!!%%%%!!?%?%%!!?%!!%%%!!%%!%%%??%!%!!%??%%?%!%%!!%%%?%!!%%%%%!%%%%!!!!%!!%%!?%%??%!!!%?%?!%?%!!%?!%%%%!%%!%!%%!!?!!%%%??%%??!!?%%%?%!%%?%%?!%!!%!!%%!?!%%?%?%?!!%%!?!!!%!%!%%%%%%%!!%%%%?%%%!%%!%%!?%!%%%?!!!?%!??%%!%!!!!%%?%!!%!%%%?%!!%??!%!%!??%%%%?!!?%%%%%?%%%%%%?!??%%%%%!%%%%?!%%%%?!%!?%%%%%!!?%%?!%?!%!!!%!??%%!%%%?%%?%!?%%!%?%%%%%%%!%%?%!!%!?%%%?%%!%%%!%!?!??!%%??!%%%%!!%%!!?%!?!%%?%%%%%%%%!%!%!%!!!!%!??!?%?!!!!%%%%%!%!%%%!!??!!%%%%!%%%!%!??!%??%?!?%!!%%!?%%%!!!?%%?%%%%?!!?%%!!%%%!!?%%%!?%%%??%!%%%!%!!?!?%%%!??%%!!!%?%?!!?!!%?%!!%%?!!%%%?%!?!?!%%%%%%!%?%%!!?%%%%%!%%%%?!!%%!!!?!?%?%?!!?%%!!%%%%?%%!!?%%!%%%%?!?!?%%%?%!%!?!!%%%?%%!?%!!!!%%%%%!!%%%!%!?%%!!??%!%%?!!!!?%%%%!%%%%???%%%!!%!%!%!!%%%%?????%!?%?!%%!%%%%%%%%?%!%!!%%%%!%%%%%?%??%!!!!%%?!%!!%%%%%!!!!!%%?!%%!%%!%?%%%%%!!?!?%!!%!!!%%!!!%%?%!?%!?%?%!!%?%!%%%%%!?!%%?!%!%!%!%%!%%%?!%%!!!!%%!%%%?%?%%%%!!!???!%??%%!%!%%%!%?%?!%!!!!%%%??!!!!%!%%?!!!!%%?!%%%%!%!%%%%%%?!%?%!!%?%%?%!!%??%?!!%!!%%%%!%?!!!?!%%%!%!%%?!%%%?%%%%!?%!%!??%!!%%%%%%%%%!!%%?!%%%!%!%!!?!%%%%%%%%!?!!?%%%!%?%%%%!%!!%!%%%%%%%%%!!!%!%%%%!??%?!%!%!!%%%%!?%!!%%!%%%%%%%%%!%?%%?%?%!%!%%!!!%%%!!!%!!!%?%!!!%!!%!!!!%%!%!%%?%?%?!?!!!?!!%%%?!!?%%%?%%%!%?!??%!!%%!?!%%%!!%!!?!%%!%%?!%!%!%%!%?%!!!!%%%%%%!%%%!!%%!%%%%????%%!%!?%%%%%!%%%!%!%%%%%%%!%!?%?!%!%!!?%%%!?%%!%%!%%!%!?%?%!?%%%%%%%!%%%!%%!?!%%%%%%%?%%!?%%%%%%!!!%?!%%!%?%%!?%%!%!!%!??%%%!!!?%%??%!%!%%!%!%!%!%!?!!???%%%!?%%!%%%???!%!!!!?%!%%%%%%%!%%%!?%%%!%%!%!!%%%%%?!%!!%%%!%!%%%%%?%!!!%%!??!!%%%!%%%!%%%??%%%%!%%%%%!%!?%%!!%?%%!%?!!%%%??%?%!%%!%%!?%%?%?!%?%%%!!%?%!%%!%?%%%%!?%%%!%!?!%%!%%?!?%!%!!%!!?!%%%%!%!%%!%!?%%!!%!%%!%?%?!??!!%???%?!!%?!%!%?%?!!%%%?%%!!%!??!?!%!%?!!%%?!!!%%%!?%!%%!%?%%%%??%%!!%%%?%%!!!%!%???%?!%%%%%??%%%?!!%!!?%!%%!!!%!?%!!?%!!!%?!!%?%%?%!!?%%%!%?!%%%!!%!%!!??%?%!!?!?%%!%%??%!%%%%%%?%!%!%??%?!!?%%!%%!?!%?!%%???%%%%!%?!?!?%%%?%%%!!%!!%!?%%%%?%%!%!%%%%?%%!!%?!%%%!%!!%!??!!!%!!!%!%%%!%%!!!%%%%?!??!!%!%?%%%%%%!%?!?%%%!%?%%%%%?!!!%%?%%%!%%!%%%!?!!%!%?!?%%%%!!?!%?%%!!!?%%!%%!%%%!!?!?!!%%%%%%%%%?!%%?%%??%%!%%?%%%%%?%!%?%!!?%%?!!%%!%?!!%%?%%%%!%%!%%!!?%!!!!!%!%%%%?%%%%%%%!%%!!%?!!%%?!%!%!%!%%??%%%!!!%%%%!!?%%%%%%!%%!%%?%%%%%%!?!?!%%%!!%%!%!%%%%!%?%%%?%!%!%%!??%%!%!%?!!%%%%%%!%!!%%%!?%!%%%!!%%%%!%%%?%%%!!!!!?!!%!%%%?%!%%%!%%!%%!%%?%!!%?%%%%%%!%!%!%!%?!%%%%!%%?%%%?!!?%!%%!?%%!%%!%%?%%!%!%%%%%!!!?%?!!!!!!!!%%!!%%%%%%!??%!%%!%!%!!!?!%%%?!!!%%?%%%?%!%?%?!%!!!!%%%%%%%??%!!!%??%%%%?%%%%%%%!!!%%??%!!%%%%%%%?%!!%%!!!%?!?%!%%!%??!!%%!?!%!%?%?%%!?%%!%?!?%?%%!%%!%%%%!%%%?!%!!?!!!!%?!!!!%!%%%%!%!%!!!%!%%?%%?%%%!!!%?%!?%%?%?%!?!?%%%!?%%?%%!!%!!!??!?!?%?%%%%%!!%!!%?%%%!!%!!%!!%%%%?%?%%%%!!!%!%?%%!%%!?!%!!%?!%%%!?!%?%!!%?!%%%?%!%%%%%!!%?!%%?!?%?!%!%???%?%!%!!!%%?!!?!?!???!!%?%!!%%?%%?%?!?%%%%!%%???%%%%?!%!%%!?!??!%!%?%?!!%%!%!%%%%%!!%!%!?%?%%?!?%%!!!?%?%!%%%?!%%?%!%?%%!!%%%%%??!!%!%!%%%%!!%%%?%!?%%?!!%%%!!!%%!!!?!?!?!%%??!%!%!%!?%!%?%%%%!!!?%%!?%!?%?%!%%%%?%%?%!%%%%!%%!?%!?%%%%!!%%%??%%%?%!!!!%%%%!%?%%%%%?!?%%?%!!!%%%%?%%!?%%!%!%!!%%%??%!%%%!%!%!%%!%%?%????%%!!?%%!%!!!%?!%%!!%!?!!%%!%?!!?!!%%?!%%!%%%??!%!!!%!%%!?%?!%%%%??%!!%%%%!!%%%!%!?!!??%%%?%%%!%%%!!%!%?!!%!%!?!?!!?!%!%%!%%!%%?%%!!%!!?%%%?!%%%!!!%%!%?%!!!%%%!!%!!!%!!%%%?!%!%!%%!!%%!!?!!?%?!%%%%!%!%!!!?!%%!?%%?%%%!%%!?%%%!?!!%!!??%%!??!!!%!%!!!%!%?%!!%%!!%%!!!%%!%!!%%?!%!%!%!??%%%%%%?!!%%!%%%?!!??%!?%%%!!!%!%?%%?%!%%?%%%?%!!%%%!%%?!%%!%?!%%?!%%??%%!%%?!!!??!%%%%!%?!%%!!!%%!%%%?%%!??%%%?!!%!!?%!?!!!!?!!%%!%%!%?%!!!%?!%%%%?%%!!?%%%!%!%?%%?!%?!?%!%!!!%!!!?!?!!!%%!!!%?%!%%%!%%!??%!!%?!!%!!%?!!!!!%!!!?%!%%!%%%%%?!!%?!?!?!?%??%%?%!%?%%!!%%?!%?!!%%!%%!%%?!%?%!%%%%!%%??!!!!!%!%!%?%?!%?!%%%?!%?%!%!%?%%%%%!!%!!?%%!%!?!?%?%%%%!!%%%!%!!%%!!!%?%%%?!?%%%???!%%%!!%!!%?%?!%%%%!?!!%%?%%%?%%%?%!!%%?%%%%%?%!%!?!%%%!%!?%%%%?%%%!!!%%%%%??!?%%%!!?%%%%%%%%%%?%!%%%%!%%?!?%!%!!!%!%?%?!!?!%%%!%%%?%!!?%!%%??!?%%%%!!!!?!!%%%!%%%!!?%%!%!?%%%?!%%!%?!%!?!?%%?!%?%!%%!!!%!%%!%!??%%!!!!%!%!%!?%!%?!%!!?!!!%!!%!?!%%%%%%%!%%%!%%%!!?!!%?!!?%?%%!%?%%%?%%%!!!!?!%%%%%!!%!%%%%%?%!?!?%??%%?%!%!%%!!?%!!%%%?%%%?%%!?%!!??%%%!%%!!??%%!%!%%!!!?%%!!!%%%%%?%%%%%?%%!%?%%?!%%?%!!%?%!!?%??%!%%!!!%!%!!??%!%%%?!%!?!!%%!!!%%%%!%%!%%%%!!!!?%%!!%%?%%%%!!%!%%?!!?%%!%?!%!%%%!?!!?!%?!!%%!%%%%%%!!!!%?%!!!?%%%%%%!?%?%%?%!%??%!!%%!!!%%%%!%!??%%!%%!??%!!!%??!%%%%%!%%%%%!%?!%!!!!!!%!?!%?%%!!%!!%?%%%%!%%!%!??%%?%%%%%?%%%%!!!%%!!%%!%!!!%%%?%??%%!!%%!%!%!?!!!!!%%?!!%!??!?%!%%%!%?%!%%%%%!!!!%%?!!?%%%!%!%%!??!?%%%!%%?!%!%%%%?%%?!%?%%%!!?%%%%%!%%!%%!%%!!%%%!!!%%!!!%!??!?!%%!!%?%%!%!%%!%%%!!!?%!?%!?%!!%%%!!!!%%%!?!%!%!%%!!?!?!?!%?%?%!!%?%%%%!?%%!%%!%%%%!!%%!%!?%%!%%%%%%%!!!%%!%??!%!%!!?%!%%!?%?%%??!%%!%?%%?!%!!%!%!%?%%%!%%!%!?%%?%!?!%!%?!%!%%?%?%%%?!!?%%%%%%%!%?%%?!%??!%%!!%!?%%?%!%!%%%!%!!%??%%!?%!%%%??!%%%%!%?!%??%%!%?%%?%%%%!%???%!%%%!?!%?%%%%!%!%%!!%??%??%%!?!!!%%!?%%!!%!%%!%%?%!!%??%!%!!!!%%!%%!%%%!%??%!%!%!!%%!%%%?%%%??!??%?!!!%%%?%!?!%?%!%!!%!?%%%!!!%%%%?!!!%!%%!!%?%?%!!!%!!%%?!%?%!%%!%!%!!%!%%!!!%%?%?%%?%%%!%?!!!?%%%%??%%%%%?!%!%%!%!%%?%?%%!?!!!??!?%!%%%!%?%%%!%%!%%?%!!%%!%!%%!%!%%%%!%?!!%%%?!!?!?%%%!%!!%%?!?!%%!!!?!%!!!%!!%%%!%!!!%%%%%%!%%%?!?%%%!%?!!%%!%!%!!!!%%?%!!!%!%%?!?%!%%!%%!!%%%!?!%!%%%%%%%!!!%!?%%%?!!%!!%!%%%!!%!!%%!!%%%?%!%%?!?%%!%%?%%%%%!%%%%%%!%%!%%?!%%!?%?%?!???!%!?!!?!?%!!!!%%%%!!!%!!%%%!%!?!%%!%%!%%!%?!%!!!%!?%%!!%%%?%%?!?!!!?%%?%!?%%%!%?%%?%?!!%%%!!?%%?!!!%%%?%?%%%%!%%?!!%!%!%!%%%%!%!%%!%!%%!%!%%!!%?!%%!%?%!%!%%?!??!%%!%!%!%%%!!%?!%%%?%?%%%%%%?%!%%!%!%%%?%?%!%?%!!!?%!!%%?%!!%%!%%!!%!?%%%%%%%?%!!!%!!!?%%?!%!%%%?%%!%!!!%%%!!%!!%!%!?!%%%!%?%%!!%%!%?%?%!%%%!%%!%!!%%%!%%!!!!?!%!%%%%!!!?!!?%%??%%!!%??%!%?%%%%%%%!!%?!!%?%%%%%?!!%!!%%%!?%%%%%%%?%%?!%%%%?%%%%!%!%!%%!!!%?!%!!?!!!%%??!%!%!!%?%%%%%%%%?%?!%%%!%!!%%!!!!!!%??%%%%!%%%!!%%%!?%!!%%%?%%!%?%?%!%?!%!%?%?!!%!%!!%!?%?!%??!!%!%!%%%%!!!!!%!%%%%???%%%?%%!%!%%%!%!!!!!!%?!?%%%%!%?%!?!%!?!!!!!??!%%??%%!!%%%%!%%!!!%%%?%%%%!%?!%%!%%%%!!%!%?!%%!!%??%?!%?!?!!!%?!%!!?!!%%%%%%!%%!?!???%%%!%!!?!%!!!%!!%%!?%!??%%%!!??!%??!?%!!%?%!!!%!?%!!??%!?!%!%!?%!!%!%??!!%!!!%%?%!!?!%%!!%!!?%%!?%%?%%!%!%%%%%?!?!%!!%!%!%%%!%%?%??%%%%!??%?!%%%%!%%%?!?%!%!?%!%%?!!%!!%??!!%%%%%???!!%?!%%?!!%!%!%%!!%?%%!??%!!%%!!%!!!?!%?%?%!%!!!?!%!%!!%%!?%%%%?%!?%!%%%!%!!!%%%!%!!%%%%!??!%?%%??%!?%!%%%!%!%!%!!%%%%??%%!%%%%!??%%??%%!!%??!?!?%%%!!!??!%!?%?%!%%!%??!!%?!?!!!!%%?%%??!%%!!!?!!!!?%?!!!??%%!%!!!!%!%?%%%!!%%%!?!%%%%!!?!!!%%!?!%%?%!%%%?%%%?%!??%%!%??%%%?%!!?%%%%%?!%%!?%%???%%!%%!%!%!!%?!!%%%%%%%!%%%!%!!%?!!%%??%!!!?!%!%!!%!%!!!?%%%%!!!?%!!?!!?%!%%%%!!%!!!!%%!%?!!!?!%%%?%%%!!%%%!???%%%%?!!!%?%!!!!?%%%!%%?!!!!%!%%?%%!%%%!!?%%!?%%!%%%%!%?%%%%!%%%%!%%%%!%?%%??%%?%%%!%?%%%%%%!%?%%?%%!!?%%!%?%%%%!!!??%!!%%%%%!!!%%?!%!!!%?!%!%%!?%%!%%%!?%%%!!%!!%%!!%!%%!!!%%!!%!!%!%%%%%%%?%%%!%!!!%%!!%!!%%%?%!%%%%?%%!%%%!%%%%%%!!!%%%!!%%%?%%??%!!%?!!%!%%%?%!!!%!!?!?!!!!!!?!%!%%?%%!?%%%%!%!%!!%!?%!%!%!!!?%!!!!%%%%%?!%%!?%%%!%%?%%!%%!!!!!%%%!%%!%!%?%?%!%%!?%?!!%?!?!?%%!%%%!%%?!%%%?%?!!%%?!%??%%%%!?!%!%?!%?%?%%!%%%!!%!?%%%!?%%!%!%!%%!%!!!%!%!%?!?%%!%!?%!!?!%?%%!!%%?%!%?!!%!%!%!!%!%%!%!%%%%!%%%!?%%%%!!%%!!?%?!%%%!!%!%!%?!?!%%%?%%%%%%??!!%%!%%!%%!%%!??!??!%?%!!!?!%%?!%!%??%%%%!%%!!??%!%%!%%!%%%!%%!%%!%!%!%%??%!!%!?!!%!%!!%?%%!!%%?!!!%!%!%!!?%!%%%!?!?%%!%%!!!%%!%?!%%%!%%%%?%!?%?%!!%!%!?!!!!%?!%%%?%!!%?%?!%%!!%%%?%!%%%%!!%!%!!!??%%!!%%!%??%%%%?!!%%%%!?%?%!%!?!!%!!%?!%?%%%!!!%!!%%!?%%%%%?!!%!!%!!!?%!%%!?%%??!?!%%!?%%%%%!%!%!!%%%%!!%?%%%%!%!%!!?%!!!!?!!%%%?%?!%?%?%!%%!%%%%!!%!%%%??%%%?%!%?!?%%!%!!%!!%?%%!%!?%!!?!?!%%%!%%!!%!%!?%%%!!!%%%!%!!%?!?%?%!?%%?!%!!%?!?%%!%%!%!%%%??%!?%%%%%?%%%!!?!%%?!!%%%%!%%!!!%%!%?!!%%%!%%?%%?!%!?%%!%%%?!!!!%?%%!%?%!?%!?!!%!%?%!?%%%%!?%!%!%%?%?%%%!%!%!%%!%!%%%%!%%%!%?%%!%%?!%%%%!!?!%!!?!!!!%%?!!!%!%%?%%%!!!!%%%??!%!%!??%!%%%%!?%%?!!!%??%%%%%%%!!%%%?!%%!?%!!%%!!!%%!%!!!!%!%%%%?%?!%%%!%%!!%%?%%%%%%!%%%%!%%%%?!!?!!%%%?%%!??%!!%%!!%!?%%%!%%?!!?!%%%??%!%!!%%?%%%%!%!!%!!%!!!%%%%%%%%!%!!%%%%?%?%?%%!%?%%%%!!%%!?!%%!%!%!%%?!!!?%%!?%?%%!??%%?%!??%%%%%?%%%?%!!!%%%%%!%%%!!!%?!?%!%?!%%!?!%?%!%%!!%%%%%%%!%%%?%!%%!%??!%%%%%!%!!%?%%%?%!%!!%?%!!!%!?%!?%%%??%!!%%%%%!%!?%%%%?%%%%%%!%!??%!!%!%?%%%!?%%!%%%?%%?%%!%?%!?%%%?!!%%%!%?%%%%%!??%?%%%!?%%%%!%%!!%%%!%%!!!%%?!%!%%%!!??%%?!%%%%!%!??%!%%!!!%!!%%%!%%!!%%%%!%!!!!%!%?%%!!!!%!!!??%%%!!!%!??!%!%!%?%!?%?%!%%?%!%%%!!%?%!%!?!%!!!%%%?%%%%%%?%%?%%%%%%%?!%%%!%%???!!%%%%??%%%??%%?%%%%!%%!%!!!?%?%%!?%%%??%%%!%!!!!!!%!%%?%%%%!?%!?%%!?!%?!%%%!!%!!%?!%??%%!!?!%%%!%%!!!?%!%!?%?%??!!?%%!%!%%!%%?!%!%!!%!!?%!%%?%!!!%%%!??%!%%!%?%!??%!?%!!%%%???%%!%?!%%%!!!?!%%%!%?%!!%?!!%%%!%%%!!!!%%!?!%%?!%?!%%!%%!?%%%%%!%%%%%?%%!?!!%!?!?%%?!%!%!%%!%?%%%%%?%%!!%%%?!%??%?!!!%%%%!%%??%!?!?%%!!!!?%%%%%?%%!%%%%%%?!%!!!!!%!%%%%??%!?!!%%%?????%!?!%!??!%%!!%%!%?%%!%%?!%%!%%!!!%%!%%%%?!?%%%?%%!!!%%!?!??!%%!!%?%%!%!!!??%!!%!?!%?!!!??!%%!%%%%!%%%?%!%!!%!%??%!%!%!%!!%!??!!%!%?%%?%%!!!!%?%??%!!!%%%!%!!!?!?!!%?!%%!!!%%%%?!!%%%%%?!%%!!!%!?%?%??!%%%!%%%!?%!?%%?%!%!!!!%%%%%!?!!?%%?%?%!?%%%%!!%%%!%!?%%?!?!%%!%?!!%?%%?!!%!!%%!!%%%%%%%%?%!?!?!%%!?%?!!!%!!%%%!%!??%%?!%?%%!!!?!?!%%?!%%?%!!%%??%%%!!!!??!?%?%!%!%%!!!%%%%!%%%%!?%%!?%%?!%%%?!!%!!%%%!%%%!%!!?!!!!!%!%!%%%%!%!%%??%%!%!%%%%%%!!%%%%?!?!?!%!%%%!!%!!!%%?%%%!%%%?!%%%%!??!!%%!!%%%!!%%%!!%%!%%?%%?!%%?!?!!%%%?%%!%%%?%%?%%!!%!!%%!%!%!%!!?%%%!%!!%!!!%!?%%%%!%!%%!%!%%!%%%?%??!!!!%%??%!%?!!?%?!??%!%%%!%??!%%!%!?!%!!%!%?!?%??%!!?%!%?!%%%!%%%!!!!%!!%%%!%?%!%%??!?%%%!%!%%%%!%%?%!!%?%%??%?%%!??%%?%%%%%??!!%!!!%!%!%?%%!!%!%?%%%%?!!!!%!!!%%%!%%?%%%?%%%%%%%%?%%%!%!!%!%??%!%%!%%%?!!!??%%%%?!%%!%?!?!!%?%%%?%%?%%%%%%%%%!%?%!%%!%%!??!%%?!?!!?!%?!%%!%%?%%!%%%!%!%!!%%!!%!!!%%!!!?%%!%!?%%!!!%%!?!%%!!!%!!%!%!!!??%%%%!%?!?%!?%!%%%%%!!!%%?%?%!%!%!%%??%?!!?%!%%%!%!%%%%%!!%?%!%%?%!%%%%%!%!%%!%?%!%%?%%!?%!?%%%%!!!%!!!%%!%!%%%?%!%!?!!%%!!%??%!?%?%%%%%%?!%!!%!%%%!?!%!%%!%%!!%%%%!!%%!!!!?!%!!%?!%%%%%%!%%!?%!?!%%!%!%!%?!?!%!!%%??%!%%!???!?%!%!!?!!%!%%!!%%!%!%!!?!%%?%%!%!%%%%?!!!%?%!%%?!%?%!%!!!%!%%%!!%!!%??%%!?!!!%%!%%!%!%%%%!!%%%%!!%%?!%??%!%%%??%%?%%!!!%%%%!%!?%?!!%?%%%!%?%???!!!%%?!?%%%%!%%%%%!%!!%!%%%%%%%%?!!!!!%%%%??%!!?!%!!!%%%%%%%?%%?!%%?!?%%?%???%???%??!%%?%%%?%%%!%!%?%%!%!%?%%%%!%?%%%%%!!%%??!%!?!!%%%!%%%%?!!%%%??!!!!!%!!%%!%%%!%?!?!%??!%%%%%%%%%%!%%%%%%?!!?%%%%?%%?%%%?%%?%?!!!%!%%?%%!%%!%!!!%!%?%%%%!!%%!?!!%?%!!?!?%%%%?%%!!!!!!?!%!!!?%!?%%%!!?%%%%%!!?!%!!%?%!!%??!?%!!??%!!?%!%?%!?!%%%%?!!?!%??%!???%%%!!???!%?!%!?!%%!%!%?%%%!!%!%%%!?!%%%?%%%!%%!!?%!%%!%!!!!?!!!%%%%%%!?%%%%%%!!!!%?%%!%!%?!!%%?%?!%!!!%%?%?!%?%?%?!%?!%%%!%??%!%!%%%?%!%!!?%%!?%?!?%%%??%?%!%%%!%%%%?!!%%%?%%%%%%%%%!%!%%%%!%%!%!!?!%!!!!%%%%!!?%!?!%%!%?%%%?%!!!!!??%!!!%!%%!%%!%%?%!!!%!!%?!%%!!%%!%!?%!?%!%!%!%%%!!!!%!%%!!!%!!%!?%!%!?!?!?%!%%%?%%%!!!!%%!%%%%%??!?%!%%%%!%%!!???%!%?!%!%!%%??!%%%!%%!!%?%%?!!%!%!%?%%!!%%%!?!?%??%?%??%?!%!?%!!%%?%%%!?%?%!!?%%!!%%%!!%!!!!?!%%%!%%%%?%%!%?!%?%!?!%!!%?%%!!%!%!?%%!%%!%!?%%%%%!??!!%%!%%%%%!!!?%?%!?!%%%!!!%%!%!%%?!?!%%%!!?%%!%!%%!%!%?%%%?%%!?!%%%?!??%%?%%!!%!?%!!%????!?!?!%%!%!?%!%%%?%%%%%%?!?%!!%!?%%%%%!??!?%?%!%!!%%%%%%!?!!?%?%?%!%!%!%?!!%!!%!%!%%%%%%!%%%%!%!!!%!%%?!!%%%!!!!!%!%%%!%!!%!%%!%?%%%%%%%%?%!!%!%??!%%%%%?!!?!!%%?!!?!%?%!!!%%!%!!!%%!?%?%%!%!%?%?%?%%?%?!?%!%%?!!%%?%%?!%??%%%!%%%!%!?%%!%%!%??%!!%%??%%%%%?!%!!%%?%?!!%!!%%%!%?%!?!?%!!%%%?!%%!%!%%%??%%!?%%%??!!!%?%%!!?!!!%%%%?!!%?!!%%!%%%?!!%%%%!%!!?%!?%%%%!%%%!%%%!!!%!!!%%%%%%!!!!?%?%%!%%!!!!!%%!%!!%!%?%?%!%%%??%?%%%?!?%!%??%%%%!!!!%%!%%!!!%%?!?%%%!!%!!%%%%?%%!?%!%?%!?!!%!!%?%%%%%??%!%%?!%??%??!!!%%%!!%?%%!%%%!%!!%%%?!%!!%%!?!!?%!!%%!%!%%%%!%%??!%%%%%!%%%?%!%%%%!%%%!!!!?!!!?%!?%%?%!!!!%%??%%%!?!?!!%!!!%%??!!?%%?!%!??%%%%!%!%%%%?!%%%%%%!?%!!%%%%!!%?%!%%%%!!%%!%!%!!!%%!%%?!!%!!%!!%?%%%!%%!%!?%%%!%%?!%!%%!?%!!%!?%!!!%%%%?%!??%!!?!%!%%!%!%%%%!!!!%%%%%%%%%%?%!%!%!%?%%%!%!!!%!?%!!!?%%?!%%?!!%%%%!%!!%%!%%!%!?!?%%%!%?!%%%%%!!!?%!!!%%!!%%!%?????!!!?%!%!%%!%??%?%%??%%?%?%?%!%?%!%%!%?%%%%!%%%%???!%%%%%!?!!%%%%%%%!!??%%?%%!%!!!%!!%?%!%?%%!!%??%!?%!!%!%%%??%%!!!%%!%%%!%%%%?%%%%%?!%%!!%?!!%!%%??!!%%%!!!%%%%!!!!%%%?%!?!?!!%!%?%%%!!%%?!%%!%%%??!!!!!%%!%!!%?!!%%?%!%%?%%%%%!%%%%!%%%%?!!%?%%%%%!!?%%%%%%%?%!!%%?!!!!%?%%%%??!?!!?!%%?!!%!!!%!%%?%!!%%%!??!!!!!%%!%%%!!?%!!!!?%%?%%!%%%!%!??!%%?%%?%%%!!!?%?%%?%%%!%!!%%!?!%%!%!!%%%!!%%!%%!%%?%%%!!!%%%%%??!%!%%%??%%?!!%!%!%%%%!!%!%%%%?!%?%!?%!!%!%%?%%%?%%!%%!%!!%%%%%?%%?%!??!!%!!?%%?!!%%?!!%?%%?!%%%!!!%%%?%!!!!%!!!%!?!%!%!%!%!%%%?%%?!%!!%%%%!%!%!%!%%!%%%%%%!!%%?%%!!%!!%!!%!%?%%!!!!%?%%!%%!?%%?!!!%!!%!%%!%!?%!!!!%%?%%%%!%%?!?%%!?!!!%%%?%!?!!%?%%%%%!%%!%%?!?%!%%%?%??!%?%%!!?%?!!%!%!%!??%!%%!%%%!!%?!!%?!%?%?!?%%!%!?!!!!!!%!%%!%!%!%%%%%%!!?%?%%%?%%%%!!%?%?!%!!%!!!%%!%!%!?%?%%!??%!%?%%?%!%%!%%%!!%?%!!?!%%!!%?%%%%%%??!%%?%!%%!!%%%?!!%!%%%!%?%!%%%!%!%%%!%!?!???!!!!%%%%%!%%%??!?%?!%%%!%!%%%!!%%%?%%%%%?!!%?%%!%%%!!%%??%?%!!??!!!%%!%%%%%%!!%%%!%%!!%%?%%%%!%?!%?%!%%!!%%%!%!%%%%%%!%%!?%%!%%%!%%!%%!%%%%%%!%!%%%%%%!%?%%%%%!!!?%%!%!?!?%%!%!?%%%%?%%!%??!%!?%!!%!%?!!!%?!%?%!%!%?%%%!%!%%!?!%%%!%?%!!!!?%?%%%!!!%?%?%?!?!!!?%!%!!%!%?%%%!!%!?%!%%%%!!!%%%!%%!?%!%%!!!%!%?!%????!%%%%!??%!?%%!!%!%%!?!!%!%!%%%!%%%%%!%%%%%!%%!%!!?%%%%!!%%%!%%%!%%%!?%!!!%!!%!!?!!%%!%!!!!%%!?%%%%?%%!%?!!!!%?!!%?!!%%%%!%!%!%%%!!?!!%%!!?%!%%%?%!!!!!%?!%%%!?%%!?%!!%%?%%!%%%?!%?%!%!!%!%%!!%%%%?!%%?%?!%!!%!%!!%?%!%?%%!%!!%%%%%%!%?%%!?%%%!%%?!!%%?%%%%!%?!??!%%?!%!%!%%!%%%%?!%?%?!!%%?%%%!%%%%??%?!!%%%%%%?%%!!%?%%%%!!!?!!!%!!%!!!%?%!?%%%%?!%!!!!%!!!%%%%!!%%%%%%%%%!%!!%%!?!!?%?%%%%?%%!%!%!!%%%%!%%%%%%%%%?%%?%!??!%?%%?%%?!!%%?!%!?!!?!%?%%%%!%!%%%!%%!%?%!%%?%!?%!%%%%%%!%%%!%%?%!%%%!!!!!%%!%%!!!!!!!!!%%%!%%??!!?%%!%%%%%!?%%!??%%%%%?%!!!!%!%%!%%%%?%%%!%%%!%%?%?%!!?%?%%%%?%%%?!%?!!?!?!%?%?!%%!!?%%!?!%%%%%%!%%%%!%?!%??%??!?%?%%!%%?%??%%%!?!%??%!!%!!?!??%!%%?%%!!%??!!?%%?!%%!!!%%%!%!%%%!!%?!%%%!%?%?!%?%!!%%!%%%!%%%%!%!%%!!%!%!%!!%%%!!!!?!?!%!%?%%%%%!%??!?!!?!?%%?%%!?!!!%?%!%%%?!!?%!!%%!!!!?%!%%!!!%%%!!?!!%%!!%%!%????%%!!!%%!%!??!!%?!!!%%%%%!%??%?%%%!%%%!%%??%!%%%!?%%%!!%!%%%!!??%%%!?%%%?%?%!!%%%?%!%!!!%!%%%?%%!!%%%%!!%?%?%%%!%?!%!%%?%!?!%!%?%??%!%%?%!%!%?!?!!!!!%?!?%!!?%%%%%?%!!%?%%!%%%!?%??%%%%!!!%?%%%!!??!!%%?%%%%!%!%!!%!!!??%???!?!%??%!??%!?!%%%%%%%!%%%!!%!!%%%%?%?%%%?%%!!%%!%%%!!%%%%?%%!%%!%%?%%!%!%?%!?!!%!%%%!!!!!??!!!?%%!!%%!?%!%%%?!!!%!%%!!%?!%!%%%%!%!?%?%??!%!!%%?!!!?!%?%%?%!!%?!!%%%!!%!%%%!!!!!!%!%?%%?%!%%?%%%!%!!%%!!%%%%!%%?%??%%%!?%%%%%!?!%?%!!!%!!!!%!%%%%?%!%%!?!!!!%%%!%%%!%!?%!!%?%!!??%%!%?%!!%%?%%%?!!%%%%!%%!%%%!%%??!?!!%%?!%?%!%??%?!!!%%!%%!!%!!%!%!%!!?%!!!!%?!%%!!%%?!%?%%!?!%?%!!%!?!%!%%%!%!%%!!%!%%%%%%%?!%%%%%%%?%!%!!%%!??%%!?%!%!!%%%!%%%!%%%??%%%%!?%!?%%%%%!%?%%!%!%!%!!%?!%!!!%?!?%!?!%!%?!!%!?%%!!!%!!?!%!?%%%%!?%%!%%?%%?!?%%!?%%%%%%%?%??!!%!%?!?%?%!%%?%%!!%%?!%%?%%%%!%%!??!?%!%%%%?%%%%!!?%%!%!%%%%%%%!%%%!%!!%%!%%%%!!!%%!%!%%%%!%!!??%!!%!!??!%%%%!%?%?%!%%%?!!%??!!%%%%%%%!%%%%!%??%!!%!?%!?%%%%!!%%!%!%%!!!%%!???%!!?%!!%!%!%!?%!%!?%??!%?!%%!?!!%%!!%!??%?%!%?%?!!%!%?!!%?!!!%%%%%%%%%!!!%!!%%!%!!!%%?%?%!%%?%!!!!?%%%!%%%%!?%!%!!!!??%%?%%!!!?%!!!%?!%%%!%!%!%!%!!?%%%??%!%!%??%!!!!!!%?%%!%%??%!!%%?!!?%%%?%!!%?!%%!!!%!?%%%%?%%%%!%?%%%%!%!%!%%!?%%!%%%!?!%?%?%!!%!%%!?%!%%%?%!%%%!%%!%?%%%%%?!%?!!%?!%?!!%!%!!%%%?%%%%%%!!%%%%%!?%%%?%%!%!!!?%?%!!!%%!%!%%%%%%%?%%?!!%%!??%%!%?!%%%%%!%%%!!%!!!%!!%%%!%!!%%%!%%?%?!?%!%!?!%%!%%%%!%?%!!!!?%%%!?!?!!!%%%%!%!%%?%%%?%?!%?%?%%!!??%%!!%%!%%%!!?%%%!!%?!%!%%!%!%??%?%!!?%?%%%!!!?!!%!%!!!!%%??!%!!?%%!!%%?!?%%%%%!%!%!%!%%!??!%%%%%%!!!!%%!?!!!%%%%?!!!%%%%!?%%%!%!%!%?%!%%?!?%!!!%!!!%?%%?%%%!%%%!%%%%?!%?!%!?!!!%%!!%!!?!%%%%!!?!%!!%!!?%?%!?%%%%!%!?%%%!%%!%!!%??!!%%!%%?!!?%!!%?!?!%!?%!%!!%!%%%%%%!?%?%%%%!!%%%!!%!%%%?%%!!!%%%%?%%!%%?%!!?%?%?%!!!?%!%%?%%!?!%%%?%!%?%%%%!!!?%%??!%%%%?!%%!!!%!?%%%!?%%%!!%%%??%!!!%%%%??!!%?%%?%%!%!!!%!!%%!%%%%!%????!!%%%%!?%?!!!!!%%%%%%%%!%!%??%%?%%%%!%??%%%?%%%!?%%!%%!%!%%!%!%%!?!%!?%!%!%%%%%??%?%??%%%%!!!?%%%%!%%%!%%%!%%%!!??%%%%%!%!!%!%!%%%%%%%?%%%!!?%%!%?%??%!??%%!%?%!!%?%??%!%%%!%%!%!%%%!!%?%!%??%%?!%!%!!%!!!!?!?%%%?%%!??%%%%!!%%!!!!!%%!%!!%%%%%?!!%%%?%%?%%!%!%!!!!%%%?!!%%!%%!%!!!!?%%%%%%%%!%%!!%!?%%%%?%%???!??%%%?%%%?!%!%!!!%!!%?%?%?!!%%%%%!!?!!%?!%!%!%%%!%%?%%%!????!%!%%%%%!%?%!!!%!%%%??!%%%%!%%!%!%%%!?!%!!%%!%%%!?%%???%%!%!!!!!!%?!%%?!?!%%!!!!%%%!%%!?!%%!%!?!!!%?%!!!%??%?!%%!%%!%?%!!!!!?%!%%!%%?!!!%%%!%%%!%%%%%!%%?!%%!!%%%%!%%?%%?%%!%!!%%%?!%%!%%?%!%%?!!%%!!%!!%%?%!%%%!!!!??!%%!%%%%%?%!!%%!!%?!!%%%?%!%%%%?%!?%!%!?!??!%?!%!?%%!%?!!%%!%?%!?%%%%!?!!%%?%%%!%!%!!!!%!??!!!%!!!!?!!%!!%%%?!!%!%%%%%!%?!!%%?!%?!%??%%%%!%?%!%%%%?!%%??!!%?!!!%%!%?%!%%!%%%%%!!%?!?%?!!?!%%?%!%%%%!%%!%!!%%!!%?%%%%!%!%%!%!!%%!%%%%!?%%%!%%?!!%%!?%?%!!?!?!!%%!%?!?!!%%!%?%%!%%%!%%%%?%%!!%!%?%%%%%%%!!%%%!!%%%%!%!???!!!!%!%!!%!%!!!?%!%!%!!%!!!%!!%?%%!%%??%%%!%!%%?!%%%!!%%%%%!%?%%!!!%!%%%%%%%%!!!%?%?!!?!!%%%%%!%!!?%!%%!%%!%%?%%%!%!%!!!%!!%?%%!%%!%%%!%!!%!%!!%%!?!!%%%!?%%%!!%%%%??%%%!%?!%!??!%%%%%%!%%!?%%!!!%%%%%%?%%%%!%!!%?%%%%?%!!?%??%!%!!%%!%%!?!?%%!!%%%%%%%%%!%%%!!?%%%%%%%?%%!%%!%!%%%%%!!?!!%?%%%!!??!%%%%!%%!!%%%%?!??%%%!!%%!%?!%%!??!!%%%!!!%?%?%!!?!!!%%!?!!!%%%%!!!%%!?!!!?%?!!!%!!!!!?!!%??!!!%!%!?!!?%%!!??%?!%%?%%%%???%%%!?!%%?%?!?%!%%?%?!?%%%?!%!!!%!!%!!%%!?!?!!!!%?!%%!%%!?!%%%%%!?%%%?%%?%%%?%!?!%?%!?%!%%%%!!%%!%%?%%%!%%%?%!%%!!!?%%%%?%?!!%!!!%!%%!!?!%!%?!!?%!??%!%%!?!%!?%%%!%%!!!?!%%%!%?!!%%!%%%%!%?%%%%!%!!%!%%!!%%%!?%?%%?%%!???%%%?!?%%%%%?!%%!%?!!%!%%%!?%!!?!!%??!%%%%!??%!!%%%!%%!%!%%%%%!??%%%?%%?!%%!!!!%!!?!%!?!%%%%%!%%!%%%%%%%?%%!%!!?!!%!?%?!!!!%%!!%%!?!%%%?%!%%!%?%%!!%!!!%!?%!%!%!%%?!%!%%%%%%!%!?%%!%%%%?%!!%?!!%!%%?!%!%?!%%?%!?%%%!!!%%%%%!%%%!!%%%!%%%%%%?!!%!?%!??%%!%!!%!%%%!%%!?%%!%!!!%%%!%%%%%%%%%%!??%%!%!%%%!?%%%%!%%%!%%!%%%!%?%?%?%!!%!%??%!??%%%?!!!??%!!!%%%%!%?%%%%!%!%!%!%%!%%%!%!%!?%%%?!!!?%%%%!%%%!%?!?!%%%!!??%%!%%???%%%%??!!%%%!%%%%%!!%!!!?%?!?!%%%%?%?%!!?%!!%%?%%!!%!!!!?%!?%??%!!!!%%%?%%%%?!%%!????!%%%%%?%%!???%%!!!?%!?%?%!%%%%%!!!!%!%!!%!%%%!%%?%%!%!%?%%%%!%!?%%?%%%%%?!?!!%%%%%!?%?!%%%%!!?!?%?!%%%!!%%!%!!%!??!?%%!!?%?!%%?!%%!%?!%%%%?%%!?%%%?!%!!!??!%%%%?%!?%%%%%?%!%%!%!%%%??%%?%%!!%%%!%!%%?%!!%%%%%!%%%%%%%!?!%%%!!%%!!%!%%!%%?%%!%%?%%?%%%%?%%%%%%%!??!!!!!%%%%?!!%?%!%%!%%!?!!!%!!!%?!%%!%?!!!!!%%!%?%%%%%!!%!!%?%%%?!%!%!%?%!%?%%%!%?!!?%%!!%?%%%!!!%!!!?%!!!%%?!?%%!?%%?!%%%%?!%??%%???%?!!!!%%%!%?%?%!%%!%!%?%%%%!!%%???%?%%%%%?!%%%%!%%%!%%?!?!!%!!%!%!%!%??%%%%!!%%%!?!?!%%%!%!?!??!%?!%?%%?!%%!%%%!%%!!?%%?!?%%!!%!%!%%!!!%%%??!%%?%!?!%%%!?!%?%!??%?%%%%%%%!!!%!?!!!%?!%?%??%%??%!%?%?%%!%%?!?%!%%!!!%%%?%%!?!%!%%%%%%!!?%?%%%!%?%%%!!%!?!%?%?!%%%%?!!!!%%!!!%!%%%%?!!!?!%%?!%%??%?!%%?%??!%!%%??!%%%%!%%!!%?!!%?!?%??%!%!!!!%?%!!%%%?%%!%%%!%?%%?%%?!%?%%!!?%??%%?%%!%%!%%?!!!!!!%%%!!?!!%!!%%%%%!!?!?%!!!!!!%!%%!%!?%??%%?!%%%?%%%!%%%?%!%%!?!%!%?%%!??!%!?%!?!%!%!!!%!%%?%!??%!!%!%!%!?%?!!!%?%!?!?%%!%!!!!!%%!?%?%!%%!%!%%!%!!%!!%%%%?!!%%!%%!?%!%%%!!!%%!?%!%!!%%?!%%%%%%%?%!%%%?%?!%%%%%%%%?!%?%%!!!!%!%%?!?%%!!???%?!!%%!!!%!?%%!%!?!%!%!??!?%%%%%%!?!%!!%??%!%%!%!%?!%%%!?%!!%%%%!%?%!!??!!!%!!%%%?%?!%%?!!%!%%%!%%!!!%%!??!!!%!!%%%!%%!?!%%!!%%%!?!%!?!%%!!!%%%%%%%?!???!!%%?%!%?%%!!?%%%%%%!?%!%!?!%%%!!%%%%%%%%%%%!?%!%%!!%%%?%!!!?!%?!!%%!%%%?%%%!!!???!%!%!%%?????%%%%%%%!%%!%?!%%!!?%%%!%%%%%!%!!?!%!%%!!!?%!?%%%!%%%%!%??%%%%%%!!!!?%%!%%%!%?%?%%%!??%?!!?!%??!!%%%%!?%%?!%%%%%%!!%%!%?%%%!%%!%!%%!%!!?%%%??!%%%?!%!!!!!%%!%%?!!%%!!!!?%%??!%?%??!%%%%?!!!!%%%!%?%!%!%%%?!%!%?%%?!!%%%%!!?%!%?!%%!%%!%%%!%!%!!%%%!%!!%!???!%!%%%!?!%?%!!?%%!!%%%%??%%%?%?%%!!%??%!%??!%%%%%%%%!!!?%!?%%?%%!!!%%%%%!%%%!%%?%?%%%%%%?%%??!?%!!???%%!%%%%!%%!!?%??%%!!!!%?!%!%!!%%!%%%%!%%?%%!?!?!!%!?!!%%??%!%%!!%!%%?!%%!!?%%%%!?!!!%%!!??%!!!%?!%%%%!?%!%%%!%?%?%!%%%!%%!%%%!!%!%%%!%%!%!!!%!%??%!%%???%!%??!%%%?!?!%%!!!??%!!%%%!%%!?%%?!%%!%%%?%!??%%%!!!%?%?%?!%%%%%%!%!!%?%%!%??%%!%%!%%!%?%!%!!!%%!!!%!!%!%%%%!?%!!%%%!!%%!%%%%%%%!?%%%%?%!?%%!!?%%!%%%%?!?%!!%!%!%?%%%%!???!%%%?%?!?%%%!%!%?%%%?%%%%!!%%?!!!!%?!!%%?%%!%!!%?%%?%%!!%%?!!!?!!!!?!%!!%!?%!!?!%%%!!!!!?%!%%!!?!!%!%!%%?%!%%!!?!!!%%%!!%!!%%!!?%?%?!?%?%?!%?%?!?%!%!%!!%??%??!%%!!%%!%%?!%!!%!!%!!%!%%!%%%!!%!?%%!!%%%?%%!?!%%%%!%%!?!!?!%%%!?%%%!!?%!%!%?!!%?%?!!%%%%!!!!%%?%?%?!%!%%%%%%%%%%?%%!%%?!%!%!%!%%??%?%?%%!%!%?%?!!%???%%%!%%!%%%%!%!!!!%%%%%!?%%%!%%%!%%%%%!!%%%%!%!%%!%!!!?!!!%%!%%%%%!%?!%%%!%!!!%%?%%!%%%%!%%?%!!!??!!!%%??!!?%%%!%%!!%!%%%%%!??!%%!%%!!%!?%%%!?%%%%!%%?%?%%%!!!%%!%%%%?%%%!%%!!%?%!!%%!%%%%%%?%%%%!!%%%%!%!%?!%%%?%%%%%%%!%!?!%%%?%?%!!%??!%???%%!?!?%%!%%!%!?%?%%!%?%!?%!!?%!%!%%!%%%?%%!!?%!?%%%!??%?%%?%!%%?%%!!%!!%%%!%!%%%%?%?!!!!%!?%!!!%%%?%%%%%!?%!?%%!!!%%?%!%!%%%!%%%!?%%!%?%%%!%%?!%%%!?%!??!!%?!!%%!?%?%!%%!!%%%%%!!!%!!!%?!%%!?!!%!!?%!%!%?%%!%!?%?!!%!!%%%%!!%!?!?%%%!%?%%%!%!%%%%%!!!%?%%%%%??%%%!%%!??%%%!%!%!%!%%%?!!?%%%%%%!%%?!!%!%!%!%!?!!%!%!%!!%%%!??%!%%?%!!%!?!!%%!%!%!%%%%!%!%!%!!%%%%%!%%%%?!%!!!!??!%?%%!!%!%!!?!%%!!%%%%!%?%%%%%%%%%!!%!%%%!!%%%%!%?%?%%%%!!%!%%%%%!?%!?!?%!%%?%%!%%!?%!!!%!%!%!??%!!%??%%!%?%???%!?!?%%%!%%!?%%!?%?!!!%%!%%%%%%!!%%%?!%%%!%%%%%%%?%!!%%%!%!%!!!%?%%%%%%!%%!!?%!??!?%!%%%%!%!%?%%%%%%%%!!!!!%%!%%!%!%%%?%?%%!!!?%!!??%!%?%%%%!%%!%%!%!%!%%%%%?%!%!?%%%%%%!%%!%!?%%%%!!!!??!!%%!%%!?%%%?%%?%%?%!%%%?%!%?!!!%!%%%!%%!%%%?%?!%!!%!%!!%%%!%!%!?%!!!%%!!%%%!??%!?!!?%%!%%??!%!%%!!??!%!!%!?!!%%%%%!%!!%%%%!!!!!!%!%%%%%%!%%%?!%!%?%%%!%%%%%!!!!%%!!%?!??!%!%!??%!%%%?!%?%%%?!?!%?%!%%%%?%%%%%%!%%%!!%%%!%%%!%%!%%?%!%!%%!%%%%?%!%!%?!%!%!%%%%!%??%%??%??%%!%%?%%!%%%?%%!?!%%!?!!!%%?%!!%%%!%!??!!%%?%!?%?!?%?%!??!!%?%%!%!?!%%%%!!%%!!%!%!!%%!%!%%%!%%?%%%!%%!!%%!!!?!%!?%%%!!%%%?%!%%%!!%%!!%?%!%%%%%?%!%!%!%!%%!%%%!%%!!%!!!%%%!%%!?%%%%%%?!%%!??%!!!?!!%%?!%%!%?%??!%!%?%%?%%%?!%%%!%!?%?%%!?%!!%!!!!%%?!%!%!%!!!%%?!?%%!%?%!?!%!%!%%!?!%!?%%%%?%%%%!!%!%!!%%!%!%%%??%!??%%!%?!%%%!?%!!?%!%%%!!?!%%%?%%%!%%%!!%!%%?!!?!?%!!?!%!%?%!%!%!%??!!%??%%%%%?!!!?!?!%%?!%!?%!?!%%!!!?%%%%!%!!!%?%%%%%!?!%%%!!%!%%!%??!!%%!%!!!?!%?!%%%!%?%!!%%%?!!!?%%!!%%%%%?%%!!%%?!%!%!%?%%!%!%%%%!!!%?%?%!?%%??!?%?%%%!!!!!!!!%!%%!%!%%!%!!%!%%?!%!%%!%%%!%%?%?%%!%%%%!%%%%%??%!!!!!%?!!!?%%??%!%!!!?%!%!!%%!?%%!!!!!%%!!!%%!%!%!%%%!!!%%?%?%?%%%%?%?!%!%%!%%!%!%?%!%!??!%%!??!!%%??%%?!?!%!%%?!?%?%!?%%%!%%%%%%%%%??!%%%!?%!%??%%%%%%%%%!!!?%%!%!%!%?%%%!?%!??!!!%?%%%%!%%%?!%%!?%%!%%!!!!!%?!%%?!%%%!?%%!!!%??!?!%%%%%%%?!!%!?!%!??%!%?!?%!%!!%%%??!%!?%%%%%%??%%%%%%!%!%!%%%%%!?%!!!%!?%%!?!%%?%?%?%%%?%!%%!!%%%!%%%%%%!%%!%?!?%??%!!%?%%%!%?!%!?!!%??!?%%!%%!!%!%%%!!!%%!%??%%!%%%%%%?%???%?%!%%%??%!%%!!%!%!!%!%??!?%!%!%%%?%%%%%%%!?!?%%%!!%%?%%!%%%%%?!!%%%!%?%!%%!%!%%%%%%!?%!!!?%!%%%%!%!!!!??!!?!?%%%?!%?%%!%%!!!%%!%?%%%!!%%%%!!%%?!%%%%%%!!%?%%%!%!%!!!%%%!??!%?!!%%!%%!%?!!!!?!%?!%%!%!%%%!%%%%!%!%%!!%?%!!%!%%!??%!!%!%!!%%!%??%?!!%%%!%%%??%%!!%!!!%%!%%!%%!!%!!%%%%!%%%!%%%!!%!%%!%!?%%%!!!%%%%!?!%!%!%!!%%!!!??!!%!%!!!!!!%!%?!?%!!?!?%?!%!%%%%%%%!?!?%!!%!?!%%%!%%%%!%?%!!%!?%%%??!?%!%%!%!?!?%!!!!?!?%%?%!%%%??%!%%!%!!?%?!?%%!?%?!%!?%%?!!??!!%%?!%%%%!!%%%%%%!%%%!??!%?%!%!%!??%%!!!%!!%!%!%?!!%!!!%!!!%%!!%%%!?%!?%%%%!!!%%!%!%%%%!!!?%%%%%!%?%!%%%!!%?!!!!!%%!!%%??!%%%%%%%%?%%!%%!%%%!!!?!!!!!!!%!!%%%!%!!!?!%!?%?!%!%%%%!!!%?%!?%!%!%?%%!!%?%%??%?%!%!?%%!!!%%%?!%!!%?%!%%!%!%?!!%%!%!!?%!!???!!%??%?!%!%?%%!%%%%!?!!%%%%%?!%%%%!%??!!!!%??!?%%%?%%%%%%!?!!%%%!%!?!%!??%%%?!!%!?!%!!%%%?%!%%%?%?%%%%%%%%!%%?!?!%%%%?%%!!%%%%%%?%%%%!%!!?!?!%%?!?%%%%%?%%%?%!%%??%%?!%%%%!%%!!%!?%%%%%%?!%%!%%?%!%%%%!!%!!%%!!%%??%!%??%%%%!%%%?%!%%?!%!%!!!!%%%%%!!%!!%%!!%%%%%!!?!%!%%%%!%??!!%?%??!?%!!?%%!!?!%%?%%!%%%!!!%!%%?!?%%!!%!!!!%%?%?%%!!%!%??%!?!!!%!%%!!%%%!%!!%%%?!%%!!!!?%?!%%%!!?!%!!%%!%!%%%!%%!!%%?%%%%!!!!!!%%!%!%%!!%%%?%%%!?%%!!%%%!!%%!%?!%%!!%!?%?%!?%!?!!%%!%!!%%!%%%%!%%?!?%%%!?!%%%%%%%%%?!%!%!!!!%!%%%!?%!?!%%%!%%%%%%%!%!%?%%%%!!%!?!?%%!?!%%??%?!%!%%!!%?%!!%!!?%!!%??!!%%%%%%??!?!%?!!%?!!%!?%??!??!!%?!!?!%%%?!!%!!%!!?%%!!!!%%!%?%!%%!%%%!%!%?%!%%!%%!!%%!%?%!%!%!!%!%%!!%!!%%?%%%!!%!!%!!%%%%!??%?%%?!%%%%%%?%%!!!!?!?%!?%%%%%%%%?%%?%!%%%!%!%%%?%%?%%%%!%%?!!!!%!?%%??%?%???%?%!?!%!%!%!%?!???%!!?!?%%?%%%!!!%%%%%!?!%!!%%!%%?!!?%!%%%!!%?%%!!%%!!?!%!%?!?%!%!%?!%%%?%%%!?%!%?%%!%%!?%??!!%%!%!!!%???%??%!!?!%!?%!%?%%!??%%?!!%!!!!?%%?!%?!%%%%?!!%%!%?%!!!%%!!?!%!%%%!!%?%!%%%%!%??%!!%%%%?%?%%!%%%%!%%%%!%!%!!!??%?%!!!%?!!??%!%!?%%??%%%%%!???!?%!!%!?%!?%??%!%%%%?!!!%%!?%!!!!%!!!%!!%?%!%%%%??%%?!!%%%%%!!!?!%!?!?%!%?%%%?%%%%!%%!!?%%%!?%%!%%!%%%!%%%!?!%%%!%?%!%%!!%%%%!%?%!%!!%!?%%!%?!%%?%!?!!!%??!%!%!%%%%%!%!?!!!%%!%!%%!%!%!?%%?%%?%%!%!?%%%!??%??%!%%!%?!?%?!%?%?!!?!%%%%!%!!%!%!%%%%!%%!%%%?!!!!!!%%!?!?%%!%?!????%%%!%%%?%!!%%%!%%!?%%%!!?%?%!!%??%%!%!!!%%?!?%!%?%%%%%%!%%!%!%!!%%!?!!%?%%%%%!%%%!!%!%?%%?%%!???%!%!!%%%?!?%%!!!!%%%!!%!?!%%%!??!%!%%%!%!!?%%!%?%%!%!%!?%??!%?!!!?%!!!!%%%%???%!%!!%!%%%!%%%?!!?!%%%?%!%?!!%%!%?%??!%%%%%%%%%!!!!!%!!%%!?%?%!?%%?%?%!!%!%%?%%%!!%?%?!%!!?%%%!%%!%%!%?%%%!!!%%!!!!!%!!!%%?%?%?%!%%?%!%?!?!%%!!??!?!%!%!!!%%%%!!%!?%!%%?%%%%!!!!!%!%%%!?%!%!%!!%%%!!%%?%%%!%%%%%%%!!%%%%??%%!!!%!%?%!%?!?%?%%%?%%!!%%%%%?!%?%?%%%%%%%%%!%%%%?%%!%??%?!%?!!%?!%?%%%%!%%!%!%%!%%%%%?!!!!%!!%%%!%%%%!?!%!%%%!!%%%%!!?%%%!!%%?!!%%%%!%%!%%??%?%?%!%%%?!%!%%!%!%!!?!%!!%%%!%!%!!%%%%%%%%?%!?!!?%?!!%%%%!?%%%%!%%%%%%%?%%!!!%!%%%?%!!%%%?%!?!%%%%%!?!!!?%%%%!!%%%!%?!%%?%!%%!!%%%%%!%%%!!%!!%%%%!!?!?!%%?%%%!!%%%!%%%%%%??%??%%?%%!!%%%%!!%%%?%%%%%??!!?!!!%%?!?%%!%%%?%%%!!%%%?%%???%%!%!?%%?!!!!%%%!!%%!%?%!%!?!%!!!??%%!%!!%?!!!%%%!?%!%?%%%!?%!%?%%%%!!%%%!%%%%!!!?!!%!!%!%%%!%%%!%?!!%%!%%%%%%!?%%%!!?%!%?!!%!%!%!%!!!!?%!%%%%%%?!%%!!?%%%%!%%?!%?%!%?%%!%%!!?%%?!%%!?!%!%%!%%!%%?!%!!!!?%%%?%%%%!%?%!%%%!%??%%!?!%!%%!?!%%%!?!?%%??%!%?!%%!!%%?!%!%?!!?%%%!?%!!%%!%%!%%??%%!%%%%%%%%%%%!%?%!!%%!%!!%!???%%%!?!!!?%?%%!!%%!!!!?%%?!!%?!??!?%!%%%??%%%%%%!!%??!%%!!%!!!!%%??%!!%??%%?!!!!%!%!?!%%%?%???!!%!%%%%!%?%%%?%%!!?!%!!%%%!%%!%%!!%!%%%%%???%!!!%!%!%%%!!!%!%%!%!%%%!!!?!!!%!%?%?%%%%%%%?%!!%?%%!?%?%%?%!%?%?%?%%%%?%%??%%%!?!!%?%%%!!!!%?%???!%?%%!?%?%%?!?%!%%?!?!!!%??!%%!%%!!?!!!%!%%!!%!?%%!%%!!!%%%!?%%!!%%%!!%%%?!!%?%?!%%?!%?!!%%!?%!%%!!%%?%%%!%%!%%!%%%%%?%%%%!!!%%%!!%%?!!?%!%%%%%%?!%%%%%%%??!%?!!%!??!%!%%!?!!%!?%%!?!!%!!!!%!%%%!!?!%%?%?!%!%!!%%%%%?%?%%%%%%??!%??%!%%!!%%!?!?!!%%%%!%!!%%!%%%%%%%!?%%??%%%??%%%!%%%?%!%%%%%!%!!!%?!%!%%!%!%!%%?!%!%%!%%!!!%%?!%!%%%%%%%%?%%%%%!!!?%?%!!%!!%?!??%%%%?%%%%%?!%%%?!???%??%!%!?!%?!?%!%!?%!!%?!!!%%%%!!%!%?%?!%%!%%!?%?%??!!!!%%%?!%!%%%%%!%!!!%%!!?%!!!%?%%!%?!%%%%!!?!!?%!%!%%%%?%%%%%%!???%!%?%??%!!!%!%!%!!%!!?!%?%%%?%%!%%%!%%!?!!?%%!!%%%%!%!%%!%%!%%?%!%!%!%%??!%?%!%?%%%%%%%%%%%%%%?%%!%%%%%!%?!?%??%%%?%%%!%%?%%%!%%?%?%!%%%%%%%%%%!!!%%%%?!!%!?%%%!%!%!%!%%%%%%!!%!!!?%?%%!!%%!!%%??%!%%!!%?%?!%%!?%!%%%%!%!!%%%?%?%!%%%%!!%!!!!!??%?!%%%%%?%!%?%%!%!%!!%%?%%%?%!??%!!%?!!!%%?%!!%%!%%%?%%!?%!!?!%%%!?%?%%%!!%%!!?%!?%!%!%%!%%!!!!?!!%!%%?!!%!%%%%!%!?%!%%%??!%!!?%!%%%?!!%!!!!?%!%%%!!!%%???%%!%!!!%%%%?!?!??!!%%!!!%%?!?%!%%?!!?!!%!%!?%%?%???%%?%%%??!%%%!%%%%!?!%%%%!?%!!%!!!%%%%!%%%%%%%%%!?!!%%%%%%!%!?!%%%??%%???!!%?!!%%!?!?!?!?!?%!%%%!%?%%%%!%!!%?%!!?%!!%!!??%%!!!!???%%%%%?!%!!?%%%!?%!!%?!!!!%!?!%%%%%%%!%!%%%%!!%%%?!%!?!!%%!%!?!!!%!%%!!%!!!%?!%%!%%%?%%!?%!!%!%?%%!!%%!%!%%!!!%%!%!!!?%!!?%%!!!%!!!%!!%!%%!!%%!%%%?%%%!!%!%%!!%%%%%!%%?%?%!?!%%??!%!%%!%%%?%?%%?%?!%?%?%%%!!!!%?%%?!!?%!%%!!%%%%!%?%!%%!!%%%!%??!%!%!%!?%??!%%!?%%%%!!!?%%%%%?!!!%%%?%%%!!!!%%!??!%!??%%%!%!??????!?!%!%??%%!!?%?!%%!%%%?%%!?%!!%%%!%!?%!%!%!???%!!%%?%??%%%%%%?%?%%%%!!!!%!!?%?!%!!?%?%!??%!??!%?%!!%!%!%%%?%%!!?!%?%%%%%?!%%%!!%%%?%!!!!%!%!!!%!%%!%%%?%%?%%!%%?%!%%!%%!%?%!?!%!?%?%?%!%%%%!%%%%%%???%?%!!?!?%!%!!%%%%!!%!%?!%%%?%%!!!%!%?!%%!!%%!%??%?%?!!%?!%?%%%%!?%%%!%%%%%%%%%%%!%?%!%??!%??!?!!??!?%?!?%!!%%!?!%?%%%!%%??%%%%%%!%??!%%%!?%%%!??%!!?%%?%!%!!!!%!!!%%%%?!%%%!!!!%%!%!?!%?!%%%%!%%%%!!%!%?%!!!%?%%%!%!?!!%%!!?%!!!!%!!!%!%%!%%%?!%??%%%%!!%!!%?!%!%%%!%!!%%%?%!%!!!!!%%?%!!??%%!%!!??!!%%!%!??%?%%%%!?%%%%?%!!?%?%?%?!!%!%%%%!!?%!%%%%??%!?!%!!%%!!!!%?%%?!%%%!!!%%%%!%!%%%!%%?%%%%%%!%?%%%!!%!%%!!!%%%!%%!%%!??%%?%%%!%!%!!%!%%%?!!!%!%?!!?!%!!%!%%%?!%%??!!!%%%!%%%%%%!%%!!??%%?%!??%%!!%%%%!!!?!!?%!%%%!%%%?%%%%%!!%%!%%?%!!%%!?%%%!%%!%!!!!%%%%%%%%!??%??!%%!%!?%!%!?%%!%%%%??%!!%!??!!!???%!%%%?!!%!!!!?!%%!%%%!!%?%%!%!?%%%%%!%%%!%!%%!%!%%%??%%%%!%%%!%%%!!!%?%?!?%%%?!?%%!?%%!%!%!%%!%%%%!?!?!%?%%!%!%?%!%%%%!!!!?%%%??%!%!%%%%?!%!!%%!%!!???!!%%%?%%%!!%!%%%%%!!!?%!!%%%%%??%%!%!%?!%%!!%?!!%!%!%?%!%!!%??!%!%%!%?%%%!!%!?!!%?%%%?!!!!%!!%%%!!%%%?%!%%%!?%%%!!?%??%?%%!!%!!!?!%%%!!?%!%!??!!%!!%%%?%?%!%%!%%%%%%!%!%!!%%%%!%%!%%%?!%!!%?%!?%%?!?%%%!%%!%%!%!!%?%?%%%%%%!!%?%%%?%%?%%?%%%?%?!!!!!%!?%%!!%?!%!%%%?!%%%!%%%!!!%%!%?%%!%!?!!%!!%%%%!!!%!%%!%%%!?%%%%%%%!?%!!!?!!?%?%%!%%%?!%!%%?%%%!%?%%%?!!?%!!%!?!%??%%!%%?!%%%!!!!%%!%%%!!!%?!?%!!%%%!%%%!%%!!!%!%!?!!%%!%!%!%%%??!%%!??%%%%%%%?%!%!%%!%?!%!%!!%%!?%!%!?%!?%?!%!%!%%%%%!%%!%!%%%!!!%??!%!!%!!%?%%?!!!%%%??!%!!!!%?%!!?!%!%%%%!%!?%%%!!!!%?%!%!?!!%%%%!?%%%%%!%%!%??!%?!?!%?%%?%?!!%%%%!%?!!%%!!%!?%!%%%!%%!%%??%%!%%%!!!!!%!%!?%?%%%%%!%%?%!?!%!%%?%%!%!%!!%??!%%%%%%%%%?!%%%????!?!%%%%?!%!%!%!!%!%?%!%!!%??%%!!!!%!!%%!%%??%?!%!%!!?%!!%%%%%!!%!!!%%%%??!%!%?%%!%%%!!%!%!%%?%%%%!%%%%%%?%??%%%%!!??%!!%!!!%!!%?!?!!%?%?%%??!!%?!%?!!%?!!%?%!???!%%!!!?%%%!!%!%?%%%!!%!!?%%!?%%!!%%!?!%!?%%!%%%%%%?%!%%%?!%%!%%!!%%%!%%?!%%%%!!%%%%?%!?!%?%!%%!!%!%%!!?!!%%%!%!%?!!!!??%%?%%?!%%!!%%!%%%!%%%!?!%%%%!%%!%!?%%!!%!%!%%?%!%%%%%??!?!%?%%!!%?%%%%%!%??!%!?%%%!!%??%!?!%!?!?%!%!%!%?%%?!!??%??%%??%%!%%???!!?%%!!?%!%%%!!%%%%%%?%!%%?!%%%?%%??%!%%?!%?!%?%%!%%%!?%!!!!%%!%%%?%%%%%%!%%?%??!!%!?!%!%%%!?%%!?!?!!%!%%%?%!!!%%?!!%%%%%%!!!%%?%%%%%%%!%!!%?%%!%%?!!?%%%!?%?!?%!%???!?!%%!?%%%%%?!%?!!%!%%%%%!%%%%?%!%!%?!!!%%%%??%%%!!?!%?!%%!%!%!%?!%%!?%?%%%!?!%%!%%%%%%%?%!!%!%!!%%%%%%%!?%!?!!!%?!%%%%%%!!??!%??!!!!!%?%%!%!!!%!%!%?%%%!%?%%%%!%%%%%!%%%%%?%%!!%%%?%!!!%%%%%%%%!%%%?%?%%%%!?%?%%??%!!%%%?%%!%%?!%!!%!!%%!!!%!?%?%%%?%%%?!??%%%%?!%%!?!%!%!?!%%!!!%%!!%!?%?%!?%%!!!%%%?!!!%%%?%%!%%?!!%%?%%??%!%!%!%!%?%%?%%!%!!%%%?!?%!%!!%!%%%%%!%!%%?%%%!%!%?%!!?!%%?!!!!%?!%%!!%%%!%%%??%%%?!!??%?%%%!!%%%%!%%%!??%!%!%!%%!!?!!%%!!%!!!%%%%%?!%!!%%!?%!%%%?%%%?!%!!!%!%!!%?!%%%%!%%%%%%!%%!!%!!%!!!%%!%!?%%%%???!%%%%%%%!%%!%%!%%?%%??!%%!%!?%%??%%%!%%?%%%!%%!%%!%%%%?%%!%%!!%%%%%?%%??%!!%%%%!!!%%!!%%%!%%%%%%?%%?%??!%%%!?%?%%%!%?%%%%!%!?%!!%%?%?%????!%%!%?!%%%!?!%!!!!%!?!%!?!?!%%%!?!%%%!???!%%?!!?%!%%!%!%%!%%%%%%%?%%?%%%%!?!%?%?!%?!??%!%!!%%?!!!%!%!%%%%!%%?%%!%%%%!%!?%!!%?%!%%!%%%%?!!%%%%%?!!%!%%%!%%%!%?%!?%!?%!%%?!!!%%?%%%%?!%%%%%%%%%?%%%??%%%%%%%%%%!!%%%%%%%%%%!%!?!??%!%!!%%?!%%%%?!!!?!!%!%!?%%%%%%?%!%!!!%%!%%!!!!%%!!!???%!%!%!!%%%!!%%?%%!%?!!??%!!%%?!%?!%%!!!%!%?%???!%!%%%??%%%%%???!?!!%%?%!?%?%%!!?%!%%%%!%%%!%!?!%??!?!?!!%?!%!?%?%?%%%!%%!%%??%%!%??!?%!?%!%%!%%%%??%!%!%%%%%%%?!!!!%%?!!!!!%%%!%!%?!%%!!%??!!%%%%!%%%%%%!%!!%?%%!%!!%%!?!%!%%%?!?!!%?%%%%?%%!%?%!%%%%%%!%%!??%?%%?%%!!!%!%%%?%%!!!%!?!%%%!%%?%!?!?%!!!!%%!?%%%??!!%%!!?!?!!%!!!!!%!%%!%?!%%%%%%%?%!%%%?!!%??!?!?%%!?%!?!!!%%%%%%%?%??%!%%%%?%?%%!%%%%%!!!%!%%!%!??!!!%!%!!%!!%?%!!%%%%!!%%!%?%%%%%%%?!?%?%%?!%%!!%?%%%!?%!!%%!%%!!%?%?%%?!!!!???%%%!!!%!!%%!%%%!?!?%%%%?!!!!%%%!!%?!%!%%%%%%!%%!!%%?!%%%?%%%%?!!%%!?!%%%%!%%%!!%?!?%?%?!%%%%%%!!%!%%!%%%!%??%%%!%?%%%%?%!%%%%%!?%%%!!%!%%?%%%%!%?%!!!!!!!?!!!!?!!?%?!%%%!!!?%%!?%!%!%%?!%%!?!!!?%%%?%%!%%%%?!%%!!!!%!!%%%!%%?!%%%%%!!?%?!%!%%%%%!%!%%%%%%%%%%!%?!%!!%%!!%!%!!%!!%%!%?%%%%!%%%!%%%%!?%!!!!?!%%??!%%%!!%!!%%%%%%%!%!%%%!!%!!%!%?!!!%%?!%!!!?!?!?%%!%?!!!%%%??!%?%??!?%!!?!!!%%!%%!%%%!%??%%%!?!%%%%!!!%%!%!%!%?!!!%%?%%!??%!!%%?%?!?!%%!?%%!?%%!!!%!!!!%!!???!!?%%?%%%%%%%!%%%!!!!%??!%!?!%?%??%!%!?%%!%!%%%%!%?!%?!%??%%%!?!??!%%%?%%!!%!??!?!!!?%%!%?!?!%%!?%%?%!%!%%?!?!!%?!%??%%%%%!!?%%?%?%?%%!%!%?%!!!!%?!!%!?%%?%%%%!%!?%!%!%%?%%?%%%%!%%!%%?!%?!%%%%!?%?!!!!!%!%!%!?%%?!!!%!%!!%%!%?%!%!!%!?%%%!!!%%%!?%!%%!%%%?%%!!!%!%?%%%!%!?%%%!!%%!??%%%?!%!%%?!%?%%!%%!%!%%!%?!%!!%!!%!!!?%?!%!%!%%%%?%!?!%%%!?!%%%?%?!!!%%%%%%%!%%??%!%!%!?!!%%!%!!!!%??%%?%?!%?!!%!!!%!!%%%%%!%%%%!!%?%!%!?%%?!%????%!!%%?%!!%!%%!%%%!%%%%???%%%!%%%!!!!!%!?%?%??!?!%%!!!%!?%!%%%%!%%%%%!%!!?%?!%%%%?!!!?%%%!%%%%%%?!?%%!???!%%%%%%!%%!%%%%%%!?!!%!!%!??%!!!%?%%%!%?%!%%%?!!%%%!!!!!%?%!!!%!%%!!?!?%?%!!%%?%!!%%%!!!!!!%%%!%!%%!%%%?%?%!%%!%%%!%?%!?!!%%%%%!!%%%!!%!!%%!!%!!%!!%%%%%!!%%!%!!%%%??!%%???!?!%%%!%%?%%%%!?%%%!%%!%%!%%!!!%!?%!??!?!%!%!??%!%%%!?%%%%%%!%%?!%?%%!?%%%%!!?!?!!%!%%%!%?!%!%!%?!!!%%%%?!?!%%?%!!!?%%%%%!%%%!!!%!!!!%!%%!%!%!?%?%%!!%!!!%%%%%%%%%!?!%%!%!?!%%?!%!!!%!%%?%%!!%??!%%?%!!?%%%%%?%%!%%!!!%?%%%!!%!%%%?!%!!!!%%%%%!%%%%?!%%%%!%%%%%!%%!%%!%%!!!!%%??%??%!!%?%!?%%%%!!!%%?%?!?!%%%%??%%%%%!%%?%?%!%%!!%%%!%!?%%!?%?%%?%%!%?%%!%!%%%!!?%?!!!!!?%!%%%!%!!%?!!?!%%%%%!?!!?%%!%!%?!%%%?!%%%%?!%?!%%%%%%%%%%!!%%%%!?%!%!%%%!!%%%%???!%%?!?%!!!%!!!!?%%%!!%!?%?%!%%%%%?!!%?%?!!?%!%!%%%%??%?%!!!%%!%%!!%%!%%%%!!!%!%?!%%%!%%%!%%!?!%%%?%%?%%??!!!!!%%?!?%%%!!!!!%!!%%!%?%%%?%!%!!!%%%!!!!?!%%%?!%%!!!%%%!?!%!?!!%!!!!%!%%!!%?%%%!%%?%%%??!%!!!!%!!%%?!%?%%%%%%!!%!%%?%??%?%%%%!!!%%%?%%%%%!%?!%!!?%!%!%!%%%%!?%%%!%%!%!!?!!!!%%?!%!%!%%%!?%%%?!!!!?!!%?!%!%%%?%!?%%!%%%!!??!%!?%!!!%%!%%%?!%%!!!!?%!!!!%%!!%!!%%%%?!%?!?!!?%?%%?%%!%!!!?%%!%%%?%!%%!%!!!!??%%??!?!%!?!!%%!!%!%!%!?!%%%%!!!?!!!?!!%!?%!?!?%!!!%%?%%!!%!%%!?!!!!%%!%%???!%%%!%%%!%%%?%%%%!?!!!%%%%%!%!!!!%%%!!?%%%%?%!%%%!%%%!%?%!%%!?!!%%%!!%!%%%%?%%%%%%!!%%!!%%%?%?!%%!!%%%?%??%%??!%!!!%?!!%%%%%%!%!%?!?%?%%!!?%%%%%%!%!!?%%%?!!!%??%?%%!!%%?!%!!%!%?!%?!??%!%%?%?!!%%!%?!!%!%%%!?!%!%%%?!!%?!!?!%%%???%?%??%?%%%%?!%%!!?%?%?%?!!%!!%%%%%%%%%%?!!!?!%%%!%!!%???!%%%?!!!?!%???%!??%%!!?!%%%!?!%%%?%!!??!%?%%!%%%?%%!!%%?%%%!%%!?%%?!%!%%%!%?%%%%!%!%!%%%%!%!!!%!??%%!!%?%%%%!!?%!%%%%%%%%?%%?%%!%!%?!%!?%%%!%!?%%%?!%!!!%?%%%!%%!??%!%%%%!%?%%%%!%!!%!%%?!%%!?%%!%%?!%%%!?%%%?%%%!%%%%!?%?!?!!%!!!%???%%!?%?%!?%!?%%%%?!!!%%?%?%%%%?%%%%%%?%?!%%%!%%%!!%?%%%!%%%%%??%!%%?%!!!!!%!%!??%!!%%%!%!%!%%%?%?%%!%!!?!!%!%%!%%%!%!%?!?%%%!??!%!%!?%%!?%!?%!!%!!%!%%%!?!!%%?!!%!!!%!%%%!!%?!!!!%%%%%%%!!%%%!%%%%!!!!?!%%!??%%%?%?!%%!!!%?%%%%!?!!!%%%!!%?!%?%!!%!!%!!!!%!%!!%!!%!%!!%?%?%%%%!??!%%%%?%??!%%!!!?%%!?%?%!?%!!!%?!!!!!?%%%%??!%%?!!%%%!!%%!%!%!%%%%?%%?%%%%!!%!!?%!?%%!!%!?!%%!!%%%?%%!?!!%!!%%?%%!%!!%!!%?!%!%%%?%!%!%?!%!%?%%!!%%!%!!!%!?%!!%%%??!%%%?%%%?!%%!%!%!%%%%%%%%?%?!!%%%?%!?!!!%?%%!%!?!%!!%%!!!!%!%%!%%%!!!%!!%%!%%?!?%!!%%!%%%!%%?%%??%?!%!%%%%!%!%%%?%%%%%%!!?!%!?!%!%!!??%!!%!%%%??%%!!!?!!%!%!%%!!?!?!!!!%?%?%%%?%%!%!%!%?!!?%?!%?!%%%%%!!%!%%!%%!%!!!!%?%%%?%%!%?!%!!%??%!?!%!!!?!!%%!!!%%?%%!!!%%%!!?!?!%%!%%??%!!?!????!!%%%%%%%!%?%%?!%%!%%%!?%!%%%?%!%%%?!!?!!%!!%%?%%!!%!!%!??%!?%%!%?%!!%?%!%%!%?!?%?%?%%%%!!%%?!?!!%?!!!!?%!%%!!%!%?%%!??%!%!!%%%!!!!%%%!%!!!!%%%%%%!%%!%%!%%%!%!!!%!!!?%%%%?%%?!%!?%!%%!%%!%%!%?!%?%%%%!%!?%!?!%%!%%%?%%!%%!%!?%?%?%%%%%!!%%!%!!!%%?!!!!%!!!?!?!%!%!%!%!?!%!%?%?%?!%!%!!%%%%%%!%%%!%%!%!!%!!%%?%%?%%!%%%%%!%%%%!!!%!%??!%%!?%??%!!%!!?%!?%!%%%?%%%%??%%%%%%%!!!%%?%!%%!%%%!?%!%!?%!%?%%%!%!!?!%%%%!%%%%!???!!!%%!!?!%!%%!%!?%?%%?%%!%%!%%%?%%!!!!%?%!!%%!!!!%!%!%%!%%%!!%?!?!%%?%?!?!%??%%?!?%%!%%%%?%%!%!%%!?!%?%?%%%!?%%!%%%?%%!!!?%%!?%%?!!?%%%%%!%?%%!%%!?%?!!%%!%!!%%!!?!%%%%%?!%!%%!!%%%!%%??%%%%%%!%%?%!?!!%!?!%!?!%!!%!%!%?%%%!%?!%!%!%%%%!%%!!??!!%!%?%!%%?%!!!!%%%!!!!!!!%??!!%!!!%%%!%%%%!%%%%%!%%%!%?%!%%!%%!%!%%?!%%%?%%?!%%%%!%!!!!%%!%!%!!!%!!%%???%!!%%!!!!!!!!!%%%%!%!%%?!?%%%!%!!!!%!%%?%%?%%%!%?!?!!%!%!%%!!!%!!!%!%%!!%!%%!%%%!!!!?!%!!!%%?!!!%!%%%!%%!?%%%%!%!!%??%%!!%%!%!%%%%!%?%?!%!%!%%%??%%%%!!?%%!%%%%%%%%%?%%!!!?%%%%??%%%!%!??%%%!%!!!%%?%%!!!%!%?%%!?!!%%!%%%%!?!!%%!!?%?!!?%%?%?%%?%%!%%?!%%%%!%%!%!%!%!?%?%!?%%?!??!%!!!!!?%%%%%?!%!%%%%%?%%%!?!%!%?%%%!!%!%!%??%%!%!%?%?!?%?%%!?%%%?%?!!!?!%%!!%%!?%!?%%!%%!!%%%%!?%!??!!?%?!%%%%!%%!%%!!%%%!!!!!?%!!%%!%!%?%%%!%%%!?%%!!%%%!!%!?%%!%?!%%!?%!%%%??!%?!%!%%%%%?%%%%!!?%%%%%%!%!%!%%!%%?%%!%!??!!%?%%%?%%?%%!%!%%%%%%%?%?!?%!?%!!!%?!?%!?%%%%?%%!!%!!!!%%%??%!%%!??%%%%!!%%%%%%?!%%%%?%?!?%!?%!%!%!!!!%%%!?%?%%%%!!!!%!%%%%%?%?!%!!!!%!!!!%!!%!!%!%%!%%?%%!%?!%?%%%%!%?%!%!%%!!%?%!!!??%?%!%%%%%??!!!!%%!%!%!%%!!!?!!%%%?%!!!!%!!!!!!%!!!%%%%!%?%!%%!%?%%%?%%%?%%!!!?%!%!!%%??%%%%?%%%%%!%!%??%!?%?!%%%%!!!!??%!?%%!?!!%?%!%!%%!%?%%%?%!%%%%%%?%%!%%!?!%%%%%!?%!?%%!%!%!!%?%??%?%!???%%??%!%!%!!%!!%%%%!!?%%!!!!%?!%%?!!!!?%!?%%%??%%!%?%!?%%%!%?!!!!!?%!%!%%%!?%!?!?!!%%%%!!!%!%??!!%!%%%!%!!%%!!?!!?%%!%!%%!%%%!%!!!%!%??%%!!%%%!%%%!?!!%!%!!!!%%??!?!%%%!?%%%!?%!!%%!%%??%!??!%?%!%!!%%!%%!%%%%?%%!!!!?!!?%??%%?%%!%%!??!%%!!!%!%?%%!?%!!%%%%!!%?%!%%?%!!%!!%!%?%%!!!%%!??!?%!?%!!%?!%!!?%!?%%!%!%!%%%%%%%?%!%%%%%%?%%!%!%%!!%%?%%!%%???%%%!%%%!%%!%%!%%%%%%?!!%!%%?!%?!%?%%!%?%%!%?!!%?!!%??%!?%?!!!!%%!!?%%%%?%?%%!%%%!%?%%!??!!%!%%!!???!!!%%%!%!%%!!!!%%%?%?!%?!%?%?!!%!?%!%%?!!%?%%?%!%%%%?!??%%%%%?%?!%%!%!?%?%!%%%%!%!!!!%%%%%!%%%%?%%%!%?%%%!%!%%!%%!!?!!?%%!%!!%!!%%!%!%??!%??%?%%!!%!%?!%%%%%!%%!?%!%%??!?%?%%%!%%%%!?%%%!%%%%%%%%%?!!!!%%%!?!?!!!%!%%%%%?%%!%%?!!!!?!%%!%!!!!???%%%??!%???!%!%!%%%%%%%%%?!!!!%!%%!%%?%%%%%!%%%%!!!?%%!%!!!!!!?%!%!!%%%%!!!!%%%%%%?!!%%!%!?!%?%%!%%%!%!%%!%%%!%%%%%!%%!%!%%%!%%%!?!%%!!!%!!?%%%%?!%%!%!!%!%%?%%%!%?!%%%!?%%!%%%?%%!%%%!%%!%!%!?!%?!%%%?%%%?%!%%%%!?%%%?%?!%%%%%??!%%?!%!%%?!!?%!?%%!!%!!!!!%%%!!!?%?!%%%%?%%!%%%?%!!!%%%%?!?!%??%!!!%!%%%!!%%%%!%%!%??!!??!%!%?%?%!%!%%!%!!%??%%!%%!?%%%%%%%%%!%?!!%!%!%?%%?%!!%%%%%!?%%%!%%%?%%%%?%!%%%%%!!?!!%%%%%%?%%!!%!%%%!!%!%%%%%%??!?%%!!!%%!!%?!??!?%%%%%?%%%?%%%%!%%????%!%?%%?%!!!!%%?!%!!%%%!?%?%!?!!!?%%%%!!%!!?!?%%%%!%!%%?%%!%!!%!%!%%!%%%!!%!??%%?%!??!!?!%!!%%%!%!??%%%%!!!!!%%!?!!!?%%%%%?!!!%?%%%%?!%%!%%%!!%%%%!%!%?!%!%?%?%%!!%???!%%!!%!%%%??!?%!!?!?!?%!!%%%!?!?!%!!%!!!%?%%%%%%!%?!!!%!?%%!!!!%%%%%%%%?%%%%%%!%!%!!!%%?%!%?%?%%!%!%%%!%%!%!%%!!%!!%?%??%%!%?%??%%?!?!%%!?%%%!%%!%%!!%%??!!%!!?!?%%%!!!%%!%%??%%??!!%!?!!%!!!%!!?!%?%%?%?!%!!!%!!%%!!%!%?!%%%?!!!%%%%!!%%?%!!%%!%%!%!!!?!%?!%%%!!%!%??%!%!!?%!?!%%%%%%%%?!%%!%%%%%%%%%!%%%?!%?%%%%%!%?!!!?%!%%%%%%%!!?!%%%%!%%!!%!%%%%!%%!!!?%?%%?!???%%!!%!!%%%!?%%%!!%%!%???!?!%%!%!%!?%%%??%%!%!?%%%%???%?%%%!!!%%%!%!!!?%!?!%%!%!!%!%!?%%!%!!%%%!!?!!!%!%%!%!!%%!%%?!%!%??!%%!%!%!!!!%%%%%%%?%%!%%!?!?!!%%!%!%!%%?%%%!??%!!%!%%%!%%%%!%!%%!???%!%!!!!%?!%!!%%?%%%!!%!%%%!!%!!!%%%%??%!%!%?%%%%%?%%%%!%%%%%%%!%!%?!?%??%!%%%!%?%?!!%%%%?%!!?!%?%?!%!!!%?%!%%%%!%!!%!?%!!%!!%%!!%!%%?%%%%!%%%!?!%%%%??%%!%%!!%!%!?%?!!!%!?!%%%%?!?!!?!!%%!!?%!!!%!!%%%!?%!?%!!%!?!!!%%%%%%!!?%!!!!%?!!%!%!%!%%!!%%!%%%%?%!!?%%%!%?!%%!!!!!%!%%%?%%!!%!!!%?!%%%%%?%%%!%%??%%%!!?!%%!%?!!%%!%%%??%!!%%!%%%%%!?!%%?%!!?!%%!!?!%?!%!%??!%??!?!%?%%?!!%%?%%%%%%?!!%%!%??!%?!?!%%%%%%?%%%?%!%%%?!%%%!!!?!!?%!%??%!??!%!%??!!%%%%%%!!!!%!%!!!?%%%%%%??!!!!!%%?!%%%???%%%!%!!%%%%!%!!!?%?%!%%?!%%%!!%?!!%%%%%%%%%%%%%!%!%%%%?%!!%!!?!!!%%%%!%%%%%%%!%!!%!??%%%!!!!!%!!%%?!!?%%%?%!?%?????!%%%%!%!!?!%?!%!?%!!!%%%%%!%%?!!?!?%%???!%?!!!%!%%!!?!!%!!%%%?!?%!%%!!!%!!%%%!%!??%%%??%%%%%!!%%?%%!!??!%%!%%%%!%%?%!%?!!%!%%%%!%%%!%!??!??%!%!!%!!%%!!!?!%!%%!!!?%?!!!%%!?%%%!!%?!%%?%%%%%%!%??!!%!!%%?%%%%%?%!?%%%?!!%!%%%%%!%%??!!%%!?%%!!!!%!%%%%!!!%%%%!!?!!!%%?!%%!!!%!!%!%%!?!%%%!?%?%%!%?!%!!!!?!?!%%!!!!?%!%%%?%%!%%%!!!%??!!%%!!%%?%%%??!%?%%%?%%?%%%%%!%?%!%%%%!%%??!!!??%%?%%%%%!%!??%%%%!?%%%!%%%!%!%?%%%%%!%!!%!%%%!?%%!%!?!%?!!%!%!??!!?%%%%!!!%%%!!%%%%%%!%%?!!%!!%%!?%%%%!%!?%?%%??%%?!!!!%!!%!%%!?%?!??%%!?%%!%?!%%?!!!!%!?%!%%%%%%%!?%%%%%%%!%%!%!%%%%?%!%??!?%!%%?!%%!!%%%?%!!%?%!%%!%%%!%%%!%%%!%%%?!%%%!?!%%%!!?%!%?!!%!?%%!?!%!?!!%!!?!%!%!%%%!!!%??%%!%%%!?%??%%%?%!%!%%%%%!%%%!%!!%!?!!%!!!?%%??%%%%!%%%!%!%!?%?%%%!%!%%%!%!??!!!!%%??%!%%%%!%%%%%%%%?!!%%%!%%%%?!%!!!%%!%%!%%!%!%%!%%%%???!??%!%%%%%?!!!%%?!!!!!??!%!!!??%!!?!!%%?!!!%!?!?%%%%%?%!%?!%!%%%%?%!!%!!!?%%%%%!%!%%!??%%%%!%!?%?!%%!!?%%%!!?!!!?!%!%%!%?!?!?%?!%!!!?%%%?%%!!!%%!!!?!%%!!?%%%%%!??%?!%%!%%%%%%%%?%%?%%%!??%?%!!?!%!!%?%%%!?%!!%%%%%?%?%!%%!%!?%%%%%%%%!!%%?!%?%!!%?%!%%!!%%%%%?%!%%!!?%%??%?!!!!%!!%%%%?%??%%%!??%!?%%!!%!%%%%%%!?%%%!?%?%!!%%%!%%%%!??!!!%!!!%!!?!!!!!?!?!%!%!%%%%%%??%!%!%%%%%?%?!!!%%%%%%%%%!%%!%?%%%!!!?%%!%%%%?%%!!!%?%%%!%%?!%?!!%%%!%%%%%?%%%%?%%%?%%?!?%!%%%!%?!!%%%%!%%!?!!?!!!?%%%%%%!%%?%!?!!??!?%%%!%!%!%%%!%!%!%!%%!%%%!??%%%%%%%!!?!!!!%%!%%?!!%%%?!%%%%!%?%%%!%%??!%!%!%!%%%%?!?%?%?%!?!%!!?%??!!%%!!??%!?%?!%%!?%?!%%%%%!!%!!%?!!%%!%%%%!!?%!%?!?%!!!%%%!%!!%%!!%!!%!%!?%%!?!%%%%%!?!!%%%%%?%%!!!?%?!%%%!%!%%%%!%?%!!%!%%!%%!%!?%!%!%!!%!%!%%!!%!?!%%%%%%%!%!!%!%%%!%%?!?!%%?!?!?%%!%%!%%!%?%!%!%%??!%%?%%!%%??!?%%!%%%%%%!!!%%%%%%%!%!!!%!%%%?%%%%!?%!!%%%!!?!%%%%!!!%%!!%%%!?%!%%?!!!?!!%%%!!%%%??%%!%%?%%!!%%%%%?!?!?%?!!?%!%%!%%%!%!%?!%%%!?%?%!%!?%??!%!%%!%%%%%%%!%%!%?!!!!?!!?!%!!!%!%!??%!?!!%%%%!!%%?!%%%%!%%!%%%!%?!?%!!!%%%%%%!!!!!%%?!!!!%%%!%%?%%%%!%%?%%?%%%!%%!%%%?!!%!?!%!%!?%%%%!?%%%%%%!!!%!!!!??%?%%%!%?%%!%!?!%!?%%!%?%%%%!?%%!!??!%%%?!!%%%%%?%!%!%%%%!!!!?%%%%%!!%!!%!!!%%%!!!!%%%!%%%!!!%%%!%?!!?!%!%%%!%%%!%%%%%%%!!!%!!%???%%%%?%%%??!%%%%%!%?%?!%!!%!%?!%%?%%!!!%%%%!%!!!%!%%%??!%?!%!!!%!%%?%!%!?%%%%?%%%%?!!%%%?!?!%%!!%%%!!%%%!?%%%?%%%!!%!?%!%?%%%?%%!%%%!%?!%%!%%%?%%%!%%!!!?!%!%%%%!%%!?%%%!?!%%%%%%!?!!!!%%?%?%!!%%%%%?!%?!%??%!?%%%%%?%?%%!%?!%!?%?%%%?!!!%%%%?%%!%%!!?%!%%%%%%%%%!!!!?!?!!%%%%!!%!!!?%!??!%!%%?%!!%!?%!?!!%!!!?%!%!%%%!%!?%!??%!?%%!%!!!?!!%!!??%!!%?%?%%%?%%!%!%%!!?!%?%!?%?%%!!%!%!!%%!?!!%%!%%%!%%%!!%?%%%!%?!!%%%!???!%%%%!%%??!?!%!!%%!%%?%%%!%%%!!%%%?%%%%?!!!!!%%?!!!?!?!?%?!!!%%%!%?!!!?!%??%%!%??%!%??!?%!!%%!%%%%?!%!?%%%%?%?%!%%%%%%%%??!!!%%%%%%?!%!!!%?%%!%?!!?%!%%!?!%%%!!%%%!!%%!%?!%%!!%!?!%%!%!!%%%%!!!%!%!%%%??%?%%%%?!!%!%!%%%%!%!%%%!%!%!%%%%!?%!?!%%%%%%%%!%!?%?%%%??!%!!!%?!?%%%%%!%%%?!?%?!%?!?%%?!!!!!%%%%!%%??%%%?!??%?!%!%%%?!%!!%%%%!!%%!%!!!%!%?%!!!%!?!?!!%?%%!!%??%%%!%!%!%!!?!%!%%!!%!!!%?%?%%?!%!%%%!%!%?!%!!%%%!?%%!%%%!!%%!?%??%!!!!?!!!%!%?%!%%!%%%!!%!!!?%?!?%%?%?%!%?%%%%%?!%!%!!?%%%%!%%!%%!?%!%%%%!%!%%??%!!!!%!!%!!%%!%%!!%%!%%%?!%%%%%!%?%%?%%%!%!%?%%%!?!%?%!%!%?%%?%%%!??!!!%!%%%%%?%%%?!%!?!%%!!%%%?!%%%!%?%!!%!!?%%%%!!?%?!%?!%%%!!!%%%%!%%?%!%%!?%?!??%%!%%%!??%%%!!%%!!%?%%%%%%!?!!!!%!?%%!?%!?%%??%%!%%!?%!!!%!%!?!?%!%%%?!%!???%!%%%!!%%??!?!!%%?%%!!%!!!?%!!?%!%!%%!!?%!!%%!%%!?%???%%?%??!%!!%?%!%%%%%!!%%!%%!!%!!%%!!!%%%!!!%???!%%%%!?%?%?!?%!%%!!%%%%?%!%%?!%%?%%?%!%%!%!%%!!!?%!%%!!%%%!!!!!!!%?!!%?!%%!!%%?%%??%!?!?%%?%%%!!?!?%!%%%%!!!?%%%!!!%!%%%!%!?%!?!%%!!%?%%%%!!!%%%!%%%%%%!%!%!!?!%?!%%%!%%!!?!!%%!%%??%%%?%%!%??!!%%%%!!%!?%%!?%%!%%%%!%%%%!?%%%!!!?%!!%!%%!%!%%?%!?!%%%!%%%!%!!%%%%%%!?%%%!%%?!?%%%!?%!!?%!!%!%!!!!?%%?!!?%%%%!!%?!%?%%%!%%?%?!%?%!%!%%%!%?!%?!!%%!?!!%%!!?!?%?%%%%!?!%%%%%!%%%%%%%%!!!?!%!!%?!!%!?!%!!%%!%%%!%!?%%!%%%%%%%%%!%?!!!%!!!%%!!%?%!?%!%%?!%!%%?!!!%%%!%%!!!%%%%!!%!%%!!%!%!%!?%%!%%%!%%%%%?!%%%%%!?!%?%%%!!%%%?%!?%%?%%%??%%%%%?%%%!%%%!!!%?!!%%?%?%!??%?%?%!%!%%%%%%!%%%%%?!%%?!??%?!%%%?%!?!%%%%%%?%!%%%!%!%!!%%%!!!%?%%!%!!?%!%!%?!!?%%!%!%?%%!!!?%!%%!%!%!%?%?%%%%%!!%?%!!%!%%!%!!?!?%%?!%%!%%!%!%!%!%!?!!!!%!!!%%?!%??!%%%??!!!!%%!!%?%!!!%!?%!%!%?!%?!%%!%%!%!%!!%%!%%!%%%%??!%!%?%%%!!%?!%!!!%!!??%%!%%%?!%%!%!%%%%!%???%%%?%!%!!!%%%!!!%%%!%%!%!!%%?%?%%!%!!!?%!%!!!!!?!!%!%%?%?!!%%!%?%?%!?%%!%?!%%%?!!%%?%%%%%?%?!%%!%!!?%%%%%!%%!?%!!%%%%%%!!%%%!%%!?!%!?%!%!%%%%?!!!%%%!?%%%!!%!?%%%%%%%%%!!!%!!%%%!%!!%%?%!%%%%?%%%?!%%??%!%%?%%!!?!!?%%?!!!%!!??!!?!%%!!!%%%?!%%?%%!?%!!!%%%!!%!!?!%%%!%%!?%!%!%?!!!%!!%%%%!?!%?%!%%%%?%!%%?!%!!!?%!!?%%%%?%??%!%%!%%%!?%!%%!?%%%!?!%%!!!?%!!!!!%!??!%%!%%%%?%%%%?%%%!!%!%!!%!%%%?%!!%!!!!!!?%?!!%%%%?%%!%!%!%?!?!!%!!?!!%?!%%!%%%?!%%%%%%?!?%%!%!!!?!%%%!%%%%%%%%!%%!%!??!%?!%!%%%%!%%??%%!?!%!%%%%!%%%?!%%%%!%%??!?!%!?!%%!%%%%%%%?%%!!!?!%%%%%!%%%!%!?%%!!!%%%!%!%?%%!!%!!!!%!!%!!!%?!??!%%?%!!%%%!%%?%?!!%%%%%!!%%%!!%??!%%%%%%%%%%%!%!%!%%!%!%!?%%!!!!%%%!!%%!??!!%%!%!?%!%!?%%%%%!%%%!!!?%%!!?!!%%!%%!!???!?%%?!%?%?%%?%?!!%?%%?%%?%!%%%!%%?!!%%!%?!%%%!%?!%??!%%%?!??!%%!%!!%%!%?!!!!%%%?!%?!%!?%!!%!%%!%%%%!%%!%%%!%!!!?%!!%%??!?!%%?%%%%?%%!%?%%%%?%%%?!!%%!!%%!%?%!%!!%%!!!?%!?%!%!%%!!?%%%?!!!%!!!%!!?!!!!!!%%!%%%!?!!%%%%%%%%%?!%%!!!!%%%!%!!%%?!?%!?!!%%%%?%?%%!!!%!?!%%%%!%!!%%!!%!!!%!%%!?%!%!???%%%%%!!%%!!?!!!?%!%%!!%%%%!%?!%!%!!!!!%%%%%%%!%%?!?%?%?!%%%?!?%%%!!%%%%%!%%!%!?%%%!!%?!??!!?%%!!!!%%!?%%%!!!!?%?!%!!%!%%%%%!%%%!!!%%!!%%%%%%?!!%%!!%%??%!!!!%!?%%%%%%%%%!!!!!!!!%?%!%%%%%%%!!!%%%!??!%?!%!%%%%%%%!?%!!!%!!%%%?%!!!?%!%!%!%%%!?%%%%%!!?%?!!%?%!!%%%!%%??%%?!%%??%??%!%%%%?%??%!%!!%%%!!!!??%!%?%?%?%%%!?!!%!!!!?%!??%%%!!!%!!!!?!!%!!!!!!%?%%!%%%%%%!%!?!!!%%%!%%?%%!!!%%%!????%%%!!%%!!%%?%%%?%!%!?!!!!?!%!%%%%%%??%!%!%!!?%!!%!!%?!!!?%%!!%%!%!?%!%%%%%??%!%!%?!!!?%?%%%!!%!?%!??%%%%!%!?!%?%%??%%%!!??%%!?%%!%%!!!?%!%!%?%%!?%!!!%?!%!!!!%%%%%%!%!%%?!%%%!%!%?!!%!?!!!??%%%!%!%?!??%%%!!?%%?%%!%!%!!%%?%%%%!%?%%%%%!!!%!%%!%%%!%%%?%!?!%%%%!!%%%!%%??%!?%%!%!!%%%?%?!%%%%!%!%%?%%!%%%!!!%%!!%!!%?!!?!??%%!!?%!%??%!%%%!%?%?%%%%!%!!%%!%!%!%%%?%%%%%!%%%!!%%%!%%!?%%%!%!?!???%!%%!!%!%%%?!%!!%!%%%%%!%%%%%%!!?%?%!!%!!%?%!!%!%?%%%%?!?!%!%!%!!?!?%%!???!%!!??%!!%%!%%%!??!%%%%!%?!%%%%?!!!%%?!%?!%?%%!%!!%%%%%!%%?!%!!!%!%%%%%%!%!!%%%!%%%!%%%!%%%%%!%%%?%!%!%?!!%!%!???!%?%%%%?%!?%!?!%!%%?%%%!%%%!!??!?%?!%!!%%%!%!%!!!%?%%%!%%?%%%?%%?%%!!?%?%!%%!!!%%!!%%%?%!!!%!?%!%?%!!?%%%%%%!!%%%!??%!%%%!!!?%!%?!%%!!!%%!?%%%%%%!%%!!%!!!%?%%%%%%!!!%!!%%%%%%!!%!!%%%%!%%%%!%!?!%%%%?!%!!!%%%%%!?!%%%%%%!?%!%?%?!!%%%?%%!??%!??%%??%%%!!%!!!%%?%%%?!%!%%%!%%!!%!?!%%?%?%%%!%%%!!%?!%%?!!%!%!!!%%%!%%?!!!%%%%?!%!%%%%!%%?%?!!%%??%%%%%%%%!!%!?!??%!%%!%%?%!%?!%%%%??%?!%%%%!%%!?!?!%%%%%??%%%%%%?!%!%?!?!%?!%?!!%%%!!?%%!%%%%??%?!%!%!%??!?%!?!!!%%?%%?%!%%%%%%!%!!!%%?%%%?!?!!%%%?!%?!%!!?%?!!%%%%%%%%?%%%?%%?!!!%!!?!!%?!!?!??%!!%!!%!!!?!!%!%%%!!%%!!?!%!%%!%%%%?%!?%!!!%%?!%%?%%?%%%%%%%%%%?%%%%%%!?%%?!%%%%!%%!%%!%%!!%!!!%%!%??!!%!!?%%%%??!%!%?%?%%%%!!??!!!%%%%!?!?%%!%!!!%!?%%!%?%%?!!!%%%%%%!!%?!%%!?%%%!%?!%??%!!%%!%%%!?%%!%!!!%!%%!!%!%?%%!%%!%%%!!%?%!?%!??!%?!!%%!!%!%%?!%?%?!!%%!%%!%%%!%%%%%?%%%%%?%!?%!%?%!??%!!!!?%?%!%?%%?!?%!!!!%%!%!%%%?!%!!??%%!%?!!%%%?%!!%!%%%%!%%%!??%?%%??%?!%!%!%!%%%?!%%%%?%%%!!%%!!%%%%%?!!%!!%%!%!%%?!%!?%!!?%%!!?%!?!!%?%???!%%%%!??!%%%!?!!%?%%!%!!!%%%!!?%%!%%%%%%%%%??%?%!?!%!!!!%!!!%!%!?%%%!%!!%!%!!%%!??!%!%%!%!!!?%%?!?%!!?!!!%!!???%%%%%%%%%%%%!%!!%%%%?!!!%%!?!%?!%%?%%%!%%%%!!%%!?%!%!!%?!%!!%%!?%!?%%%%%%!%!%%!%%!?%%!%!!%!%!!%%!!%%%%%!!!!!!!!%?!%!!%%%!!!%%%!!%%??%!%%!?%%%!%!!%!?%!%!%!%%!??%%!!!?%%!%!!%!!?%?!%!%%%?!%%%%%%???!!!%%%%%!%%!%%!?!??%?%!!%%?%!%%%!!%!!%!!?!!%%%!!%%%??!!%?!%!%%?!!%%%!%???!%%%?%!%%?!?!!%%??!%%%%!%%!!!%%!%?%!%%!%?!?%!?!%!%!%!%%%?!!%%%!!%%!%%?!!!?%!!%!!%!!?!%?!?%!!?%%!?!%?!!!!?!!%%%%%%%!%%%?%%!%%%!%?!%??%!%!!%!!!?%?!%%!%%%%%!!!!!%!%??!!%?!%!%%%%%!?%%!!!!!%?%%???%!%%?%!?%%!%%!%%%%!??%?%!!??%?!%?%%?%%??%!?!!?%%?!!%%?!!%%!!%%!%??!%%?%%!%!!%!%%!?%%%%%%??%%%?!%%?%%?!%%%!?%!%%!!%??%!!!%!!!!!!!%%!%!!?!!%%%!%!!!%!!%?!%?!%%%??%!%!!!!%%!%!%!!!!%%!!!%!%?%%%%%%%%!%%%!%!!?!%%%!??!!!%!%%%?%%%!!!%!%%!%%?!%?!!!%?!%%%%%%?%%?%!!!??%!%?%%?%?!%%%%%%!%!%%%%%%%?%%!%!%%%!?%%%%?!%%!%%!%%%%!%%!%?%%?%%%!%??!%!%%?!%%?%!%%??!!%%%%!!!%%%%%??!!!?%!!?%%%%%?%%!%%%%?!%???%??!%!!!!!%!%%%%%%!!%%!!!%%%%?%%%!%%?!%%%%%!%!!!??%%%?!%%!%%%!!%%%%?%?%?%%%!%?%!%!!!?%?!%%%%%%!!%%!%!!%?%%!%!%%!%?%?%%!%%?!?%?!%?%%%%%%!!!?%%%!?%%%!%?%%%??%%%%%?%???%%%%?%?!%%!%!?%%!%??%!%!?!!!!!!%%!%%!!%!%%%%?%%!!%%%%%!?%%!%!??%?!%%%%!!%%!!?%%%!%!!%!!!%%%%!%?%!%%%!%%!!!!!%%!%!%??!%!%?%%!!?%!%%%?!%!!%?!!%%%!!%!%%?%%%%%!!%!?%%?%?!%%!?!%%%?%%!%%%%%%?%%?%%%%%!!?%%%%!%!?!?%%%%!%??%!%%!!%!!??%%?%%%!%?!%?!!%!%!!%%??!?%%!%%%!?%%%?!?%!!!%%!?%%%%%%%%?%%!??%%!%?!%%%!?!%%!!!!??%!!%!%%%!%%!?!!%%?!%!!%%!%%!?!!??!!%%?%?%%?%?%!!??!!!%%!!%!%!%%!?!!%!!%!!%%%%!?!???%%?%!!!???%%!!%%%%%%%%%!%!?!!!!%?!%%%%!!!!%%%%%%!?%!!%!?%!!!%?%%!%%!?%!%!!%%%?%%!%!!?!??%!?%%!%%%?!%!!!!%%!%!?%%%??!!!%!%?%%%%!?!%?%?!%!%%%%?%!%!!!%!!%!???%!!!%%!%%%!%!%!%!%%%!%!!%%%%%!%?!%!!?%%!%%!%!%%%%!%!!%%?%!!!%%%!%!%!!!!%%%??!!%%?!%!!?!!%%!%!???%!%%!%%!!%%%%%?%?!%!?%?%%%!!!?!!%!%!!?!!?!!?%!!??%%!!%!%?%!%%%!%!%%%!%?!!!?%??%%!!%!?%!!?!!%!%?!?%!?!!%%?!!?%!%?!%!!%%!%!%!????%%!!%%!%!!!!%!%!?%%%%!%!!!%%%!%!!%!?%?%!!%%!!%%%?%%!!!?%%%!%!!%!!!%!%!?%!%!?!???%%%?%!%!!!%%?!%!%%!!%%%!%?%%%%%%!%?%%%%!!!%%%%%%%??!!%?%!%%%?%%!!%%%%?%%!!%!!?%%%%%%?%%%%%!?!!!!!%%%%%%!?%?%!?!%?%?!!%%%%!?%!%!!!?%!%%!!%!!!!??%%%?%%%?!!%!%?%?!%!!%!!%?!%!%?%?!%%??%%%?!!!%%%?!%!?%!!%?%%!%!!??%%!%%%?!%?%!!!??!%!%!%%?%%%%%!!?!%%?%!%!!!!??%%!%!%%!%!!%%?%%%!!%?%%!?%%%!%???!%%?%%%!%%!%!?!%!%%%%%!??%?%!!%?!%%!?%%!!?!!?%%%!!%%%%%!%?%%!%!!%!!%%!!%%%%%%%?%!%!%!!%!%!!%%!%%!?%!%!!!%%!!%%%!?!%%%!%%!%%%!!!%!!?!!%!%!!%%%!?%%!?%%%?%%!??%??!!%?!%%%%!!!%%%%??!%%!?!!%%%%%%!%%%%?!%!!%?%%%%%?%!%%!!%%%%%?%%%!!!%%%%!%%%%!%%%!%%%%%%!!%!%%%%!%%%%!!?%?%%!!%!?!!!?%%%%??%%!%%%!?%%%!?!%%!%!%!!%??!%!!%!?%%!%%?!%!%%!?%%%%!!!%!%%%%%%!!!%!%%%%!%%%!!%!!%?%%%!!%?%%?!!!%!!%!?!%!??%?%!!!!%%%%%??!%%%!%!!%!!%%%!%!!%%?%!?%%!%?!%!?%%!!?%!!!?%!%%!!??%%%%%%%!!!%%!?!?%!!!%?%%%!!%?%%%%?%?%?!%?%%!??!%%!!!?!!!!%!!%%%!%%?!%?!%%!?!??%%%%!%%??%%%%!!%!!!!!!%%!%?%%%?%!%%%!!%!%%%%%!!%?%!!???%?%!?!%%%%!!%!?%!%%?%!%%?%%%!%%%?!!%?!?%%!%!%!!%!%%?!%%%%%!%%%%%%??%%!%!?%?!?!%%%!?!!%%%!%!!%%%%%?!!!%!!%%!!%?!?%!?%!%%!%!!??%?%!!%%%%!?!%%%%!%??!!?!%%%%%%%?!%!!!%%?%%%?%!?!%%%%?%?!%!!%!%%!%%?!%!%%!%%?%!?%!?%%?%%%!!%??%%!!%!!??%!!%?%%%!!?!!%%!???!%%?!!%%%?!!!%?%%%%!?%?%%%?!!%%%?%!?%?!%?%%%!?!%%!%%%%!%%!!%!%%%%!%%?!??!!%?%%!%%!%%%?!!%%?!%?%!%!?!%%!%?%%%!?%%%!?%?%%!!!!?%%%%%%?%!%?!!%%?%%!%%?!?%%!!????%%!%?%%?????%?%!!!!%%%?%!%?%%!%?!%%!!%%!%!?!!%!%?!%?!%?%%%%!%!!%?!!%%%%!!!%!!!??%!%!!%!!%%!??!!?%%%!%!!%%%%!?%!%%!%!%%%%%%%?!%?%?!!?%?!!%!%!%?%!%%!!%!%%!%!%!!%%%%!%!!!%?!%%%%?%!%??%%?%%!!!?%%!!??!!!%%%%%%?%?%%??!!%?!%%!%!%!%%?%%%?%????%%%%%%%!%?%%!!!%%!!?%!???!%?!%!!?%?!!%!%%?!?%%?%!!!%%%%%!%%?!%!!!%%!!%?%!!%%%%?!!%%!%!!?%?!%%%%%!%!%!?!%%??!!!!%%%?%?%??!!!!%!%%!%?!%!%%?%!!%%%%%!?%?%!%!?%!!!%!!%!!%%!%!%%!!!!!%%!%?!!!!%%?!%%%!!%%?%%%%%!%%%%%?!!%!%%%%!!%?%%%%%%!?!!!!%!!%!!!%!?!!!%?%!%%%%?!!%%!!!%!%%!??%%??!!%%%%%!?%!?!?%!!!!%%!!!%!%!!?%?!%?%!%%!%?!%!%??%!%!%%%!!%%%%!!%?!%%!?%%%%?!%?%!!%!%?%?%!!?!%?%%%%!%%%!%?!%%!%%!%%%???!%!%!!?%%!?%%%%%%!!%?%!%!%%!!%!%%%!%%?%!%!%%%!%%%?!!%!!?!!%%!%%%??%%?!!%!?!%?%%!%%%!%!??%!!?!!!%!%!!!!!%!%%%%%%?!!%%!!!%!!!!?%!%%%%%?%??%%?%!%!!!!%%!!%%%%!??%?!?!%%!!%?!%?!%%?%%!%%!!%!!%!%?%%%%!%!?%%!%%!%%%%!!%%%%%?%!%%!!%!!%%?%!%%%?%%?%%?!?%!?%%%%%!%%?%%!%%?!?%!%!!%!%!!%%!%!?%%%?!!!!!!%!%?%?!%%??%?%%!%!!!!%%%?!?%?%!%%%%%?%%!%!!%%%%%?%%%??!%%?!%%%?!!%?!!%%%%?%%%%?!%%!!%%%!!%?%!%%%!!!!!!!%%?%!?%?%??!%%%!%!!%!%?!%?%!%%%!%%%%%?%?%%!!%!?!%%!%%!!%!%%!%!%?%%??%!?!??!%?%%?!!??!!?%!%!%!?!%%?!%%!!%%!%%?%%%!%?%?%%%!%%!%%!?!%!%%%?%%!!??%!%!%?%%%%!!!?%%?%%!%%%%%%%%%!%%%%!?%%!%%!%%?%%%?!%%!?%%%?%%%%!%%!!!!%%%%%?%%!!%%%!%%?%!!%!?!??%%!%!?%%%%%%%!!%!%?%!!%!%?%!%!%%?%?%%!?%!!??!%!%%%%?%%!%%%%%!%%?%%!%!%%!?!!%%!%%%!?%%!!?%%!%!!%?!!%%%%!!%%?%!%!!%%%!%%%?!%!%!%?%%!%%?%?!%%%!%???%%!%%?!%%!?%!%%%!%%!%!%!%%%%%%!%%%%%%!%%!%%?%?%!%!%!!!?%%%!%!?!?!?%%%%%%!!?!%!%???%%?!?%%%%%!%?!?!%%!%!%%?!%!!%%!!!!%%%%???%?%!%!?%%?%!%!%?!?%%%!%%%?%!%%!?!%%!!!?%%!%%!??%!%?%!%%!!%%%%%%%%!%%%%%!%!%!%!!%%!%%?!!%%%!%%%%%%!%!?!!%%!!%%%%%!%%?%!!!%??!%%!%?!!%!!%%%%%%%!%!%%!%%%%%%%%%!!%%%%%?!!%%!%!%%%?%??%%!%!?!%!!!%%%!!?%!!!%%!%%%?!%?%!?%%%!%%!%%%?%!%%%%!%!%!!!!?%!!!!?%!%%%%%!!!%%%!!%%%!!%%%%%%%%!!!!%%!!%%!%??%%%%!%??!??!?%!!!!%!!?%!?%!%!%%!%%%%%!?%!%%!!%%?%%%!%%%?%!%%%%!!%%?!%!%!?%%!?%?%%%%%!!?!?%%!%%%!!?%%!?%?!!?%%??%%!%?!!%%?%%!!?!%?!!?!?!%%!!%?!?!?%%???%%?%%!!!?!!!?%%??%!!%!!!!%?%%%!%!%%%?%%%%%%%%%!%!%%?!!!%??!!?%!?%!%?!%!!%!%%%%%!!%%?%!%%!!%%%!!%?!!%!!%!!!!%%%!%%!%%!!%%!?%%%%%%!!%!!!%!!%%?%???!%%%?%?%!?%!!%?!?%%!%?%!%%!%!%!!!%!%%%%%??%?%%%!!%!%%!!!!%%%%!%?!%%%!%%?%?!%%%!%%%%!%%?%?%%%%!?!%%!%!%%%!!??%!%!!%!%%%!?%!?%%!%?%%%?%%!?!%%%%!!?%%!!%%%?%!!%%!?%%%%?%%%!!%%!%?%%%%!%!?%%%%?%?!%%?!?%%?!%?%%%%!?%!!?%%%?!!!%!?!%%%!?%%!%%!%?%!%?%!%!!!?%!!%?!!%%!?!!!!!%%?%%?%%%%%%%%%!%%!!!%!!?%%!%%%?!%!!?!%?%!%%?%%?%!??!%!!!%??%%%?!!!%%%%%%%%%!%%!?%!%%%%!%!%%!!?!!!%%%!%!!??%!%!%!!%%%%%%%%!!%!??%%!!!!!%!%%!%!!!%!!!%!%%!!%!?!?!%%%%!%%?!!!!%%!!%!!%!%%?!%?!!!?!!%%!!%%!!%%!%!!!%%%!!???%!%!!%%?%%?!%%%?%!!%%?%%!%!!!!%%!%!!!!?%?!%!?%!%!%?%%?%!%%%!!%?!?!?%??!!?!%%%!%%%?%??%%%%%%%!%%%%!!!%!!?!%!?%!%%%%%%%!%%?!%%?%?%??%%?!!%!!!?%!%!!%%!??!??!%%!%%!?%?%%??%?%!!%?%%!!%%%%%!??!!!%%??!%%!!!??!%!%!%%%%!%?!?%!%!%%?!!!?!%?%%%!!%%%!%%%!!%%%?!?%%!%!!%!!!%%!%%!!!!!%%%?%!!!!%!!!?!%%!??%%!??%!%%%%%%??!%!?%?%%!%?%!?!!%?!?!%!%?!%?!%%!??!%!%%??%%%?%%!?%%!%?%%%?!!!!!%%%%%%%%%%!!%%%!%%!!?%%?%!%?%%!%?%%!%!!?!!!%%?%?%!%!!!?!%%%!%!%!%?!%%!%?%%%?!%!%!!!%%!%%!%%!!!%?!%?%!%%%!%%%!!?!%?%%!?%!?!%?%!%%!%!!??%%%%!!?%%!!?!%%?%??!%!!!%!!?%!%%?%!!!!!%%%?!%%!%%%%!%%%!%!%?%!%%%??%%%?%%!%?%?%%!%%!%%%%!!!!%!%%!!%!!%!%%?!%!!%!!%??!!%!!?%!%?%?%%%??%!!%!!?%%%!?%%!???%?!%!?%?%%%!!%?%?!%%!%%%%!!%%%?!%?%%!!%!!%!?%!%!%!!%!%?%%%!%%!?%??%!!!!?%?%!??!%%%%%!!%!%!%%%%!%%??%%%!!!??%!!%!?!?%%!!!%!!%%%%?%?%!%?!%!%%?%%%!%%%?%%!!?%!%%?%%%%?!%!%%?%%%!!%?%%!!%%!%%%!!%%!%%%%%?!!%!%%%!%%!%%?!!%%%!!%!%%?!?!%%%%%%!??!%!%!?%!%%!%%%!%%?!%?%!%!!%%%?!%%%?%?%%%%?%!!!%%!%%%!%%%!%%%%!%!?%%!%%%%!%%%!!!%??!%!%%%%!!!!%?%??%%%!!%!%!%%%%??%!%%%%?%??!%%%%!!%!%!%%?!?!%%!%!%?!!!%%!%?%%%?%%%%%?%%?%!%!%%%!%%%%!%!%%%??%?!%??%%???%!%%%??%%?%!%%!%%%%!%!%%%%?!%??!?%%%%!%!?%%%!!%?%??%!!%%!?%%?!%%%%??!%?!?!!!%!!%%%%%%!?%!!%%!%%%!%%%!%!%!%%%?!!!%%!!%!%%??!%%%?%?!?!%!%!??%%%!?%!%!!%!?%!%%%!!%!%%%%?!?!?%?%%%%!%!%%%%%%%!!%!%%!!!??%%%!!%%%!?%%%!!?!?!!%?%!%%%%%?%?!%%!%%%%!?!%%??!%%%%%!%%%%?!!%%?%!%?%%%?!%%?!%?%!%!%%!???%!!?!?!%?%%%%%%%!!?%?!?%%?!!?!?%%%!?%%%%?%?%%%!?!%!!?!%?%%!%%!!%!!%!%!?%%%!!%!%%%%%!???%!!%%!!%%!%!!??%%!?%!!!%!!?%%!!%%!!%!!%%%?%!!?%!!%?%%?!%!!%!%!%?!!!!%%%%!%%%?%??!%%%%!!?%%!!%%!?%%%%!%?%%?!%!!%%%%!!%!?!%???!%?%?%?%%%!!%%%!%%%%?%!?!%%%%!!%!?%!%%?%?!?!%%%%%?!%%%?%!%%!%%%%%!!?%%!!%?!%?!%!%!???!%%?%!%!!?!!%%%%%!?%!%!?!!!%%%%!!?%!!?!%%%%%!!%%%!%%?%!?!%!%%!%?%!?%%??%%%%!!!%%%?%!%!?%%%%?!!?%!!%%%%%!%%%?!%%%%%!?!!%!?%!%%?%?!!?%!!??%%%%!!!%%!%!%!?%!%?%%%%%%!!%!%!%?!%!!%?!%%!!!%%%%?!!!%%!!!%!!%%!%!%%!!%!%?%%%!%?!%!!!%?!?%!%!?!!!!%!!!%%%%%%%!%!!?%%%%?!!?!!!%!?%%%%%%!!%%%!%!!%!%?%%!!%%?!%%!!?!%!!%!%%!!!!%!%%%%%!?%%?%!%%%%%!!%%?%%?%!%%?!%%?!?%?%!%?!?!%%!!%%%!%%%!%%%?%%?%!%?!!?!%%!%?!%?!!%!!!?!%%!!!%!%%%%%%!!?%!%!??%%%!!%?!%?!%!%!%!!%?%%%!!!%!%!?!!%%%?%%%%?!%%%%%!%%!!%!%%?%!%??%!%!%!!??!?%!?!!%!!!%!%?!!!!%%!?%%!%?!!%%%%%%%%%%?%%%!%%!%?!%!%%%%%%!?!!!?%%%%%%%%%?!!!!%?%!?%!!!%%%%!!!%%!%?!%%%!?!%!!%%?%%?!%!!!%!%!!%!%!%!!!??%%%?!!%!!?%!!%%%?%!!??!??%!!!?%?!%!%%%!%%!!?%%!!!!!%%!!%??%?%%?%%!?%%!!%!?%!!%%!%!%%%?%!%%!!%?%!?%!%!!!!%%%%!?%!%!%%!!%?%%!!%%!!!??%!!?%%!%!%!!%!?!%%%!%!%%!%%?!%%??%%%%!!%%!%!%!?%?!%!%!%?!%!!%!%%%!%!%%%?!%?!%%%%?!!!%%%!%%%!%??%!%?!!%!!!!%!!?!%!!%!!%%%%%?!!%%!!!%!!%?%!?%%!%?%!%%?!!%%%%%!?%%!!%!?!!?%%!%%%!%%%!!%%?%%!?%!%%!%??%%!!%%%%??%!%!%%?%??%?%%!!%!%!%!!%%%%!?%%%!%%%!%!!%!%%%?!%%%!%%!!%%%%!!!%!%!%!%!!?%!%%%%!?%%%%%?%%%%!%%%%%%%!??%!!%!!%%%!?!!%!!!%!!!?!%!???!?%!!!?!!%%?!%%?%%%%%%%!%%!!%?!%%%%!!!%%!%?%%!%%%?%!%??%%!%!%%!%%%%%%%!!%!%%!%%%%%%%%!%%%%%%%!%%%!%%%%%!%?%!??%!%%%%!!??!%!%%?%%!%%%!%%%%!!!%!%%!?!%!!%!!?%??!!!%%?!!%!!%%%%%%!%?%!?%%!?!%?%%%!%%%%%?%!%!?!%?%?%!?%%!%!?!%%%%%%%%!!%%%%%?%%?!!%%%!?%%%?%%%%?%?%!%?!!!?!%?%?%!%?%!!%%!%%?!!!%!%%%!!%%%?%!%!!%%%%!!%%%!%!?%%%!%?%%!?!%?%!%%%!!?%!%!%%%%%!!%?%%?%?%!%?!!!%!%%%%!%!%!%!%?!%%%%%%%%%???%%?!!?!?%?%?!!%%%??%%?!%!??%!%?!%%%%!%!%?!%%%?%%%%!%%%!!!!!%%%%%!%?%%?%??!%!?%%%!!!!!%?%?%!%!%?%%%?%!?%!!!!!?%?%!%?!%%!!!?!%!?%%%%%!?!%%%%%!??!%%%%!%?%!!%?!%!???!%%!!!!%?%%%%%%%%!!??%?!!%!!%%%!!%!%!!!%%?%%%%?!!!?%%%!%%???%%%%%%!!???%%%%!%%??!?%?%%%%%!%!!?!!%!?!%%!%!%!!?!?!%!!%?!?%!!%!!??%%!%??%?%%%?%!!!!!!%?!!%%??!%%!%%!!!!%%%%%!?!!%%%%%%%!!%!!?%%%%!!??!%!?!!!%%%?%%%??%%!!!%!%!%%!%?%%!%!!%%%?%!%?!?%%%!!!!?!?%!%!!%%!%!!%!%!!%%%?%!%?!!?%%%!%%?%!%!?%%!!!?%?!!%!!%%%!!!%%%?!%!%?!%%!!%!!!!?!!!!%?%%%%??!?%!?%%%%%%!%%%%%%!%?!!?%%!%%!%!%%%%!!!!%!%%!!?%?!%??%%!%?%?!%!%%%%??%!?!!!%!%%%!%%%?%%?!%%%%?%%%?%!!!!%%%!%?!!!!%%%%!!!%%?!?!?%%%%%!%!?!%!%%?!%%%%%%!%!!?%%!%!%!%!?!%%??%%%!%%%%!%!%?%?%?%!??%!!%%%%%%!?!!%%%!%%!%%?%!!!!!?%%%%%%%!!!!%%%!!%%%%!?%%!%!!%?!%%%!!%%!%%!!!%!%!%!%!%%%%?%%%%!!!%!%%%%!%%!!!%%?!!!?!!%%%%?%!%!%%?%%%%%%%%%%%?!!?%!!?!%!??%%!%%!!?%%!!!%%%%!?!%%!%?%?%!!!%!%!?%%%%%!??%?!!%%??%!%!%%!%?%%??!!%!%%?%!%%%!?%%%?!!!!%??%!?%!%%!?%%%%%%%%%?%!!?!%!!?%?%%%%!%?%%!?!!%!%%%%%%%!%%?%%%!!!%%%!%%!%?%!!!?!%%%!!!?%?%!!%%%!!!%%!%%%%!%?%%!%%%%?!%!!%%%%%!!?%?!%!!%!?!!%??%%?!%%%!!!!%!%!%?%%?%!%!%%!!!?!!%%?%?%%?!!%!%%?%%!%%!!!%!%%%??!??!%?%!%?%%%!%?!?!%%?%%!%%%%%?%%!!?!%!%!?%!%%?!%%?!!%%%%!%!%!!???!?%%%?!!?!%?%%!?!%%%%%?!%?!%!%%%%%!%??%!%!!?!?%?!%??%%!?!!!%!?%%!!%!%!%!%?!%!!!%!?%!%!!!!%%!%?!!%%%%%!%%!!!?%!%!?%%!!%!!%%%!?%%!?!%!?%!%%!!%%%%%%%%%!%%?%%!%%%?!%!%!!%!%%%%%%%!%%%!!%%!%??%??%%%%?!%!%%?!!%?!%!%%??%%%!!%%!%%!??%!!%%%%??!%%!!%!?!%%!%%%%%?%%%!%%!%%%?!%%%!!%%%%%!!!%?!!??!%%%%%%%!!%!!%%%%?!?%%%%%%%!?!!%%%%%%%%%%%%!%%!?%%!!?%%%%%!?!!%?%%%!??%%!!%?%!%?!%?!%!%!!%!!%%!%!%!!!!%%?%!!%!%%%%!%??%?%?!!?%!!%?!%!!%!%!%!%!!%%!%%?!!%%%%%!!!!%%%?%%%%!%!%?%%!!%!%!!%%!%!%%%!!!!%!!%?!%!??%?!!%%!%%!%%%!??!%!!%!%?%!!%%%%?%?%!!%!?%!!?%!!%%%%!%%%!?%%%%!!?%!!%%%%%%%!!%%!!%!!%%%%%%!%!%!!!%%!%%!%%?!%%!??%?%%%%?!%!!%%%?%%%%?!!!!!%%%!?%%%%??%!%?%%%%???%?%%%!!!!!%!!??%%%%%!?%?%%%?%%!%%!!%%%%?!%%?%%%?%%?!!%!%%%%!!?%?%!!?!%%%?%%%?%%!%!%!?%!!%%!!?%%!%!%%%??%%%%?%??%%%%?%!%!%!%?%%%?!?%!?!%%!?%%%!!!!?%%!!%%%?!!?%%!%%%%%%!!!?!%!%%%!!%%%%?!%%%%%%%%?!%%%%%?!!%%%%?!%?%?%%%%?!!%%!?!%??%!!!%!%%%%??!??%!%%?%!!!%%%?%!%%?!%%%%%%!%%!%%%%!!%%%?!%!%!%!%%%%%?%?%%!!!%!!%%%%?!!%!%!%?!%!%!!!?!?!!%!%!%?%%!!??!?%!%%%%?%%!%!!!?!!!%!%!??%%?%?!!%%?%?%%%%%%%!!%%%%?!!%!!??!??!%%%!%%%??%!%!!%?%%!%%%%?%!%%%!!!!?%!!%?%%%!!!!?%!%%%%?%%!%%%%%%%!!%%!%%%%%%%%!%%%?%%%%%!%%%?%%%%?%%%!%%%%!!!!!?%?!%!%!!!%!%%%!!%%!%?%%%??!!!!!!%?%!!?%!%%%!%%%??!!!%!!?!%!!??!!%%%!!%%??!%%!%!%!%%?%%%!%!%%!!%%?%%%!!%!%%?%%?!!%%%%?%!!%!%!%%%!%!%!%%!%!?%%!%%!??%?%%?%%%!%%%%!%%%!?%?!!!!!%!%%??!%!%%!!?!!%!%!!!?%!%!%!???!%?%??!!%?%!%%?%%%%%%!%!%!%!!%!?%%??!!?%?%?%%!%%?%%%%%%%%!%?%!%??%!?!?!%%!%!!!%%%%?!%%%!?%?%%!%%%%??!%?!!%%?%%%!!%%!!%!?%%?%!?%%!%%!%%%%%%??%!%!%!?!%!!!!%?!%??%!?%!!%%%!%%???%!!!!%?!!%!%%%%!%!!!!!%!%%%%!!%%%%%?%%%!!!!%%%!?%%?%!%!%%%%%!!%%!!%!?!!!!%??%!?!%!!!%%?!?!?%%%%%%?!%%%%!%?%!%?%%?!%%%!%!!??!!%%!??%%%%%!%!!!%!!!!%%?%!!!!%%!!!??%!!!%%?!%%%!!!%!!?%?!?!!%!!?!%!?!!%!%!!?%!%%%!!!%%?!%!?%?!%%%%%%%?!!%%!!%!%?!%!!%!?%%?%%!!%%%!!%%?!%%!!!%!!!%?!%%!!%!%%%!%?%%%?%%%!??!%?%!%%!?%%%!%?%%!!!!%?!%!%?!?!%%%!%%%%!%%%%!%!!%?!!%!%%%!%%!%!!%%%!%!!?%%!??%%!%?%?%!%!%?%!%%?!!!%%%%!%%%!!%%!!%!!%?%%?%%%!!!??%!%!!!!%!%!%%?%%!!!?%!%!?!!%?%!!!?!!%%?%!%%!!%!%!%!%!%%%%!%?%?%%!%%?%!%!%?!?%!!!?!%!%!?%!%?%!%%!%!!%%%!%!%?!%!%%?%%!%%%?!%?!!?!%?%!%!%!?%%%?!%!%%!%%!!!%%?!%?%%?%%!%%????%?!%?%%%!%?%!!%!?!?%!%!%!!!?!%!!!%?%!!%%%!%?%!%?!!%!%!!?!%%!%%?!%?%!?%?%!%!%%%%?!%!!%%%%%%!?!%%!!%%??%%%%%!%%!??%!%!%%?%%!%%%%!!%!!%!!!%!!!%!!!%%%!%%?%%%%%!%!%!!!%?%%!%!?%%%!?%?!!%%%!%%!%?!%%%%?!?%%?!!!%%!%%!%%!!%%%%%%%%!%?%%%!%!?%%%%%%%%!!%??%!??!!%??!%!%%?!%!?%%!%!!?%!!%?%!!%%?%%?%!?!?%!%%%??!!!!?%!%!!%!%%!!!!?%!!!%%!?%!?%?!?%!!!!!?%%%%!!?%%%%%%?!%%!%!?%%%%!%%!%%%?%%%?%%%%??!%??!?!%!%%!?%%%%!!%%%%!%%?!%%!!!%%%!%%%!?!%%!%%?!?%!?%%%!!?%%%%%%?%!!%!%!?!?!%%%!!!!%!%%%%?!!%!!%%%?%?%!!?%?!?!?%%??%%%%!%%!%!!%%%%!?%!!%%%!?%%%%%!%%!!!%%!%??%%%%?%?%%%%%%!%?!%!?%?%!!!%!!!?!%%%!%%!!!!%?!!!%%!%!%!!%%!%?%%%%%???%?!%!%?%%!%%%%?!!!%!%?!%%!??!???%!%%%!!!?%%%!%!%%?%%?%?%%%??!!!!!%!!%!%%%%?%!%%!%%?!%!%%!%!?%%%!%!!%?%%?%%?%?%?%?%?!!%!%??%%!!!!%!?%!%%!%!%?%!!%%%%?%!%?%%!!!%%!!%%?!%%!%%%%!%%%!%%!!!?%%%%%?%!%!!!%%!%%!!%!%?!!?%%!!!!%!??!%%?%?!!%??!%???%!!%?%%!!!!%%%!!?!%!!!!%?!!%%%!!!%!%%!%?%%!%%%!%%?!?%%%%!!?!%!??!?%!?%%%!!%!%%%%!%!%%!%??!%%%%%%??!%!%%%%%%%%%!?%!%%!!%!?%%!!!!%!%!?%?!!%!%!?%!!!%!!%%%!%!%%%%%%!%%%%%%?%!%%?%%%%?%%%%%%%!%!%%%?%?%%?%%!%!%??%!%%%!%%!!%%!!%!%%%%%%!!!%?!!!??%%!%!!%%!!?!%%?%!%%%%%?!%%!!%%%%?!!!!%!!%!!%%%%?!%?%%%%!!%%%%%!%%!!%?!!%?%%!%!?!%!!!?%%!!%%!%!%%%%%?%%%%?!%%!%%%%%%%%%%%?%!!!%!!?%!%!%!%%??!!!!!!!%?!!%!%%%%%%?%?%!%%%%%%?!!?!?%!?!%!!!%%%%%!%%?%!!%%?!%%!%!!?!%!??%!%%%%%!?%??%?%%??%%%??%%%%%!?%%%?!%%%%%%%%!??%!%%%%%?%%!?%%%%!!%%%%%%%%%?!%%!%%?!%!%%!%!!?%%?%?!%!!!?%%!!!!??%%%%%!?!%?!!%%!%?%?!?!%!%!%%%%!%!!%%!%!%%!%?%%%%%!!%%?!?%?!%!?%%?!?!!!!!??!?!!?%%%%%%%??!%?%!%%%%%?%!!%!!%?%%!%%%??!%%%!%!?!%%?%%!??%!!!%!%%%!%%%%!!%%!!?%%!?%%%!!!!!%%%!%??%?%%!!!?%!!%?%%%%%%%!!!%%%%!%%%?%%?!!%%!!%?!?%%%?%???%%%!!!???!!!%%%!%%%%%%!!%!!%%??%?%%!!%!%!%!!!%%%?!!?%!%%%%%?%%?%%?%?!%!!%?%%?%%!!!%%%%?!?%%!%%!?!!%!%!%!?%?%%%!%%%%%!!?!?%!%?%%%%!%??!!%%%!!%%?%!%%!%!!!!%%!!?%!?%%%%?!?!%?!%!%%?%%!!%%!%!%!!!?!%!%%%!%%!!!?%!?!????%!!%%%%%%%%!%!%!%%!?%!!!!%!?%!!%?!!!!?%!%%%?%%!%?%%%!%%!%%%!!%%!%%%%!%%%!?%?%!%!?%%%%!!%?%!%%%?%%%?!!%%%%%!%!!!!??%?%%%!%!%!%!%%%!!%!%?%%?%!%!%%%!%!?!%%!%!%%??%!?!%%%%!%!!%%%%%!%%?%%%!?!!%%%!?%?%!!!%!%!%%%%?!%!%!?!?%%?!?%!%%%?!!!!?%!!!!%!?%%%%%?%?%!!%!!!%%%%!!?!!!??!%!%%!%%?!%%!%%!%!%!!%??%%%!%?!!?%?!%!!!???!%!?!%%!%!??%%!%%%%%!%%!%!!%!?%?!%%%%%%%!%?!!%%%?%?%!?%!%!%%??!!%?!??!!%!%?%?!%%%!?!!??!%%?%?!%%%%!?!%!?%%%!%!%!!!!%%%?!%%%%%%%%?!!%!!!!%!%%%!%??%!?!?!%%?%!%%?!%%%%%!!%%%%!?%!!%%!??%%%%??!!!!!!!%!%%?%?%?%!%%%!?!!!?%%!%%?%?%?%?!%!!%?%%?!!%%!%%%%!%??%?!%%%%%%?!!%%?!%%!!%%?!%?%!%%!?%!%?%!?%?%%?!!!!!%%%%!%!%%??!!%!%?!%%%%!!!%%!%%%?!?%!%!!%%!%%!%?!!?%!?!%%!?%!?%%?%!!?%%%%%!%!!%%!%!!%%!%?!?%%%!%?%%!?%!?%!?%%!%%!%!!!?%%%%!?%?!!%%%%%?%?%%!!!!!%%%!%%!%!%%!?!?!%%%%%?!%%?%!%%!?%!!%%!%!?!!%!%!%%%??%%%%!?!?%%%?!%%!%%!%!?%!%%?%!%!!%%!%%!%%%!%%%!!%!%!%%%!%!%!!!%%%!!%!?!!!%!!%?%%!%%%%%%%%?%%!%?%%!!!!%?%!?!%%!%%%!%%?%%!%%??%!%!?!!%%%%!!!!!!!!!%%%%!%%?%%%%?%%!%%!%!?%%!%?%%!!%%%%%!%!!%!%?%?%?%%!%%!!%!!?%%%%%%!%%%%%??%%%!%%?%!%%%%%%!!%!%?%%%!%!%%!?!%?!%!%??%%!?%?!!?%%!!%!!!%!?%%!%%%?%%!%?!!!%??%%??!!!?%%!!%%%%%%!%!%!!!%?%?!%!?%!%%%!!?!!%%%%%%%??%%%%%?!!%%%%?%%%!?!%%!%%%%%%!%!%%%%%%!!?!%!%!%?%!!%%!%%%%!?%??%!%%?!%!%!%%%%!%%?!!?%%%!??%!%!!?!%%%%%!!%!%%!%%%%%!?%!%%%!?%%%%!!%???%%!!%!%!???!!%%!!%!%%%!!!%%%%!!%%!!%?!%%%%?!!!%!%%%%%!!!%%%%%!%?!!?%%%%!?!%!!!%!%%?%!!%!?%%?%!%!%!%!!%!%?!!%%%??!%%!!?!!%%!!%!!%%%%%!%!?%%!??%%?%!!%!??!!%%?!%%!!%%%%?%!%%!%?%!%?!%?!%%!%%!?!%%!!?!%!?%!%!%!!!!?!%!%%%!?!!!???%%%?!?!?%%%!?%!%%!?!!?%%%%%%%?%!!%!%!?%%?%%%%%%!%?%%%!%?!!%%%!?%!!%%!!?!!%!?!%!!%%%%%?%!%%%%%%!%%?!%!!%!%%%!%%?!?%!!!%%%??%!%!!%!!%%%!!%%!%%%!%?!?!%%!%!%%%?!!?!%!?%??%!%%%%!!!%!%%%%?!!%%!%%?!!?%%!%!%!%%%%%!%%%%!%%%%!%!%%!!%?!%??%%?%%%?!%!!%?!%%!!%!?%?%!!%!!%%!%!?%%%%%!??!%%?%%%?!%!%%%!?%%!!?%%!!%!%%%!%?%%?!!!?!%%!?%%?!?!%!%%!?%%?!%%%?!%%??%!%%%!!?!!%%?!!%%?!%!%!%%%!%?%?%!!!!!?!??!!!?!%%!??%!!?%%!%%!%%!??%%!%%?!%%%?!?%%%?%%%!%%%!%%!?!%%%!??%%!%?%%%!%%%%!%!%%%%%!!!?%!%!%%%!%%%%%!%%%??%%!%%!%%%%?%?%%!!!!!??%?!%!%%%%%!%!%!%%?!%%%%%%%?%%%!%!?!?!%!%%%?%!!?%%!!%??%%!!?%%!!%%!%%!%!!%%?!??!?%!%!%%!!!!%?%%%?!!???%%%%%%!%!%%%%%%!%%!%%?%!?!!%?%%%%%%?%%%??%%%%%%%!!!%%%%%%?!???%%?!?!%?%%%%%?!%?!%?%!!!!%!?%!%%?%!%%?%?!!!!%%!?%%!!%??!%!!!!!?%%%%!%!%!!?%!%!?!!!?%%!?!!??!?!%%?!!%%!%%%%!%%%?!!%%%!?%%!%!!%?%!%?!?%%%%?%%%%!%%%%%!!%%%!!?%%?!%%!%?%%!%??%%!?!%!%!!%%%!%?!!%!!?!%!!?%!%!!%!!!%????%%%!?%%!%%?%%%%!%%?%!%%%!?%%!!!%%!%?%!%!%%?!?%%%%?%??!%?%%!!!!!%!?%!!%%!%!%%%%%!!%??%?!%%%?!!?%??%!!%%!!?%?!?%?%!!%%!%%!!%!%%?!%%%%?!%!%%!%%!%?%!%%!%!%%%!!!%%%?%%!!!%?!%%??%%!!?!!%!!%%?%!%!%?%!!!?%%!!%%??%!?!%!%%%%!!%%!!?%%%%!!!%!!!!%%!%?%?%%%!%%!%%%%%!?%?!!?!%!%%?!?%%%%%%!%?%%%?!%%%!%!%!!??%!?%?!!%?%?!%???%!%?%?!??!%?%%%%%%?%%!%%!!!%!!?%%%?!?%%%%%?!!%%%?!!%?%%%%%!%!?%%!%%%%%!%?!?%?%%??%%!%%!!%%??%!%%?%?%%?%%!!!%%?%!!%%%!?%!%!%!%!%%%%%!!!%%?!!!%%%??!%%%%%%%!?%%%%??%!?%%!!!%%!%!!!!!?%%%%??%!!%???!%!%%!?%!!!%?%?%!!!%?!%?%%%!!%?%?%%?%?%%!%!!%!?!%%%%%%?!!?%%?%%!!?!!!%%!!!??%?%%!%!!%%%!!%%!!%!%%!%%!?%!!!%%!?!!%%%!%!%?%%?!!%!!!%!%%%!?%!!%%?%%?!!!%%?!!!!%%%?!?%!%!%%%!!!%%!!!!%%!?%%!%%%!%%%%!?!%%%%!?!%!!%%?%%%?%!%!%%%%%%?%%%%?!!!%?%!?!?%%?!%!?!%!!!!%?!%%%!!%%!%!%?%?%!?!%%%%?%%!%!!!%!!?%%%%!%?%!%!!?%!!%%%%!?!%!!%??!?%!!!!%!%!%%?%%%%?%?!!!%%!!%!%!%?!%!?%%!%!%%%%%%!!%?!?!%!%%%%!%%!%%%%!%%%%%%%?%!?%%!!?%!!?%!%!!%?%!!%!%%%?!!%??%!!%%%!%%!%%%?%%%%%!?!!%%!??%?%!??!%%%!%!?%%!!?%%!%%%!%%!!!!%!%?%!%!%!%!!%?%??!%%!?!%%?!%?%!??!!%%%%!!%%%?%%%%%%%?%%%!%%%?%%?!?%!?!!??!?%??!!%%%!%?%?%%%%!?%%%%??!%%?%%!%!!!!?%!%%%??%%%%%!%?%%!!%%!%%%%%!%%%%%%?!!%?%!%!%!?!!%%?!!%!%!%!!%!!!!?%%!%%!%!?!%!!%?%%!!!%!%!%?!%!!%?!?%!?%%%??!%!!%%%?%?!%?!?!%!?%%%%!%!%!%!%!?%??%!!?%%%%%%!%%!!%!%%%%!%!%%!?%?!?%?%%%!%%%%!!!%%%%?%%%!%%%?%!!%%!%!%!%%!!??%!%!?%%%!!%%!!%!!%!?%?!!%%!%%%%!%!%%?!%?%!?%%%%!!?%!?%%%%!?!%?!%%!!%%!%%!%%%?!!%!!%%?%%%%%%?%%!%%%?!!%?%%!!!!%!!%%%?%%!%%%!?%%%%%??!%%%?%%%?!!%!%%?%!%?!!!!%%%!%%%%!!!??%%??%%%!%!?%!?%!?%%!%??%%%!!!%!!!%!%%?!%%!%!%?!%?%%!%!!!%!%!%?!%?!%%!%%??%?!!%%!?%%%!%!%%%!!!!!%%!!%!%!%%%!%%%!%%%%%%%?%%!%%!!%?!%%!%!!%!??!%!!%%!%%%%!!?!%!%!!?%!?%!%%%%%%!%%?%%!!!?%?!!!!!%%%!?%?%!%%??%!!??!%%!%!%!%%!!?%%%?!%%?%%!%!%!?!!%%%%!!%%%%%?!%%%??%?%!!!%%%%%!%?%!%%%?%%%??%%!!??%%!%%!%%%%%!?%%%!%%?%%!%%!%%!%!%%!!?%%%?%%%%%%%%%%!%%!%??%?!%!!?%%??%!%%%?%%%?!!?%%?%!%%%!?%!%?%!%!%%%%%!%%?%!!?!%%%!!%!!%%%%%?!!%!?%!%!!!%%%!!?%%%!?!%!%??!?%%!%!?!!!%%%%!%%%!?%?%%!!!?%%!!%%%!%!!!!?%%%%?%!!%%!!!%%!%%!%!!!%!%%%!!?!%%%%%?!!%%!%%%?%%?%%%!!!%?%%!!%%%%!?!%??%!%%%!%%!%!?!%%?!?!%??!?%%%%!?!!?!%%!?%%%%?%%%%%%%%%!%%%?%!%%%%?!%!%!%!!%%%!?%%%?!!?%?%?!!?!!!%?%!?%?!!!%?!%%%%!%!!%%%%%%!%!!%%%!%!?!?%!!!!?%%%!?!%!!!?%!%!!%%%?%%%%%%?%%?%!%%?%%%%!!?%%??%%!%!%%%%%!!%!?%!%!%!%!%!!?!!%???!%%!%?%%%!!!?%%!%!???%%%?%?!%?%%!!%!!?%?%%%!%%%?%%%%!!!!%%?%?%%?%!%???%!??%%%!%%!%!%%%?%%?!!!%%?%%%?%%%%!!%%!!!!!?%%?%%!!!??!%%%??%%?%!!!%??%!%?!!%!?!?%%?!%%!%%%!%?%?!???%%%!%%%%?%%!%%%??%%!%%%%%!?!%%%!!%?!%%%?%%%%%!%%%%?%!%?%%%!%!%%%!%%!%!??!!%%%%!%%?!%!!%?%?%%!!!!%??%%!%%?%%!%!%?!!!!!?!%!%?%?%%?%%%%%%?%?%%%!?%!%%%?!!?%%%!!%!!%%%%!%!!?%%%%!!%!%?!?!!!??%%%%!%%%!!!!!!!!!%%!!%%%!%!%?%!%%%%?%%%%%%!%?!!%!%!?!%?%?%%%%!!?%?!??%?%!%%%%!!?%%!%%!!%!%!!%!%?%?!%?%!%%!!%!%%%?!!%?%%!%%?%!%%?%!?!%?%%!?%%%%%!%?%%%!%!!?!!?!?!%%%?%%%!!?%%!%%%%%?!?%%%!!!!!%?%?%%!!?%?%%!%?%%!%%!?%!!!%?!!!!!!%%!%%!!%%!%!!!%!%?!%?!!%%%%?%%%%?%%%%?!!%%%%%%?%!%%?!%%%?!%%?!%?!%!%%%%!!?%!%%%%%!!!?%?%%!%%%?%%%%!%%%%!%!%%!%%!%%!??%%%%!?%%%%!?!%!!!!!%?%%%!%!%%!!!??!%%%!!!%%%?!!%!?!%%!%?%!!%%??!%!%%%%!%!%%%!%%!%!%%!%%%%!!%??%!%%?%%??%!%?%!!%%%!%?%?%!?%!%!%%?!%%!%%%?%%!%!!%?%%%!%%%%!!!!!!%!%!%!%%%%%%%?%?%%?%%%%%%??%%?!!!%%%%!!%%%%%?!!%%%%%%!!!%!%%!%%?%%%!%%?%??%?%%!%?%!?%%!%%!!%!%!!%!%!?!%%%%!%%%%%%!?%?%!%%%%!??%%!%!%!%%!?!%%!%!?!%?%!%!?!?%%%!!%!!%%?%!%!!!?%%!%%%%!%?%?%?%?%!%%%%%%%?%?%!?!!!%%%%!!?%%%?!%?%%!?!%!%!?!?!%%%?%!%!??!%%%%!?!?%?%%%%%%%%%%!%%%%??%%!%%%?%!%%!?%!%??!!%%???!%!!!!%%!%%%!%!%!!!!!%!%!!%!!!!%?!?%%%%%%!%!%?%!?%!?%!%%!%!%!!%%!?%%%!?%!%!!?%??%?%%!%%%!%!!%!%%?!!%?!!%!!%!!%%?%!%!?!%??%%%%!?%%%%!?!%%?%!%!%!%%%%%%!?%%!!%?%!!%?%%%!??!!???%!%%?%%?!!%!%!%%%!%%%?!!%!%%%%%%!!%%!!%?%%%%%%!!%%%!!%%%!%%!!!!%%%%!%???!????%?%?%%%??%!%!%%!!!%!%%%%!!%!?%!%%%!%%!%%%!%!%!%%!%%%!%?!%!%!!!%%%!!!%!%??%%%%%%!%!!!%??%?%%?%?%%%%!%%%!!%!!%!!%!%%!!%%!!!!%%%!!??%%!%%!%!%%!%%!%!!%!%%%%%?!?!!%%%%%!!%%!!%!%%%?!%%!?!%!%%%%%%%%%%%%%!%!!%%%!!!!%%%!%?%%%%!%!%??%!%!%%?%%%?!%%%%?%%?%%!%!%%%!%%?!???%%!!%%!%??%%!%%%%?!%%!%?%%!%!%%%%%%!%!?%!!%%!?%%%%!!%!%%!%!?!%!?!%%!%!!!?%%?%!%%!?!%%?%%%%!??%%!!%%%%?%!!%%%!%%%%%!!?!%??%%%?!%%%!%%%%%%%%!?%!%!%!!%!%%!!!!%%%!!%%!!%%?%?%!%%?%%!%%%!%!?!?%%!?%?%%%!%!!%%!%?%!?!!!%??!!!!?!?%?!%!%%%!!!!!?!%%!%%%?%%%%%!?!%!!!?%%%%%!?%?!???%!!!?!%%%!!!!%!%%!%%!?!%!%%!%%?%%!!!%?!!%%?!!%%!!%!%?%%%%%%%!%!%%%!!%??%%%%!?%%%%%%%!%?%%%%!!!%%?!%%%%%!!%!!!!!%%?%%%%!?!%%%%!??%?%%%%!!%%%!!%!?%%%%%!%%%?!%!%%%%!%!%%?%%?!%%?%??%!!%?!?%???%!!?%%!%%%%%?%?%%!%%%%!%%%?%%%?%%!?!!%!%%??!?%?!?!%%?%?%%%%!!!????%%?%!!!%!!%%%%?%!%%!?!!!%!%?%!%%%%!%!!%!%%%!!!?%%!%%!?%!!%!%%%%%%%!%%%%!?%!!!%???%%!?%%!!%!?%%!%%?!%%%??%!!!%%%%%%?!%!%?!!%%?%!%?!!?!!?%!%%%!%%!%!?%%?!%?!%?!%!%%%?%%%%!!?!!%%?%%!%!!!%!!%%%!?!!!%!%%!!%%%!%?%!%?%!%%%%%!!!!!!!!?!!%%%%%%?%!!??%!!!!%!?%%%!%%%!%%?%?!?%%!?%!!%!!%%!%%!%??!!!!%?%!%??!!!!!!??!%%%%!?!??%!?!%?%%!%%%!?%%%%!%!??!?%%%%!%?%!%%!%%%!%?!!?!%!%??%%!%!!%%%%!!%%!!!?%!?%?%%%!??%%%?!?%??%!!%?!%!?!%!!!%!!%%?%%%?!%%!%%!!?!%!%!???!%%!!!%?%%%%%%!%%?%!%!%?%!%!!?%?%%%!%%!%!%%%%%?!%%%%!%!?%%%!%?%!%!!!!%%%!?%%?!%?%%!!?%%%!%%!??%%!%?%?!%!%%%?%%!%!!%%%%!!%?!?%%%%!%?!!%%%??!%!%%?!%%%!%!%!?%%!!?!?%!%%%!%?!%?!%!!?%%%%!%%%%%%!%%%%%%?!!!!?%%%!%%%%!!%%%%?%?!%%!!%??%%%!%%?%!??!%%?!%%%%!%!%%!!%!%!%%%%!%%??!%%!!%?!%!%?%%?!%!!???%%?%!?%!%%?%%%?!!!!%!!!!%!%?%%!%%%!%%!%%%%%!!?%!%!%%!!%!?%!%!???!?%%!%?!!%!?%%%%%!?%%!!?%%%%%!!?%!!%%%%?%!!!%%%%?%?%!!!%!?!!?%%?!%!!??%%%%%%%%%%?%!%%%?!!%?%!%!%!!!????%!%!%??%!%?%%!!%??!!%%!!?%%%%?%%?%!!%?!?!!?%?%%!!%!!%%%%%?!%?!%%%!%!!!!?%%%%%%!%!%%%!!!%%%%%!?!%%!%?!??%!!!?%%%!!!%!!???%%!?!!!%!%%%%%!%?!%!%%%?%%%%?!!%%%%%!%%%!?!!%%!?%?%?!!!%!?!%!%%%?%!%%!%?!%%%?%%??%!!!%?!%%!%%%%!!!%%%!%?%%?%%!%%!%%!%%%?!!?%!!%%%?%!!%%%%?!%%?!!!?%?%!!%%!%%?%!!%%!!!%?!!?%%%!%%%%%!%%!%%%!?%?%%%!!%?%?!%!!%?%!!!%?%%%!!?%%%%!%?!?%%%%%?!??%%%!%!%%?%!?!%%%%%!!%%!%%?!%!!??%%???%%%%?%%%%!!%%!?%!!%!??%!%!%%???!%%%!?%%?%!!?%!%!?%!%%%!%!!%%!%?!%%?!!%%?%?!%!%%!%%%!%%%%!?%%%%!?!?!%%%%?%%!%%!!%%%???%!%!%?!?!!%%?!?%?%%!%!?!?!%%%%!%?%!!%%%?!!!%!%%?%?%!!?!%%%%!%!%%!%%%%?%%%%!%%!%%%!%%%%%!?%%%%%%%%?!%%%!%%%%%%!!%!!%!%%!%?%!?%%%%%%%?%%%?%%?%!!%%%?%?%%%%%%%!%%%%?!!?%%%!%%%%!%?!%??!!???%?!%%!!!%!!%?%!%?%!%?!?!!%!!?%%?%!!%%!!%%?!%??%%%??%?!?!!%%%%!?%%%%%%!%%!!!%?%!%!%%?!%%?%%!!%%%!!!%%?%!%%%%?!%%!!%%!%%!%?!%%?!!!?%??!?!%%%??%!!?!%%%!%%%!??%!?%%!!%%!!%%!!?%?%%%!?%?!%%!??!?%%!!%%%??%%%%%%!!?!%%%??!!?!?%%%!!!!%!!!%%!%!%%%%!%??!%%!%!%?!%!%%%?%!%%%%%%%%?%%%%!!!%%%%!%!%%!?%%%!?%!%!!%!!??!%%%!%%%!!!%%%%!%?!!%%%?%%%%!%%%%%%!?!!%%!%%!!?%!!%%!!?!%!!!!!!!?%%!%%??!%%%%!%%!%?%%%!%%%%%!%!%%%%%%!?%!%?%%?!!?%!!%%?!?!%%!%!%!%!!%?%!%%?!?!!%!%!!%%%%%?%%%%!%%?%!!%??%!!%%%%???%%!!!%%%!%!%!!!!?%!!%!!!!%!%!%%%%%%!!%?%!?!!%!!%%%!?%?%%%%%?%%%%%%%%%%%%!!%!!!%%!%?%%%?%!%%%!!!%%%?%%%%%%!!%?!!??%!%%%?!%%%%!?!!!%!%%!%%%%!%%%!!%%%%%%%!%%%!!!!??!!??%!%?!!!%%!%%!!%%!%???%!?%!!??%!%%%%%%%!!!!%!!%%%!%%!?%%?%%%%!?%!!!%?!!%%?%%%!!?!!%!%%%!!%%!%?%!?%?%!%%!?%%%!!?%!?%%??%!%?%??%%%%%!?%%?%!%!?!?!!%%!!%%!%%!!%!%%?!%?%%?!%%??!%%!?%%!%?%?%%?%!!!?%?%!?%??%??%%!!%?%!%%!%!%!!%%%%%%%!??!!!??%?!!!!%!%%!%%%!!?%%!%??!%%!!%!%%%%%!!%!%%%?!%!%!%%%%%?%?%??!%%?!?!!%!%??!%!!%!!%%%%%%!?%%%!??!!%!!%!!?%%?%!%%%!?!!?%%%%%?!!!%%?%%%?%!?!%%%%!!!%%!??%!%%%?%!%!%%!?%?%!%%%%%%%?!?%?!!!%?!!%%!!%?!?!%!?%%!%!!!!%?%%%!!%%%%%%%%%?%!%?!!!%%!%!%%!!%???%!!!!%%!%%%??!%%?%%!?%!%!%%%!%%%%%%%%%%!?%!??%!%??%%%!?%!%?%?%??!%%!!!!!?%%%!%%%%?%!%%!%%!%?%?%!?%!!%%%!!?!!!!?%%!!!!!!?%?!%?!!!?%%!%!?!%!%!%??%%%?%%???!!%%%%!!%%!%!!%%%%?%%!!%%%%!?%!%%?!%%%%!%%!%%%%!%!%!%!%!!!?%!!%%?%!%%%?%%%%?%?!?!!%??%%%%%?%!%%%%!!%!%%%%%%!%%%??%!%!!%!?%?%?%!!%%!!!!%%%?%!%%%%%??%%%!!!!%!%%!!!!%%!?%%?%!%%!%?%%!%!%%!!?%!%%%!!!?%%!!!?%!%?!%%%!?!!!!!%?%%!%?%!!%%!?%!%?%%%?%%%%%%?%!?%%?%%!!%%%%??%%!%%%%!%%!!!%?!!%%?%?!%?!%%%%%!%%!%%!??%%?%!%!!%%%?!%%%%%!%%%?%?%%%%!%!!?%%!!%?!%?%!!?%?%!%%?%?%?%%%%!!!!%%%%%%?%%!%%?%%!%%%?%%?%!%%!?!!%%%!?!%%!!%%%!!%!%%?!%%?%!%?%%!%%!%!!?!!%!!!?%!%%!%??%%!%??!?%!%?!!%?!!?%!!??%%%!!%!!%%!!?%%?!!?!%!%%!!!%!%%%%!!%!?!!!%%?%!!%%?%%!%!?!%?!%!%!%!!!!%%!%%??%!%%%!%!%!!%!!%!?!!!!?%%!%!!!!!?%%!%%!!!%%%%!!%%!%%!?%?%%%%%?!!!%!%!!??%%!!%%?%%!%!?%!%!!%!??%%!!!%%%?%%?%%%!!%%%?!?%%%%?%?!!?%!%%%%%%%%?%!!?%%!!%%%!%?%%%!?%!%?%!!!%%%%%%%%%%!?%!%%%%%?!!!%%?%%!%%%!!?%%%%%%?!%??!?!?!!!%%%?!%%!%!%%%%%!%!%%!?!%?%%?!%%%!!%?!%??%!%?!?%%!?!!%%%%%!%!%%!!%!%!%%%!%!%%?!!%?%!%!!?%%%!!%!%%?%%!%%!!%!%%!?%!!%?%!%?%!!%%!%%%%%%%%!!%!?%%%!%%%%%%%!!!????%%?%!%%%!%?%!?%%%%%!%%?%!%%%%!%%!!%%%%!%%!%?%%!!%!!%?!!!%!%%%%?%%%!!?%!!%!!!%%?%!!%!%%!%%%?!%?!!!%%?%!%!!?!!!%?%%%%%%%%%%!%%!%!%%%?%%%%%!!?!?%%!!?%%??!!???%?%%!??!%!?!%%!%%!??%%%%?!!!!%??%%?!%%%!%!%%%!%%%%%!?%%!%?%!!!??%%%%%%%!%?%!%%!!%%?!%%%%%!!!!%%!%%%%?%%!%?!?%%%!!%%%%!%%!!?%%%%!%%?%%%%!!%%!%%!%%%!%%%%%!%%%%%!!%!%!%%%%%!%%!%%?%!!!!?%?!!?%%!!!%!%%%%!%?%?%!%!%!%!%%%%%%!%%?%%!?!%%%!%%%!!%!%%!!%%%?!%!%%%?%%?%%%%%!!%!%!!!%!%%!%%%%?%!!%%%?%!!!!%%?%%%?!!%%!!?%!!%!%!%%!%%!!%%%?!%!!??%!!!%!%?%!%%%%%?%%!!%!??%%%%?%!%!?!%!!%%!%!!!!!!%!!?%%?!%%%%?!%!!%%%%!!%%!%%%%%%?!%%!!%!%!!%%%!%%?!%%!?!?%??%%!%%!%%%%!%%%%!!%!%?%%%%%?%%!?%!%?%!%!?%%!!!%%%%%!!%%??%?!!%%%%!%!?%%%%!?%!%%%!!%??!!!%!!%%%!!!%%!%%!??%%!?!%%??%!??%?%%%!!%%%!%!!%%%!?!!?!!!!?!%!%%%!!%??%%?%%%!?!!!!%%%??%?%%!%!!%%!%%%!%%!%%?!%%%!%%%%%?%!%!?%%!%?%!!%%%?%%!!%%%?%!?%!%%!?!%!!%!%%%!?%%%!!?%%%%%!!?%%!?!%!!%%%%!!!!?%??!?%!%!!!??%%%%%%%!!%%!!!%%%%!!%!%%!!!%%%%!?!%%!%!%%%!%%!?%?%%!%!!%!?!%%%!?%%!%%!%!%?!?%%?%%!%%?!!!!!?%%!?%%%!%%!?!%%%%%%%!?!%%!?%%%%%!?%!%!!%?%%%%!!?!!%!%!%%%??%?%!%?!%!!%%!!!%!%%%%!%?!%!%%?%%??%!%%!?%?%?%!%!!!%%%%?!%?!!%?!%%!!?%?!??!!%!%?%!!!%!!%!%%%%?!!%%!%?%?!?%%%!%%!%!%%?%?%%%%%?%!?!!%?!!%%%?%!%?%%!%%?!%!!%%%?%%!%%!!!?%%!%%%%%!%!!%!%%%%!?%!!!%%!%!!%%%%!%!%%!%!??!%%!!?%!??!?%!!%!!%%!!!?!?!!!?%!!!!!!!%%!!!%!!!%?%?%%!%%%!%?%!!%!%%?%!%%%!!!%%!!?%%!%%?%%?%!%%!!%!%!%?%?!!??%%%??!%%%!%%%%!!!?!%!%%!%%?%%%%%!!!%%?%!!%%!%%!??!%%!!%?%%%%?%!!!%!?%%?!!%%!??%!!%%?%%%??%!!%%%%!!!%%%!%!!%??!%%?%%%!%?%%?%!%!%!%!!%%%!!!%%%%%%%%%%%???!%%%%!%?%%!%%%!%!%!%%%%!!!%?!%%?%%???%!!%%%!!!%!?%%?%?%%%%?%!%%??%%!!%!!%%%%%?%!%!!%%!%%!%%?%?!!%%%%!??%!!?%?%!%?%?!%!%%%%!%%???%%?%%!%!%!%%?!!!%%%!%!?%%!%%%%?%%%!!%%%%!%!%%%!??%%%!%%%%%%!%%%%%!!!%%%%!!%!%?%!?%%%%?!%%%!?!%?!%%?%%!!!??%?!!%%%!%?!%?%%?%%?!%%?%?%!%?%%%%%?%!%%!%%%%?!%!!?%!?%%!??!%%!%!%!%%%?%%%%%%!%!%?%%%%%%%!?!!%!!?%!%%!!?%?%%!!%?%%%%%!%???%%!%!%%!%%%!?!%%?%%%!!%%%%!%%%?!%!%!%%!??%%!??%!%???%?%!!?!%%%%!!!?%?%!%%!%%%!??%%%!%?!%?%!%%?%%!!?%%!!%%!%!%%!%%%%%%%!%!%!!%%!%?!%%!!!%?!%%%%%!!%?!!%?!?%%!!%!%!!%%?%!%%%%%%%!!%%!%??!%!%?%%!!%%%!%%!!?!?!%%?!?%%!!%%!%%?%%!%!%!%!!?%%!!!?%%%%%%!%!!!%%?!!%%?%%%%!?%?!%%%%?%!%!%%?%!%?%!!%%%?!%??!??%%%%!%!!%%%!!?%%%!?!%%%%?%!%!!!%!!%%%?%!%???%!!!!%%?!!%!?%%%%%%%%!?!?!%?!%!!%%%?%?!!%!!%!%!%%%%?%??%!%%!%%%%%!!!!%!%%!%?%!!%%%!?%%%%%?%%!%%%%???%?!%%%%%!!!%?!?!%?%%!!%!??%%%?!!!%!!!!%!!%%!%!%%!!%%!%%!%%!%?%?!%!%%!!!%!%%?%%!%%!!!%!?%%!%?%%%?!%%%%!%!%%%!!%%!!!%%%!%!!%%%%?!!?!%!?!!!!%%!!%?%%!!%%%?%%%%?!%!!!!%!?%%!!%%%!!!%!!%!%!%!%%??%?!%%%??!%!%%%?%%%!!?%%%%%!??%?%!!%%!%%%?!%!%?%%?%%%!!!%?%?%%%%%%%!%%%%!%!%?!%%%%%%%%%!!%!!%%%%!%%%%%??!!%!!!%%%%!%%!%??%%?!%!%%!%%%%!%%!%%%%!%%!%%%?!!??%?!?%!!!%%%!!%?!%!%%%%!%%??%%?!!%%!%!!!!%!!!%%!%%%?%%%%!%!%?%?%!!%!%!%!!!!!?%!!!?%%?%%?%%!!%%%?%%%?%?!%!%%?%%%!%!%!!%%%%%?!!%%%!!%%%%%%!%%%!?!%%%%!%%%!%?%%%%?%%%%?%!!!??%%!%%%!%%%?!??!!?!%!%%%%!!??%%!!%!!?%%!%%%!%!??!%?%??!%%!!!!??%!!%%!%%%%!!?%?!?!%%!%?%%%%%%%%%%%%%%!!%%%!%%?%%%%!%!%!?%?%?%?%!%%%!!%?!%%%?%?%%%?!?%!?%%?%%%!!?%!%!!%?!%%!%%??!%??!?!!!!%%%%%%%%%!!!?%?%!%%%?!?%%??%!%%%%!%%%!!!!!!%%%%%%!%!%!%!%?!!%??%?%!!!?%%!%!!%%%%%%!%%%%!%%?%!%!?!%%?%?%%!%%%!?%!!?%!!?!%%!!%??!!?!!?!%%%%%!?!!%%%?%%%%!!%!%%%!!%!%%%%?!%%%??!%%!!%!!%!%!!?!!%%%%?%%%!%%%%%%!???!!%%%!!?!!!%%!%?%!!%!%%??%!!%?%!%!?%%%%!!%%%%!%%!!%%!%?%%%%!%!!%!?!%%!?%!%!%?!%!%?%??%!!%!%?%%!!!!?!%%?%%%?!!!!%%?%%!!!%!?%!%?%%!%%!%!%?%%%%??!%?%?!!%%?%?%%!?!%!!%!?%!%!!%?!%%!??%%%!%%?!!?%%%%?%!%!%!!%%%%%%!%?!!!!!%!%?%!%!%%!?%!!!!!!%?%%!!!%%!?!?%%%%%?%%!%!?%%%?%!!!?%!!?!%%!?%%!!!%!%!!%%?%!!%%%!!!??%%!!%!!!?%!!%??!%%!!%?%%%?%%%%!%?!!!%?%%!%!%!%%%?%%!%%!%%%?%%%%!!?!%?!!!?%%%%%!??%!%?%%!%%!%!%%!%!!??%%%%!!??!%!!??!%?%%%%%%?%%!?%%!%%?%%%!%!!%%!%!%!%!!?!%!!!%!!!?%%%%%%%%%!!!%!!%%%%%!%%?%?!%!?%%%!?%%!!%%!!%?%%??!!!%?%!%!!?!%?!??!%%%%?%%%?!%?%!!%%%?%%%!%!!?%%%%%?%!%%%%!!!%!?%%%!!?%?!%%%%%%%%%%%%%%?%!%%?%%!%%%%%?%%%?%!%%!%%%%%%%!!!??%%?%?!%%%%%%?%%%?!!!%??!!%!!%%%?!!!%!%?!%%?%?%!?%%%!!?!?%%%%!%%%%?%%!%!!%!!%!%?!%?%?!%!%!%%%!!%?!%?%%%%%%!%!%!!%%?!!%?%%!%!%%%?!!??%%%!!!%%%%%%??!!?%%?%%%?!%%%%%?%%%%%%%%%%!%?%??!!!!%?!!%!!%%%???%!%%%!%!%%!%%%!!!%!!%??%%%!%???%%!%!!%?!!?%%!%%%!%%%%%!%!%!%%%?%%?!%%!?%%?%?%%%!!%!%%!!!%%!?%%%?!!??%%%%!?%%%%%!%%%!%%?!?!!%%%!%?!!%%!??%!%%%?%%!%%!%%!%!!?%???%?%?!%%%%?%%?!!?%%%!%!!%!?!%%%%%?%%!%!!?!%?!%!!?!%%!%!??%!%%!%%%%%%%%!!%%!%!%%%%%%!?%?%!?!%%!%%!?!?!%!%%%?!?%!%!?%%!%%!!!!%%!?%%%!%%%%!!%%%%%%!!!%%%%!?!%%%%?%%%!!!%!!?%%?%?%!??%?!!!%%!?%!%%?%!%%!!%!!!%%!%%%!?!%?!%?%%??%?!%?!%!%!!!?!!%%??%%!!!!?%%!!%!?%!!%%??%%%!?!%!%!%?%%!%%?%!!?%?%!%%!%!%%!%%!%%%!%!%!!?%%!?%%!?%%%!%%%%%%%%%%%%!?%!%%!?%%%!%!?%%??%%?%%!%%%!!?%?%?%?%%!%%%!!%%%%%%%!%%!!%?%!%!!!%%!%%%!!!!%%!%!!%!!?%!!?%!%!?!?%??!%??!%%!%!%?!?%!??!%!!%%!%!%!!%?%%??%!%!%%%?!%!%?%%%%!%%%!%!%!%%!%!%!%%!%%!%%%?!%%!??%%!!?!!!%?%!%%%%%!!%!%?!%!%!?%?%%!!%%%%!!%!%%%%%%!%?%%?!%!%!!!%%%%!%!%?!%!%!?%!%!!!?%%!%!!%!!!!%%!!%%%!%!%?!?%!?%!!!%!%!!%!!?%%%%!!!%%%!%??%%!%!%%!%%?%?%!%?%%!!?!??%!!?%!%%%!%%%%!??!!??!!?!%!!%%%%%%%!%%!%%%%%!?!!%%%%%%%!%?%%%?!!!!!%%%!!!%!!%%%%???!!?!!!?!!%?!%%!!?%%%!%?!!??%%!%!%!??!%%!?%??%%%!%?%!%!?%%%%!!%??!%?%%%%?%!%%!?!?!!!%%!?%%%%%!%%!%?!%!!!%%%?%!??%!?!%%!%%!%%%%?!%!!%!?!%!%?%%%%!!%%%%%!!%?!%!!?!?%%%!!%!!%!?%???%%%%?!%!?%%%%%?%%%?!%?!?!?%%%%!!!%%!%!%?!?%?%!%%%!%!%?%%!!!%%!!%%%%!!!%!%%%%!?%%%!!%%!%!%?%%?!?!!%!%!%%?%?%!!%%%!%%%!!!?!%!?!%?!!!%%!?%%%!%%%!!%?!%%!?!%%%?!!?!%%%!!%%!!!%%??%%%!%%!!?%!%!!!%!%%!%!!!!%%%%%!%!?%!!!%!?%%%!!%!%!%%%%??!%!%%%?%%%%%%%%%!%?%?!?!??!!%!%%!%%!!%!%!!%%%%%%%%%!!%!%%%?!!?%?%!%!!!%?!%%!?!%%%!!!!%%%%%%!!?%!%?!%!%%!?%%!!%%%!%!?%!?%%!%!%!%!!!%%%?%???%%%%%%%!!%!???%%%!!%!%?%%%%%%%!!!!!%%%!!%!%??%%?!%%%%%!!!!?%%%???!%%%%%%%!?!?%!%!%%%%%!%!!%!%!!%!%%!!%%%%!!!!??%%%%%??!?!?!%!%!!%%?!!%!%%%!!%!%?%!%!!?!%!!!?!??!!%%%%%!?%!?!!!!!!%?!!%%!?%!%!!%!%!!!!!!%%?%%!%%%%%%%?!%!%?!?!%!%%!%%!%%?%!?%!%%%!!!!%!!!%??%!!%%?%!%?%%%%!%?!!%%!%%!%%!%!!%!?%%!!?!!%%%??%!%%!%!?%!!!!???%%!%%%%%!%!%?!%!?%!%%!%!%%!%%%%%!%!%%!!%!!%%?%%%%%%%%?%%%!?!!%!!?%%!%%?%%?%!!%!?%!%!?%!!%%%?!%!?%%%%%%!!%!!!!!%?%?!!%!%!?!%%%!%!%!%%%!%??%??%%%!!?%?!%%?%%!%!%?%!%%?%!%%?%%%%!%!%%%?%%%%%%%%%%?%??%%??%!!!%!??!?%?!%%%?!?%!%%%%%%%%!!??%!%%!?!!?%!%%!%%%%!!%%%!!%%!%!!%%%!!%?!%!%!%%%%!!%?%!!!%%!%!!%%%%!!%%?!%!%!!%%%%!!%%!%?!%!?%%??%!??%!!%!%%%?%%%%!%%!!!!%%%%%%??!%%%!!!!%!%%%!%%%?%%%!%!!?!%!!%%!%%%%?!%%%%%%%%%?!%%?%%%!%!%%%!%?%!%%!!%!%??%!%%%?!?%!%!%%%%%!%%%%?%!%?%%%%!??!!!%%??!%!!%!?!?%%%%!%?%!%%%%?%%%!%?%!?!%%?!?%%?!%%!%?!!%?%!!%!!!?%%%%%!!!?%?!?!?%%%!!%!%%!!!!!!%!%%%!!%%!?%%%%??!!!%!%!%%%!!!!%%%!!%%!!?%%%%!?%%!%%%!%%%%%%??!?!%!!?%!%%%%?%%?!%!!!?%%?%%!!%?%%%%%?%%%????!%!!?%%%%!%!!%%?%%?!!?%%%%!%%!!%%%!%%%!?!!!%%%%!%!!%%!?!%?!?%!%%%!!!%!!%!!!??!%?!%%!%!!%%%%%!!%?%??!%?%%!!%!!?!%!!%!!!%%%%%%%%!?%%!%!%!%%%%%%!%!!!?%!!!!!??%%!!!%?!%!%%?%%??!%%%%?%!%%!%%?!!!!?!%%!%%!%!?!%!!!%%!?!??!%%%%%%%!%?%%!%!%%%%%???%!%%!%%%%%%?%!%!?!%%!%%!!%!!%%%?!%!%%%!!%!%!?%%!%!%%%%!%%!%!!!!!?%%!%!%%!%!%%!!?%!!?%???!!%%%%%%!%??!!!!%?%!?!%%%%!!!%?%%!%?!%!!%?%%!??%%?!!?%?%!!%!%%%?%%%%%%!%%%!?!?%?%%?!%!!%?%!%!%!?!?%%%!!!%%!%%?%%%?!!%???!%%!!%%!?%%%%%%%%!!%!!%?%?!%%%%!?!!!!%?%!!%?%!?%%??%!!!!%%%%%%?!!!!!%%%!%%%?%!!!!%?%!!%%%%%%!%???%?%!%%!!%%%%!!!%%!%!%!%??%%%!!!%!!%?%%?%%%%?!%%%!%%?%!!%!%?%?!!%%%!%%%%!!%!%!%!%?%!!%!!%%%%!!!?%%%%?%%%%?%%%!%?%%?!!%!%%%%%!?%!%!%?!!%%%!!%%%%%!!?%%%??%%%!!%%!?!?%%%%!!!%%%!?%!!%%!%%%?!%%!%!%!%%%%%!!!!?!%!!%%?!!%%%%!!!%!%!!%%%%%?!%%?%%!!%?!%%!%%%!!!%!!?!%%!%?%%??%%%?%??!%?%!??%!?%!%%!!%%!!!%?%%?%?%?%?%?%?%!!%%!!%%%%?%%%?%!?%%?!!!!%?%%%!!!!??%!%!?!%!%?!?%%?!%%%!?%%%?!%!?%?%%?%!%%!%%%?!%??%!%%!!!%!?!!!%?%!%%????%?!?%%%!!!%%%%!!%%?%%%!%?%!?!%!%!!%%!%%??!%!!%!%%??!%?!%%%!?%%%%%%%??!!??!%%%!!!!?!%!!!%!%!!?!?!%%!%%%?!?%%%?%%%%?%%?%?!!%?!!!%?!?%%%%%?%%??%%?!%!%!%?%%%%!%!%!%%!%?%?!!?%%!%!%!%%!!%%%?%!%!!?!!!%%%%!!?!%%!%%%%%%!%%!!?!??%%?%%!%%?!%!!?%%!!%%%%!%%%??!%!%%%??!?%%!?%!!?%%%?!%!%!!?%%%??%%!%!%!%%%?!!%%?!%!?!!%!!?!?!%%!!%?%?!%%%%!!%?%?%!%??%?!%%?%%!%%%!%%!!%??%%!%!?%?%!%%!%%%%%!%%!?!%%%?%%!?%%%!??!!%?%??%?!?!!!?%!!%%%%!%%%%%%%?%?%?%%%%!?%%%!%%!%!%%%%!%%%%!%%%!!%!%%!!!%%%!%!!%%!!!%%!%?%%%!??!!%??!%?!%%??%%!?!!??%!!%%%%%!?!?!!%!!%%?!!!%!%%%?%%!??%%??%%?%%%%?%%%%!%%!%%!%?!%?!?%!%%!%!%!%%%!?%%?!!!!!%!%%%?!%%%!!!%!!!%??%!%!?%?%?!%!!%%?%%!!!!%%%!%%!%!%!!%%%!%?!!%!%%??%!!!%!!?%%?!%%!%?!%!!%%!!?!?%!%%%%%??%%!!?%!%%?%%?!!%!!?!%!?!?!%!%%?!?!%!%!!%!%!%%%?!!%!!!%!?!%!?%%%%!!%!%%!%!%?!!??%%%%!!%!%!%%%!!?%%%?!%%%!%%?%%%%%%%%%%!!%?!!%%%%!!!%?%%!%?%!!!%%!%%%%!%%%%%!!!!%!!%?!%!??!?%!%?!!!%!?%%%!!?%%?!?%%%%?%%%%%%%!????!%%?!%%!!%%%%!%!!!!%%!!%!?!%!%%%%%%%!?%%%?%%!?!%%%!%?%!%!%!??!!%?%!?%%!%!!?!%%%!!%%!!%?%!%!%%%!%?!%%!!%!??!?!%!%%%%%!!?%!?%%?%?%%??%?!!??%!%!%!!%%%%!?!!%??%?%??%!?!!!!?%!%%%??%%%%!!%!%%?%!%?%%%%%?%%!!%!%%%!%!%!?%%%%!??!!%%!%%!%%!?%%%?!%?!!!!?%%%!!?!!%%!%%!%%%%%!%%!!?%%!%?!?!%!?%%?%?!%%%?%%%!!!%!%%%%%!!%!!%??!!!%!!!%%?%%%!!!%%!%?%!!%!%!%!!!!%?!?%%%!%%%%!%?%!!%%!!!!%%!!?%%%!%!!??%!%!%!?%?%!!%%%%!!%%%%%!?%%%?%%%%?%!%!%?%%?%!%%%?!?%!%%!?%!!%?%%%!%%!%!!!!?%!%?%%%%%%!?!%%!?!?!?!!%?!!!%!??%!%!!!%%!%%?!!%!??!%?%!%!!%??%!%%!%%%!%%!!%??!%%%%%%%%???%%!%!%%%!%?%%%%%!%%%%!?!%!!%!!?%%!%!%!%?%!%?%?%!%!!%%%%!%!!!?!%!%%%!?!%%%%%%%%%%!!%?%!!!%?%%!%?!%!%%%!%?%!%!?%%?!!%%!%!%%!%%%!!!%?%?%?%!%!!!%!%%!%%%%!%%!!??%%%!?%%%!%!%!?!?!!%!?%!???%%%?%%!%%%%!?%%%!?%%!%%%%%%%%%??%!!%!?%?%%?%%%!%%%!%%!!!!%%?!!!%!!%!!?!!!!%!!%!!%%!%!?%%%%%%%!!%!!!!%??!%?%%%!%?%%%%%!?%!?%!%%%!??!%%!%%??%%%%!%%?!?!!%!?%?!%%!!!%%%?!%%%!%?!!?!%%%?%%?%?!%%%!%%!!%%!!!%%%%!%%?!!%!!%!%%%?!%!!!%!%??%%!%%?!!%%%%?!%%!??%!%!%%%%?????!?%?%%%%%!!%?%!%%%%!???!?%!!?!??!%??!%!!?%?%%!%?!%!%?!!!%!%%%!%%!%%%%!!%!%%!%%!!%%%!!!%%%!!%%%!!!!%!%%?%%!%?%!%%%!?%?%!!%%%!!??!?%%%?%!%%%!%%!%%!?%!%!!%%!%!%%!%!????%!%%%%%!!!!?!!?%!%%%!%!%%%!?%%!?!%%%%??%%?%%?!%%?!%%?!%?!!%%!%%!%%%?!?%%%%!!!!%!%!!%%%?%%%?%%%!!%?%?%?!%!!??!!%%%%!!?%%%!%!%?%%?%%!!%?%?%%??!%??%%%!!!%!%??!%%??!??%%!!!!?%%%%?%!?%?%!?%!??%!!%%%%%%!%%!!!%%%%%%%%??%%!!?%!!%%??%%?!%%?!%%%?%%!!!%!?!%%%!%%%!%%!%!?%%%%%%%!!!??%!%%%!%%%%?%%!!%!%!!%!%?%%?%!%%%%??%%%%%%%%!%!!??!%!%%%%%%!%!%%%%!%!%!!!?%%?!%%%!!?%?!%%!!?!%%?!%%%%%!%%!!!%!!%!!%!%!??%%%%%%%!%!%?%%!?!?!%%?%!?%%?%%%!?!!!?%%%%%!%!!%%??%%!%??%%!%%!%!%%!%%!%%%!%%%%%%!?%?%%?!%%!%%?%%%!%!?%!%%%%%%%!?%%!!?%%?%%%?!%%?%?!%?%?%%%%!??!?!!%!%!%?%%%!%?!!!%%!%%%%%%?%%%!!%?!?%?!%%???!!!?!?!!%!%%%!%%%%%!%%!?!!!!%!!%?%??!!%%%?%!%!%?%%!%%?!%?!%?%!!!%!!?!?%%%!!%%%!!%%?%!!!%%%?%%!%%%%%%!%!!%%%%??%%%%%%%%?!!%!!!!!!!%%%!!?%%%?!!?%!%!%%%!?%%!!!?!%!%?%%%!%!%!%%%%!?%%%?!%%!%!%?%?%%?!?%?%!!!?!!%%!?%?%?%!%?!%%%%%!?!%?%?!%!%%!!%%!!!%%!!!%!!%!%!%!!!!!%!!%!!%%!?%%?!%%%!%%%!%!%%!!%!%%!%?%!!?%%!?!%%%%?!?%!!!%%!%%!%!%%?%?!%??!??!%%%??!!%!!?%!%%?!?%!?!!%%!%!?!%?%%?%!%!%!%%%!%%%%%!?!%!!?!!%%!!!%!!%%%%%%?!%!%%!%?%%%?!%!?%%?%!%?%%%?!%!%?%!?!%?!%???%%%!%%?%%%%%!%%!!?!%!%!!?!!?%!%%!?!%%?!!%!?%%%%!%!!%%%%!%%%%%%%%!%%%?%!?%%%%%%?%?%%!%%%%!?!!!%!%!!?!!%!%%!??%%%%!!%%?!%?!%%%%%?%!?%%%!??%?%!?%!%!!!!%%%%%%%%%%?%%%%%!%!%!!?%%%!%%%%%!?%!%?!!%!%?!%%%%!?!%!?!%!%%%%!?%!%%!%%!%!%?!%!%!!%%%!%?!!??%?%%!?%%?%?%!?%!?%?!!!!%%!??%?%%%?!%?%!%%%%!%?!%??%?!?%?!?!%%%%%%%!?!%%%!%%%!?%!!%!!%%%?%?!%!%%%?%?!%%%%%%?%%%???%?%%!%?!?%??%%%?%!?%%%?%%?%%?%?!%?%??%!!%%%%%%%%%?%%%%!%!%%???!%%%!%!%%?!%%!?%!%!%%%?!%!!?%%!!%%%%%%?%!%%%?!!!%%%?%%?%%%%%!!?%%?!%?%%?%%%%%??!!!?%%!%%%!%%!!?%%%%%!%%!%%%%!!?!%!!%%%?%?!%%!?!!%!!!%?%%?%%!!?%!!!?%!!!%%%?%?%!%%%%%?%?!%%!!!!!!!%%%%%!?!?%%!%%%%%?!!%%%%!?%%%%!!%%?%%!%?%!%%!%%%?!!%%%%%%%!?%%%!%%!!%%!%%?!%!?!??%%?!!%%%%%!%?!%!%?%!!%!%!?%%!!!%%%!!%%!!%!!%%!!!%!!!!?%%%%!?%%!!%%%!!!%!?%?%!?%%!%%!%?%%?%!!%?!%!%%%!!%%%?%!%%%??%!!%!??%%?!%%!%!?%%%!%%%?%%!!!%?%!?%!%%!%!%%%%%%!!!%%%?!%??%!!%!%%%%%!%!%%!!?!?%!%%%?!%!!!%%!%%??!!?!!%%%!?!!?%!??!%!%%!!%!!!%!?!%%%%!%%%!%!???%%!%!!%!%%!!%%%?%?%?%%%%!%%%%!!%%%!?%%%%?%%%%%%!!%%%!%%??!%%%!!%!%!%!%!?%%?%%!!%!%!!%!!!?%%!!%!?!!!%%%%%!%%??%%%%!%!%?!%%%!!!%%??%%!%%%!%%%!!%?!%%%!!%%%!!?!!%!?%%%!%?!%%!%%!!%!??%%?%?%?!%%!%!?!!?%%!!%!!?!%%?%%?%%?%%!%!!%?%%!%?%!%%%!%!?!%!!%?!%%??%%!%!!!%!%?!%%!%?%!??!?%%?!%%!?%!%%%!%!%?%!!%%!???!%%%!%%!%?!%%!?%%!%?!??%%%!!%?%!?!%!%%!%?!?%!%!%???%!?%%!%%?!!%?%!?%%!?!%%?!%?%%!!!!!%%%!%%%!%%!%%%!!%!!%!!%%%%!%!%!!%!!%!%%%!%!!?%!%!%?%?%!%!%!!%%!!%?!!!?!%%!%%!!%?%!%%%%%%!%!!?!?!!%%%%%%%%%%%%!?%!%!??%!?%?%?!?%%%!!%%!%!!!!?%%%%%%!!?!?!!%!!!!?!!%!!!?!%%%!%%%?%?%!%!%!%%?%!?%%%%?%?!%%?%%%!%%?%%!%%%!%!%%%%!%%?%!!!%%!%!%%!!??%%%?!!%%%%?%???%!%%!%!%%%%%%%!%!?!?!%!?%%%%%%!%!!?%%!%%%%%%??%?%%!%%%%!?%!%%!%??%!?!%!?!!%%%!%%%!?%!!!!!!%%!%!%!%%!%%%%?%%!!!?%??!%%%??%%%?%%%%!%%%!%?%%%!%?!%%%!%!%?%!!%%!!%%%!%!!!!%?%%%?%!%%!%%%%%%?!!%%%!%%!%%%%!%!!?%?%%%%!%%%%%%?%!!!%?%%?%%?!?!%?%!%!%%%%%%!!?!%!!!?%?!%%?!%%???!!%%%%%%%%?!%!!%%%!??%%!!%%!!%!?%!%%!!%!%!!%%%%?%%!%%%!%%!%%%%!!%!!%%!%%%!!!?%!!%!!!%?%??%%!!!%!!%?!%!%%%!%!%!%!%%!%%!!%%!%%?%!%!!%!?%!?!%!!%!?%%!%???%!%!!%%%!%?%!!%?%!?!!!?%!%%?!%%?%%!%%%%%%!%%%!!%%!%%!%!%!?!!!!%?!!%?%%!%%%%%?%%?!!?!%%!!??!!%%%%%?%%%!!%%%%%!??!%!!%%%%!%?!?%%!%??!?%%!%%?%!!%!%%%?!!?%%%!%!!%%!%!!%!%%?!%%%?%%!!!%??!%!%%%!?!%?%%%%%%!!?%%!?%!!?%%%%!%!%%%?%%!?%%!?%??!%!?%%%%%?%%%!%%%%??!%?%%!?%!%!%%!%%!%%%??%!%!?!%!?%%!%%!!!%?%!%?%!??%%?!%?!??%%%%%%%?!?!%!?!!?!%!!?%%%?%%!%!!%!!?%!?!%?!?%?%!!%%?!?%?!!%%%!%!?%%?!?!!!%%?!?%%%%?%!%%!%!%%%!%!%!%%!%?%%??%%?%!!%!!%!%!%%%?%%??!!??%%%!!!%??%%??%%!%%!!!!?%!!%%%%!?%%!%%%!%?!!%!%%!?!!!!%%%??!%%!%%!!?%!%%?!!!?%?%%%!!?%%!!!??!!!??!?!%?%?!!%%!?!!?!?%!!!%%!%%%?%%?%!%%??%%%%?%%?%%!!%!%!%?!?%%!%%%!%%!%%%?!%%!%!%%%%!%!?!%%%?%!%%%%%!!!%%?!%?!%!?%!%?%%%%!%?%!??%%%%%%%!!!%!%!!%%%%!%%%?%%!%??%!?!%???!%?%?%%!%!!%?%%%!%!%!%!%%%?%?!!%!!%%!%!%%%%%!!%%%%!%?!%!%%%%%?%!%%!?%%%!%!!!!!!%%!%%%%?!%%!%!?!??!!!%%%!%%%!%!!%?%%!%%%?!!%!%?%%%?!%!%?%%%?%%!!??!!%%%%!%%!%%%!%!%%!!%!%!%%%?%%%%%?%?%%?%%%!!%?%%!!?%?%%%%%%%%%!%%%!!?!!!?!%%!!!!%?%%??%!%%%!%%???%?!%%??%%?!!!%%!%%?%!%!%!!%%!?!%!%!%%!!!%%%!?%%%?%?!?!%%!?%?!!%?!!!%!%%%!!%!?!%%%%????%%%!!!!!%?%!!%%!%%!%!!!%!%!%%!!!%%?!%!%%?!!%!!%%!?%%%?%%%!%%!%?!%!!?!!?!!!!%%%%%%%!!%%!!!%!!%%%%%%??!?%?!%%!%!%?%%%%%%%%%!%???!%%%!!%?!%%%??%?%?!%%?%%!???!%%%%%%?%%%?%?!%%%%%%%%?!?%?%%%%%%!%%%?%?!%!?%??%!???%!%%!%%%%!!!%!%?%%!%%%!!?%%!%%?!!%%%%%%!!?%%%%??%!!%%%!!!!%%?!%%!??!%%%!!?!%%!%%?%!!%%%%%%!%?%!!%??%%%%%!?!%%%!%%%!!!%%?%?%%??!!?!!%?%%%%%%!%?%%%!!!?!%%?!??%!%%!!!%!!!%!%?%?%%!%?!%%%%%%!%!%%!!!?%!%!%%%!!%!%%!!%!!!!?!%%%!???%%!%???%!!!%%%%%?!?!!??!%?!%?!%%?%%%%!!%!%%!%%!%%?!%!%%?!%%!!%!%%!!!%%!?%!%%%%%%%!%%%%%!!%%!!%!%%%%%%!!?!%!??%?!??%%!?%%?%?%!%!?%?%?!!?!%%!%%!!!%?%?!!?%%%%!%!!%?%%%!!!%%!%%%%%!!%%?!?%%??!%?%%!?%%!!!%%!!%?!%%%%%?!%!!%!?%%!%??%!!!%!%%%%%!!%!%?!%%?%!%!!%%%%%%%!?%!!%?!%!!!%!%!%?%!!%?!?!!??!!!%%?%??%%??!!?%?%!%!!%!%??%!?%!%!?%!%!?%?!%?%%?%!!??%%!%!%%%!%!??%!%%!%%?%%!!?%%%%!!!%!%%??%%%%!?%%%!%%%?%?!%?%?!!%!%!%%!%!!!?!!!%?%%%%!%%!!%%!%?%!!%%!%%%%??!%!!!%??%%%!!?!%?%%%!%%!!%%%%??%!?%?%!!%%%!!%!%?%%?%%%%%!%!!%%!%%!!%%%!!%%!!?!!%?!%%%%!%!%?%!!!!!?%%?%%!!!?!%%%%%%!!!%!%???%!%!%%%%%%%%%??!!%%!%??!!?%%%!?%??%%%!!??%%%!!!?%!%!%!%!%!!%%!!%%%%%!%%!!!%%%!!!%%!!%%?!%%%%!!!%%!%!!!!%!%%%!!!!%?!!%%?!!!%%%%!%%%??!%%%%!%!?%?!%!!!%!%%!%%!%!!%%%%%%%%!?!%!%%%?!??%%%?!%%?%!%%%!?%?%%!?%%!?%?%??%!%%%!!%!!%%%!!%!%!!!%%?%%?%!%%%!!%%%!!?!!!%!%%?%??!%%?%!%%%%?!!%%%!%%!?%!%%%!!%%!%!%%!!%%!%!%!!!%?!!%!!%!!!?!?!%%!!?%%%!!?!?%???!!%!?%?%%%%!%?%?%?%!%%%%?%!%%!%?!!%%!%%%%%%%%!!?%???%!?%!?!!%?%!%!?!%%!%%!?%!%%%%?%?!%%%?%?!!%???%!?%%%%%%%%!???%!%%%%!%??!%%!!%%!?!%%%!!!%?%%!!!!%!?!%!?%?%?!%!?%%%%%%!%!%!!!?!!%!?!!%%%?%%%%!!???!!%??!?%%?%%?!%%%!%%%%?!!?!!???!!!?!%?!!%!?!%!%%%%%?%%%%%%?%!%?!!?!%?%!?%!!%!?%%%!!?%%%%!%!?!%%!?%?%?%%!?!!!%?%?%!%!%%%!!%%%!%!!%%%???!!?%?!!!%%%?%!!!?%%?%%!%!!!!%%?%%%%!%%%%%!!%!%%!!%!%!%?!!%%%?!%%%%?%!!%?%%!!%%!!%%%%!??!%??!!!?!%!!!%!!!?%%?%!!%??!%?%!!!?!%!!!!!%!%%!%%%%%%?!%%%%%!%%%!!!?!%%!%%%!!?%!!%%%?!%%%!?%?%%?%!?%!!%%%?%??!!!%!?!?!%%!%%???%%!!%?%%!??%?%!%?%!%%%!%?%%%%%%!%?!!!%%%?%%!!!%%!!%%%?%%?%!%%?%!?%%%%%?!%?!%!%?%!??!?%%!!!!%!%??%!?%%%%!%!%??!!!%!!%??%!!!%!?!?!%!!!!%%%%!%%!%!%!?%!?%?%%%?%%!%%%%!%%%!%%!%%!???%%!!!!?%%%!%!!?!%%!?!%!!%??%!!?%%!?%?!!%??%!%%%%!%%%?%!%!?!?%%%?%%%???%%!%%!!%!!?%!!%%%%?%%!%!!!!!%!!%?!%!%%!%?!%%!%%?%!!?%%!%%!?!%%!?%!?!%?!!%%!%!?%%%!%!!%!!%%%!?%%%%%!%?%!%%?!%%%!?%?!%!!%!%%%!!!!?%!!%%!%%%%?%!!%%!?%%%%%!%!%%!%!%%%!?!!%%%!%%%!%%!%?!!%%%!!%%?!%%!%%%%%!%%%!%%?!%?%!!%%%!%%%%!?!%!?%%!%!%%%%%!%!%?%?%%%%%?!%!!%!%%??%!?%??!!??%!!%%%!!%!%%!?%?!!%%!!!%%!%%!%!%!?!%!%%??%%%%%%%%%%?!%!%?%!%%%%!?%%!!?%!!%!%!%%!%!!%%%%%%!%?%??%%%!!%%%%%%%!!%!%%%%%%!%!%!%%%%??%!!%!!%%!?!%%!!%%%!%?%%%%%!%?!!%%%%%%!%%!?%%!?%!!!!!%%%%%%%!!!%!?!%%!%!%%%!!%%%!%!%??%%??!%?%%%!%?!%%%!!%%!%%%%!%%%!%%!!%%%%!?%!!%!%%!!!!!%%%!%%%%?!!!?%!%!?%%%!%!%!%%!!%%%!%!!%%%%%!%%%??!?%%!!%%%%%!%%%!!?%%!?%!!%%??%%!%!%?%%!%%%%%?%%!%!?!?%%?%!%%%%%!%!!%%!??%%!!!%?!!?%!%?!!?%!%%??!!!%?%%%%%%?%!%%%!?%!%%!!?%%!!%??!!%!!?%%%%%!%??%?%?!%%!!%?%%%%?!%!%!%!%%!%%?%!%%%?%!%%%%%!%%%!!!%%!!!%%%%%%!?%%%!!?!!%?!?%%?!%?%%%%?%%?%%!%%%%%%%%%%%%%!!%%!%!!?!!!!!?!!%?!%!!%%!%??!%!%!!%?!%%!%%%%?%!!%?%!!!%%?!!%?%?!%%%?%!!?!%!%?%%%%!!%?%?%%%%%???!%%??!?!%%?%%%%!%%%!?%%?%%?%!!%%%!%?%?%!!%%%!%!%%!%%%%!%!!%%%?%%%!!%%?!!%!%%%!%%%!!%%?%!!!%%%%%!%%%!!%%!%%?%!%?%%%!%%?!%?%%%%!%!%!%?%?%!%!?%%?!!%%%%?!%?%%%%%%!!!!%%%%%%%%%%!%!?!%%%!%%?!%%!!%%!%%%%!%!!%%?!?%!%%?!%!?%%%%?!%%!?%%%?!%%%!%%!%!%?%!%%%?!%%?!!?%??%?!%?%%!%%%!!%%%%%%%?%?%%%%!!?!%!%%%%%!!?!!!!%?%!!%!%%!?!?%!!%?!!%%%%!!%%%??%!!%%!?%!!%!%%%?!%%!%!!??!!!!%%?!??%?%!%%?%?%%%!%%!%!%%%?%%%!!%!%%%!?%?!!%%%%%%%%!!!!!!%%!!!?!%?!%%%%!%%!%%%?!%?%!?!%!!!!%?%!?%!!?%!%%%!!%?%!%??!?%!!!%%%!%!%!!!?%%%!%%!%!?%!!!%%%%!%%%!?!!%??%!??%%!%%???!%!%!%!%%%%!!%!%%!!!!%!!%%!!%!%?!%%!!%%%%?!%%!!%?!%?%!%%??!!%%%%%%%!!%%!%%!%%!?%%!%%%!!!%%%%%%!!!%%%!%%!%?!%!!%%%%!??%%%%%?%?%%!?%%%!?!%?%%??!%%%?%!%%%?%%%%?!%!%!%%%%!?%!!%%!%%%!?%%%%?!!%!?%?%!!%%!%!%??!!!%!?%%%?!%!%%%!%%%?%%%%%!!%!%%!!?%!?!%%%%?%%%%%!!!%!!!!?!!%!????!!!%?!!%%!%?%?!!?!!!%%%%!%%!!?!%%!%!!!!%!!?%?!%!%!%!%!!!!%%?!%%?!%%%!!%%%??%!?!%!!!!%%%??!??%!%%%!%!?!%%%%%%!?%%!%??!%!%%%??%?%%%%?%!%!?%%!!!?%%!!%!%?%%%%%!!%%?%!?%%!!!%!!%%!%%!%%!%%!%%%!%??!!!%%!!%!??%!!%%!%%%!!%!%%%%!%%%%!%%!!!%%?!!%%!!%%!%%!?%!%%!%%%%!!%%?!%!%!!%!?!%%%!!%!%!%%!%%%%!%%!!%%%!%!!%!%%!!!?%%%!!?%%!?!%%%!%!?!%!!!%%!!%%%!!!%%??%??!%!%%?!??!%!?!!%?%?!!%!%?%%%!!%%!?%%%%%%%%%?%!!%?!%!!%%?%!%%?%!??%??!%!%%%%%%%!!%!!%%%%?%%!?%%!!%?!%!?%%!%%%%%%?%?%%%%?!%%%%?%!%%%?!%%!?%%%!?!%!!!%%%?%%!%%%?%%%?!%%%!!!%%?!%?!??!%?%!%%!!%%%%%!!%%%%%!%?%%%%?%%!!!?!!%%%%!!%!%??%!%!?!!?!%%%!%!%?%!%%!?!?%%!!%%%!??%%?%!!!?%%?!??!!?!!%?!?!%%%!%?%%!%??!?%!!%??!%%%%?!%!!%!%%%%%?!%%%!%%%!%%%%!%!!%!!%?%%!!!!%%%!%%%%%!??!?%%!?%!!%!%!?%?%!!?%%%!%?%%!%%!!?!!%?%!%?!%%%%%%!!!%%%!%!%%%%%?!?%!%!!%!!???!?!%%?!%%!!!?!!!!%?%%%!%!!?%%??%%!%?%%%!!!!?%!%%!%!!%!?%%%!%!?%%!?%!%?!%!%!%%%%%%!%%?%?!%%%%%%%?%%%%!!%!!!%%%!?%!%%!%%!%%%?%?%%!!%%??%!%%%%?%%%??%?%%%%?%%!%!%!%!!?%?%%??%?%?!!%?!%!!?!?!%%%?%%!!%%%?!!!!!%%%%%!%!!%%%!?!?!!?%!!%%!!%%%%%%!!?!!%?%?%!%!%!!!?%%!!??!!%%!?!%!!%%?%!%%%%!%!%??%%%!!%%!??%%!?%!%!%!!%?!%!?%%!%!!?%!%%%%??%%!!!?!!!?%%%%%%%!!!!!%%%!%??%!!%%!?!?!!?!?%?%?!!?!!%%%%!?!!%!?%?!?%%?!%?%!%%%!%%??%!%%%%%!??%!??%%%!?%?%%!%%%??!?%!!%%?%%%?!?!!!?%%?!?!!!%?!!!%%%%%!%!%%%!?%!!%!%!%????%%!%%!!%%%?!%%?!!?%%%%%%?!%!?!!%%%%!%%?!%???%!?%!%%%!%%%??!!?%!%%%%%?%!%!%!%%%%%?%?%%%?!!%!!%%??%??!%!%%!%?%%!%%%!!!%!!!?%%%?%%%!?%!%!%!%!!!!%%!%%!!!%%!!%!%???!%%%!%%%%!%%!!!%!!%%%?%%!%%!%%!!%!??!%%?%!%%??!??%!%%!?%%%%!%?%?%!??!!%%%%%%!!?%%!!!?!?%%??!%!%?%?%!!!!%%!!%!!%%%%%%%%%!%?!%%!%???%!!!!%%%!%%!!%%!%?!!%?!%%%!!%%%%%?%%%%???%!%%%!%%%%%%%%%!%?%%%%%%%?%!?!!%!%?!?%?!!%%%!%%%%!%?!%!%%%!!!?%!%!%!%!!%%?%%%?!?!!%%%!!!!%!??!!!?!%!%!?%%%?%%!%%!!%?!%!%%!%?!!!!!%%???%!%%?!%!!%%!%%?%%%?%%%%%%!%!?!%?%%%!!!%!%%%%%!%%%%%%!?%!??!!%!%?%?%%%%%%%!%?%!%!?%?%!!!!!%??%!!!!%?!%%%%%%%%!%!%%%%!!%%!%%!%%?!!!%!%?!!?!!%%!%%%!%%?%%??!%%%%!!!!!%%!!%%%?%%%?!?%??%!!!%???%?%!?%%%%?%!!!!%!%?%!%?%!?%!?%%!?!!!!!!%%!?%%!!%?!!?!?%!!%!%!%%!!%%!%!%!!%%%%!??%!!!%!%%%%%!%!!!%%%%%%!?!%??!!%?%!!%!!%%%!%!%%%!%%!!!!?%!%!%%%!?%%%%%!%%%!!?%??%??%%%%!!%%%?!!%??!???%%?%%%??%!?!!!%?%%?!?%?%!%?%%!%%!!!%?%%?%?!%!?%%!%?!%%%!!!!?%??!!?!%%%!%%?%?%%%%%%!!%%%!!!!!!?%%%%%%!?!%%%!?%%?%?%%%!?%?%?!%%!!%!!%%%!!??%%!!%%?!!!%%??%%!!!%!%!%%?%%%!%!?!!!!%?!%!%!!%%!%%%%%!%%%??!%%?!!%%%!!%!!!!??%!!!?%%%%%!%%!%%!%!%%%??!!!!!?!?%?%%?%!!%%%%%?%%??%!%!!!%%%%%%!%%!%!!%!%?%%%%?%?%!%%??!!?%%%?!!%!!!%%!!%!%%!!%???!%!?%%%!%!%?!!%%%?%%?%?!%%!?%%!%%!!!%!%%!!%!???!!%%%!!%%?%%%%%%!!%!%?%!!?%%%%!!%!%!%!?%??!?%%%%?%?!?%%%%?%%?%%!%%%%%?%!%!!%?!%%?!%%%!%?%?!%!?%%!?!%!%!?!%%%%!%!!%!%%?!%??%!!%%%%%%!%%%%%%?%%?%!!?%!?%%!?!%%%%!%%%%?!%??%%!?%!%!!%?!?!%!%!%!%!%?!!%%%!%%%%?%?%%%%%%!%%!%%??%!%?%%!!!?%!?!!%%%%%%?%!!!!%?%?%!%%%!!%!!!%!%!!!%%?!%!%%%?!%!%%%%%!%%%?!!!!?!!!%%%%%%?!??%!%!%%!%!%%%%!%%?!%!?%%!%?%%%%!%%!%%!?!!%%%%%!!!%%?%%!%%!?%!!!?!%%!!%!?%!!!!%!%%%%?!!%%!!%%!!??%!!???!?!%%%%!%!%%?%???!?%!!!!%%!%?%!?%!!!%%%%%%!%%!!!%?%%%%!?!!!%!!?%!?%%%%%!%!%!!!?%%%%?!?%%%%%%%%?%%?%?%?!!%!??!%%!%%!!%%!!%%%!!!%!!?%?!%??!!%!%?!%!!%%??!%%??!?!!!%%!!?%!%%%?!%?%!%%%%%%?!%%!?!%%%%%!!!!!%?%%!%!%?%!%!?%??!??!!%%%!%%%%!!??%!?%%?!%?%%%%!%!%%!%%%!%%!%%%%?!%%%%!??!!!%%?%%!%?!%%!%%%!!%??%!?!!!%!%%%!%?%!%%%%%%%?!%??!?!!?!!%?!%!%!%!%%%%?%%!?%%!!%!!!?%%%?!%%%!%?!%%%!!?!%!%??!%!??!!?%!!%%?%%%%%%%!%%%!%?!%%%%!%%%??!%%%?%%!!%!??%%%?!?%!!!%%!%!!%%%%%%%!!!%%!%%?%%!!?%%%%%%?%%%%!!%?!%!?!!%!%???!%%%!%%%!%%!%!!%?!!%%?%?%%?%%%!!!!!?%%%%%!%%%!!%!!%!%%%!!%!!%!%?%%%!%?!%?%%!%%!%%%%%??!!%!%!%%!%!%%!%!%!?%%%%%%!%?!%!%%%?!%%%?!?!!?!%%???%?!!!%%!%!%%!%%!%?!%%%!%%?%!?%!%%%%!%!!%%?!%%?%%!%?!?!?!%?!%?!%?%%!%%!%!!?%%!%%!!???%%!%%?%%!%!?%?%%%%%!!%!!!%?!%!%%%!?!?!!%?!%!??%%%%%?!!%%!!!?!%!%!%??!?%%%%%?%%%%!%!!%%!%!??%%%!!?%!!!!%!%!%%?!!%!!%?!%!!!%!?%!%%%%%%%%!?!%??%%?!!%%%%?%?!!!%??%?%??%!!!!!%%????!?%?!%!%%!%%!!%%%!?%?!%%%!%%!!%%%!?%!!!!%!%!?%%%%%%?%!!%!%%!!!%%%!!%!?%%%%%%%!%?%!%%?%!?%?!?%!!%!!!%?%!%%%?!!%%!!!?%!%%%%!%%%!!%!%%%??%!!%%!%%?%!%?%%%!!%%!!!%!!!%?!%?%%%%!!!?%%%!?%%%%%??%?!%%?%%%%!!?!%!?%?%!!%%%%!!?%%%!%%%!%!?!?%%%!!%!%%%!%!???!!!%%??!?%?!%%!!!!!%!%%%!%%?%%!!%%%!%%%!?%%%%%%?%%%?!?%%!%%!%%!??%!%!%%%!%!%!%%%!!%%%%%%?%%%?!%%%?%%?!%!?%%%%%%%%%?!%%%%%!!??!%?!%%!%%!?!%%!?%!%%!?!%??!!%%%?%%%!!%%!!??%%%?%!%!!!!!%%%!%!!%%%??!?%!%%%%%?!!%!%!%%!!!!%!%!%%!%?!!?!%%!%?!?%%?%!!%%!%?!%%!!%%?%!?%%!!%?!%%%!!!!!%%%!%%%?%%%!!?%!%?%%!!!?!%%%%%%!!!%!!%%%%?!%!!?!%?!?%!?!%??%%?!%%%?!!!%??%%!!?%%%%?%%!?!!%!%%%%%!%!%?%?%!?%%%!%!!?!%%!%%%???!?!?!%??!?%!%!!!%%!%%%?%%!?%!%!!?!!?!?%%%%?%!!?%!%!%%%?!%???!%%%%!%?!!%!!!?!!%!!%%?%%?%!!!%!%?%%!%!%%%%?!!?%!!%!!%?%%?%%!%%%??%!!%!!!%!?!%%%%%%!?%!??!!!%!!?!%!%!%?%!!%%%%%?%%?!?!!!?%??%%!?%!!%%!?!!!%%%%?%%%%?!%%%%%%!!?%%??%%%%%%!%%%%?!!?%%%!!!%!%?!?%%??%?%%!??!%%?%%%?!%%%?%?!%%!!!%?!!!!!!%?!!!%%%%!!%%?!%!%!%%%%%%!%%!%!%%?%%!%?!%!%!%%?%%?%%?%!!%%%%%!?%%?!%%%?%?%?!%%!?%%%?%%!!?%%!!!!!?%%!%!??%?%%%!!%?%!!?%?%?%%%%%!%!%!%?%!%!%!!!%%!%!%!!%?%%!%??!%%%?!!%%?%???!!%!?%!?%%%%!?!!!!!%%%%?%%%%!?!!?%!%%!!!?!??%!!%?%??%%!?!?%!%!%%!?!!%?%%!%!%%%%!!!%!%%%%?%%%!%!?!%!%!%%?!!%!!?!%%%%!!!?%?%!%?%%%%%!!?!%%%%!!!%?!!!!!!%!%%%!%!!!?!!%%%?%%%!%%!?%!%%!!?!%!%%!%?%%!%!!?%!!!!%%%%??!!%?%%%%%%!!!%?!%%%%!%%?%%%%!%%%!%%!%!?%%%!?%!%%%?!%!%!!%%!%?!!%%?!?%!??%!!??!%%%%!%%?%%%%%!%!%%%!!%!!%!!??!%!?!!??%%!%%%%%%!%%!%!%!%!!?%?%!?%?%%%!!???!%%%!!?%%?%?!!!!!%!!%%%!%!?!!!?%%!%%?!?%!!%%%%?!!!!%??!?%!!?!!?%%%%%%%!%!!%%%%%??%!!%%%?!!!%!!%%%%!%!!%!%%%%!!?!!?%%%!?%!%?!%?%%%%%!%!%!!!?%%?!%?%%%%?%%!%%%%%?!!%!!!%??%%??%%%%%!!%!%%%!%!%%!%%%!%?%%%%!%?%!!%%?%%?!%!!!%?!%%%%%!!?%?%!!!%%!%!%%%!?!%!!!!?%%%%!%%%%?%%!!%??!%%%!%!%!!!!!%%!%!!?!!%!%%?%%?!!%??%%%!?!%%%%!?%%!!%%%%%%%%%??%!%%%%%?!!!!%%!%!%%??!%!%%%%!%%%??%%%%%%!??%%!%%!?!?!%?!?!?%!!%?!%%!?%!!%!%!!!%!%%%%??%%%%?%!%%?%%%%!?%%!?%%!%%??%!??%!%%%%!%!%%?%!!?%!%%!%!%!%!!!?!%??%?%%%%%??%%!?!!%!%%%!%%%?%!%%!%%%?!?!%?%!%%%?%%!!%%%!%%%%%%%%!%!%!%!%!?%%!%%%%%!!!!!%!%!%!!%??%%!%%%%!%%?%!!%?%%%%%%!!%%%?!%?%!%!%!?!?%%!%!%%?%!%%!%!%%%%?%!%?%%!!!%%%%!!%%!%%%!?%%!!?%%%%!%%%%%!%%%!%%?!%!%%%?!?%!%%%%%?%!!!%!?%%?!%%%%%%?%%%?%%%%???%%?!%%!?!!%!!!%?!?%%%%%!!%%%!%%%??%%%%%%%!%%!%%!%!?!%%!!!%!%!!%%!?!!!%?!!!%%!%!%!!!?%?!%?%%!%%!!%%%!!!?!!%!%%!%!???%?%??%!?!%!%%?%%??!?!%%!%%!%%!!?%!%!%%!!%%%%?%?%%%%?%!?%%!%!%?%%???%%!?%?%?%%%!%!%%%!%%%?%%%%!%?!%%%%%%?!%%!%!?%?!%?%%%!?!%%!%%%%%?!!!%%%%%%%%!%!%!!?%%!%%%%!!!!%!?%%?!%!?%%!!!!%??%%%%%!???%!!%!?%%!!?!!!!?%%!???%!!%%%!%!%%?!%!?%!%?!!?%!%?%%!%%!?%!!?%!!%%!!!%!!%%%!!?%?%!!%?%!?!?!!%%%%???%%!!%%%%!%%%%%%!?%%!?!%?!%%%%%!%?!%?%!%!%!%!%%%%?%%!!?%%%%!%%?!?%!!?!!%%%%%%%?%!!!?%!!?%%%!?%?%!!?!?%?!!%%%%!?!!!??%?%%%%!!!!!%%%%%!%%%!%?!%%%?!%%?!%!%%%!%%%%%!!!?%%!!?%%!!%%?!??!%!%!?%%%%%?%!!%?!?!%!%!%%!%?!%!%?%!%%!%%?%%%%%??%?%?%%!%%?%!%??!?%!!%!!!??%!?%!%%!??%!%%?%!%!?%%!%%%%%%!!?%!%!??!?%?!!??%%???!!!%?!%%!!%%%?%!!?!%!%%%!%!!%%%?%!%??%!!%%!!%?!!%%%!!%%!%?%!!?%%%!%?%%?%%%%%!%%!!%%?!%?!!!!!%%%%!%?!%!!%%!!%%!%%!%!?!%%%%%%%!!%?%?%!%?!!%%!!?%!!%%?%%!!!%?!?%%%!!!??%?%!%%%%%%!?%!?!%%!%?%%%%??%%!?!!%?%%??%%?%%!!!!%%?%%%?!%%!%!?!%%%%%%%%%%%%%%%!?!?%%%?%!!%??%%%%!?%%%!%%%%%!%%?%%!%?!%!%?!!%?!!%!!!%%!%!!%%!%!%???%!!!!!%!%!?!?%?%!%??!!%%!!!!%%!?%!%%%!%%!!!%%!%%%!???%!%%%??%!%%?%%!%%!%%?%%!!!%!?%%!!%%%!%!%%%%!??!!!%%%!%!%%?%!%!%%??%??!?!%!!??!%!!%%%%%!!%!!%%%!?!!%!%%?!%!!!%%!%!!!%%?%?%%!?!!%!%!!%%%%%!?%%!%!%%%!!?!!%%%%?%%!%?!%!??!%%%!?%!!%%%%%!%%!!%%?!%!?%%%%%!!%!%%!!?!%%%??!%%!?!%!!%!%??!?!%!?%!%%%%?!!%??%%?%%%%!!!%%?%??!%%!%%!%!!!%%%%!%?%%?%!!!%!%%%%%!!!?%%?!%%%!!!%%!%??%%%!%%%?%!%%%!?!?!%?%%%%%%!?!?!!%?%!%%?%%!%?!!%!%%?!%%%!!?!%!!!%%%%%%!%?!!!%!?!%!%?!!!?!!?%?%!!%%?%!!%?!%%!!?%%!%%?!!%!!%!??%%!!%?!!%%!!%%!!?%?%%!!!%!!%%%!?!%!!!!!%!!?%%?!%%%!%%%%%%%%!!?%%%!!%%?%%%!?!?%!%?%%?%?%%%%%%%!%!!?!!%%%%%%!!?%!?%%%!%%%!!%!!%%%!!?%!!??%!%%%%!!!?!!%%%%?%%?!%%%!??%%%%%%?!?%%!!!%%%%!?%%!!%?!!%%!!%!!%%%%%%%%%!!%%%?!!?!!%!?%!%!%!%!%?!!?!!%%!%%?!%%%!!%%%!!!?%!%!?%!%%??%!??%%%!%%?%%%%?%%!%?!!%!%%%!!%%%?!!%%%%%%%?%!%!%%!%%%%?!%%%!%!!%%%!%%%%%?%!?%?%!??%!!%!%%!%%%?%%%?%!!!%%%!!%?%!%!?%!?!?%%!!%%%!%%%%%?%%%%!!!?%?%%!!%!!!%!%!%%!?!%!%?!!!?%%!!!!?%!!!%!!!%!%!!%%%%%!?%%!!%!%!%%!!%%%!%!?%%%?%?%%!%!%!%!!????%!%!?!%!?%%?!!!?!!!?%%!%%!?!!!%!%!%!%!%%?%!!!%%%%%%?%!%%%%%!%%?!!!%?%%!??%??%?%%%?!%!%%?!?%!!%!%%!!?!!%!%%?!%%%!!%!!?%!?%?!!!!!!!!?%!!%!!%%!%?!?!?%!%%!%%%?!!??%!!!%!%%%!%!%!!!%?!!?%!%!%%!!%?%%!???%?!%%%%%%%!%!!!%%?%!%!%%%?%?%%%!%!?%%!%%!!?!%!!%%!%!!!!?!%%%%?%!!%?!?%?%%?!%!%?%%%%!!%%!!%?!!%?!?!%!%?%?%!!%!%!%%%?%?!%!!%%%!%%?%%!%!%%%%!!%?!!%%%!%%%?%%!%!?!%%%!!!%%%?%%%%?%%%%!?%?!!%!%%%%!!!%!%%%!!?%%?%%%!!%!%%!%!?%%%!%!!%!%%!%%%%!%!%%%?%%%%%%%!?%?!%%!!%!%%%!!%%!%%%?%%?!%%!!!%%%%%??%%%!??%!%!%!?%????%!%?%!!%%?!%?%%%!%%???%!!%!%%%%!!!%?!?%?%?!!!!!%%%!%!!%!!!%%%%%!!!!!?%?!%%?%%%%?!%?!!!?%%%!%!%!!%%%!!%?!%?%%!%%!%!%!!?%%%%?!%?%!%%?!!%!%%%!!???!!!!%!%%!!?%%%%%!?%!%%%%%%!??!%%%%%?%%?%!!%%!!%%!%!??!%%%%%!%%%%%?%!%%%?%!%?!%%?%!!%!!%!%%?%%%!!%!!?!%%%%!!%?!%!?%!?%%%%%?!%%!%%%?!%%?%??%%?%%%!!%%!?%%!%!?%!!%!%!%%%!?%%?%%%%%%%?!%!%%%%!!%%%%%%!!??%%!!%!%!?!%%%!%%?!%%?!!%!%!?!%!?%!%?!!%%%%%!%%?%%%!%%?%%%!!%!!%!??%!%%?%%!%%!%!%!%%%!%%?!!%%!!%%!%?!%%%%?%%?%!%!%%!!??%%!%?!%%%?!%%??%!%%%!%%%!%%!%!!!%%%%!%%!%%%!?%%?!%%!!%%!?%%!%!%!!%%!%!!%%?%%%%%!%%%%!%!%%!%%%%!%%%?%%!%!%%!!!!!!!?%!!?!%%??%!%!!?!%!!%%?%!?%%!?!?!%%!!%%?%!!?%!%!%%?!%%?!!%!%%?%%!%!!%%%%!?%%%%%%!%%%!%?!?%%%%!!!!%!!%!??%%%??%%%!%%!!%!%!%!!%??!!%%%?%!%%?!!%%?%!%??%!%%!??%!%%%%?%%%?%?!%?!!%!!!%%%?%%%%!%%%%%!?!%%%??%%!%%!!%!%%!!%?%%!%%!!%!!%%%!!?%?%!!%%%!%!%!?!%%!!%?!%!%?!?!?%!%!%?!!?%%%!?%!%%?%!%%!%!!!%!!!!!%!%%%%%??%%!%!%%%%%!%!%!%%?%!!??!%%!?%?%?!!!%?%%!%%!!!!%!%%!!!%!!%?!%%%!!%!%??!??!!!%!%%%%!!!?%!%%%!%%%!%%!%%?%?%%%!!%?%?%??%!!!%?!%!%!?%%!??%!!%?!!%%?%?%%%%!!!??!!!%!!!%%%!%!%%%%%!!!%!?%%%%!??!!?!%!!%!%%?!?%%!%!%%?%!?!%%%?%%!?%%!?!!%!!%!%%?%!%!%!!?!%!!%%?%!?%%?%!%??!?!!%?!??%%?%%!%!%!!%!?%?%?%?%%!%%%!%%!?!%!%%!%%!%!%!!%%%%%!!!%%%!!%?%%!%%?%%??!?%!??%%!!!!?!%%???%!%%!!!%%!!%%?%%!!!!%%%!%%%%!??%!%!?!%!%%!???%!%!%!%?%?!!%%%!%%??!%?!?!!%?%%!%!!?%%?!%!%???%%%%%!?!???%!%%?!%%?%%??!!?%%?!!%%%!%%%!?%!!%%%!%%?%!%!!!!%%%!%%??%%%???!!?%%%%!!%%!!%!?!%%!!%%?%%!!%%%%%!!%!!%!?!!%!?!!%!!?!!%%?!!%?!%%!%?!!?%?%%%?!!!!%!%%%!!%?%%%!!%!!%!%%!%%%%!?%%?!%%!%%%?!??%%%%%%%%%!%%!%?%%%!!?!!!%%%%%?!%!%!%%%!!%%%%!!%?%%%!?!!!%?%!!!!%%?%%!!%!!%!!%%!??!!%%%%%%!%?%%%%%?!??%!!?!%%?!!%%??%%%!?!!!%%??%!!%!?!%%%?!%!%%%%%%!%!%?!?!%%?!%%%?%!%%%%%%!%??%%!?%%%?!?%%!%%!%%%%!%%%%?%!%!%%%%!%!!!%!%!%?!%%!!!%?%%!%!%%%!?!!%%%%%%%?!??!%%%?!%%%%%%%%%!%!!!?%?%%!%!?!!??%!!%??%%!%%!!%%!%?%%?%%%!%!!%!!%?!%!?!!%!%!%!?%%?%%!%!!!!%%!?%?!%%!%!%%!!!%%%%!%!!!%!!%!!??%%%%%%%%%%%!%?%%!%%?%?!%!%%!%!%!!?!%?!!!%?!%!!?!!?%%?!?%?%%%%%%!!!%%%%%!%!%!%%!%??%%?%%!%!?!%%%!!?????!!?!?!!!!!!%!%%?%?%!%%!%!!%%!!%!?%?%!!!!%!%!?%!?!%!?%%%!!?!%%!!!!%%%!%%?!%%?!!?%!!%!%%!?!?!?%?%!!!???!!?%!%!%%?!!!!%%??%!!%!%!!%%!%%!?%!%%%%%%!?%!%??!!%!%%?%??!%!%%%%?%!!%%!%?%!?%!%??!%%?!!%!%?!???%!!%!%%%?%%%%%!?%!?%%%%!?%?%%%%??%%!%%!!%!!%%!%%?%!%?%%!???!?!!!%%%%?%?!%?%%%%%!?!%%%%%%!?!%%%%%?%!%!?%!%%!%?%%%%!!?%%!?%?%!!%?!%!%!!%%%!%%!%%%!%!%?%%%!%%%!!!%%%??!!!!??!?%%%!!%%?%!!%%?!%%%%?!!!?!%!%!!??!%!%%%%!!%!?!%%?%%%%%??%%!%%?!%!%!%%%%%%%!!?%!!!!%%%%%?%%%%?!%!!%?!%!!!!?!?!%%%?%?!%?!??!%!%!%%!%%%%%%!%%?!!%%?!%!?!?%%!!!%%%!?!!%!!%!?%%%?%!!%%!!?%!!??%!%%%%!!%!%!?%%%%?%%!!!%%%!%%%%!!%%%%?%%%%?%%%?!!%%%!?!!%!!!%%?%%%%%??!!?%!?%%%%!%!!!%%%!!!%%%%!?%!!%%%!%%!%?%!%!!%???%!%!%!!%?%%%%%%%%%%%?%%!%%!%?%!%%?%?%%!?!!?%!?%!!%!?%?!!%!%!%%%%%%!%%!%%!??!%%!!%%!%%%!!%%%%!!!%%??%%%%%%?!%%?%%!!%%!!%!?%!?%??%!!!?%!?!!?!%%%?%!!%!!!%!%%?%%!?%!!%%%!%!?%%!!!!!!%%%%!?!%%!%%%%!?%%!%!?!?%%!!!%?!%!?%%!%!!%%!!!!%!%%%%%!%!!!%%?!!?!%%%%?%%%!!?%%!%%%%??%!%!?%!%???!%%%%!!%%!%%?!%%!%%%%!!!%%%%%!%%!!%%?%?%%%%%%!?!%%??!%%!?%%??!!!?%%??!!%%??!!!%%!!%%!%!!!%!!!%%%!!!%!%!!%!!%%!%?!%%%%?!%???!!?%%%!%%%!!%!?!%!%%!%??%!!!%!?!%%!??!!%%!%%%%!!!%%!%!%%%!!%!%%%!%%!?%%%%!%?!%%%?%%!?!!%%%!%!!!??!%%%%!!%!%?%%%%??%%?!?%??%!%!?%%%!!%%%%!%%!%!??%!%!??%%%!%!%!%%%%?%%!%%!%!%%!!!%?%%!%!%????%%?%?!!%%!!%?!%?%%??%?%%%?%!!%%%!%!!?%!!!%!%!!!!%%%%%?%%%%?%!!%!%?!?%%%%!!?!%!!!?%%!%!%!%%%%%!%%%!!?%!!!?%!%%%%!%?!?%%!%!%!?%%!?!%%%%%%%%%%?%!%%%%!%%%%%%%%%?!!!!?!!%!!%?%!%?!%!%%%?%%%%%%%%%!%%%?%??%%!%%%!!%!%!%%%%%%??!%%%?!%!%!!%?????%%%%%!!%%?%!%??%%!%?%!%!!!%%!%??!%%!%%%%%%%!%?!%%!!%??!?!!!!%?!??%%%??!%%%!!??%??%%%!??!%!%%!%%!!?%!%%%?!%%%!%%%!%%!!!%?%!%%%?!?%?%??!!%!!%%%%%%!%%?%%?!!!%%%%?%%%!!!?!!!?!!%!%%%%!%%!?%%?!%?!!!?!%%%%%%%?%?%%!%%!%!%%%%!?!!!%!??!%%%%!%!%%!%?%?!!%!!%?%?!%%%!%%%!?!%%%!%%?%%!%?%%?%%?%!%%%?!%??%?%!!!!%!%!!%%??!%%%%!%!%!!%%!!?%%%%%?!%%%%%!!%%%%%!??!!!?%%!%!%?!%!?!!?%??%?!!%??!!%%!!%%!!%?%!%%%?%%??%%!!!%!%?!?!%?%!!!%!%!!!!%?!!?%%!%%!%?!!??%?%!!%!%?%!!?%%??%%!%?%%%!??!%%%%%%!?!%?%%!!%%!?%!%%%!!?%!%???!%?%!%!!!%%%?!!%??!%!%%!%!%%%!?%%?%!%!?%!!%???!!!%%?!?????!!%!%!%?%%%?%?%?!!?!!!?!%?%%!!?!%%!?!%%!!%%?%!%?!!!!?%!%!%??!%%?!%%%%%%!??%%?!%!!%?!?!%!%%?%?!%!%??!%!%%!??%%%%!?%%!%%?!!%!?%!!%!%!%%%!?%!%%%%%%%!%%!!!!!%%%%?%!%?!%?%!!%%%%!?!%%?%!!%!%?!!!%%%%!!?%%%!%%!%%%!%??%%%!!!%%?!%%%!%?!%!%!!%%?%!%!%?!%!%!%%?%%!%?!!%?!%!!%??!%!%%%%?!!%%!%%%!%%%?%%!%?%!%!%!%%!%?%?!?!%!!%%!%%%%!%%%%?%!%%?%!%%%%?!%!%?!%%%!!!%%%%%%!!%%!??!%!!!?!%%%%?%%%%%?!!?%%!%%%%!!%!!!!??%%?%%%%%%!%!%!%!?!%!%%?!?%%?%%%!!%%!!%?%%!%!?!!%%%%%%!!%?%%%%?%!%?!%!!?%%?%%%!%??!%%?%!%!%%%?%%!%%%%%%%%?%%!!%%?!%!%!%!?%%??!%%%%!!!!%%!%%%%!%%%!?%%?!%%%!%%!%%%!!%?!!!!!%?!%!%%!%%!%%!%?%?%%%!?%%%?!!%%!%?!%?%%%%%%%??!?!%%!?!%!!??%??!?!!%!?%!%!%!?%%%%!%!%?%%%%!%%!%?%%%!%!%%?%!!%%??!!!!%%%%?!%!!%%!!?!??!?%??!%%%%%%%?%%!%?%%!!?!%%!!%%%!!%%!%!%%?!!!%!%%%%?%!%%!!%%%%%?%!%%%%%%%%%?%?%%??%!%!!%!?%!%!%%%%?%%!%!?%%???%%?!!%!!?%!%!%!!!%?!%!%?!?%%%!%!!?%%?!!%%%%!?!!?!%%!%%%!?%%!%%%?!!?!!!!!%%%!!!%!%%%%%%!!%%%%!!%!!%?%?!%!!%?!?%!%!?%%%!%?%%%%!!%%%??!!!!!%?!%!%!%%!%%!%%%%%!%!?%%%%!%?!?!%%?!%!!!?%%%%%?!%?%%!?%%!!!!%%!!?%!%%%?!!%%!!%!%?%%?!!%%?%%%%%%!%!%%?%!%!?%%%%%!%%!%%%?%%!%%!%!!!%%%!%!%%%!?%!%?%!!!?%!%%%!%!%%%%?!?!?%!!!!!%??%!?%%!!%???!%%%%%%%!%?%%%!%%%%%!!%??!!!?!%%%%%%!%%%%%!!%%%?%%%%!%?%!%!%!!!??%%%!%!!!!%!%%%!?!!!%%%%!%!!%!!!!!%%!%%%%?%%%!!!%%!%?!?%%?%%?%%%?!%!!%%!!%%!???!?%%??!%%!%?!%%%!!%!%!!!%%%%%!!%!%!!!!?%!%%%!%!%!%!!%?%%?%?!!?%%!%!%?%?%!%!!%?%%%%%!!%%!%%%%!!%?!!!%%!%%%!%%?!!!!!%!%%%!!%!!!%%!!%%!%?%!!%%%?!%%%%?%%%%%?!%???%%%%?%!%%%%!?!?!%!%?%!%!%%%%!%??%%!%!%???!%%%!%!%%!%%%!%%?!?%%?%%!%?%%%%%%!%%%!!!%!!%!!%%!%!%%%%%!%!%%?%?!%?!?!%%!?!%%!%%%?!%!!!%!%%!%%?%%?%!%%%!??!???!!!!??%%!!?%%%!%%%!?%?%%%??%?!!!!?%?!%?%%!%%??%%%%?!!%%%%%%??!!%!!%????!%%%?!?%%!%%%?!%????%%%!!?%!%%%%?%!%?!!%%?!%%!%!%!%%!%%!!!???!%?%%?!%%!%%%!!%%?!%!%?!%!!!%!%%%!!!%?!%%?!%%%??%!!!%!%!%%%!!%%!!!!!??!%%%!%%%%%%!%!%?!!%%!%%!%!%!%!%%%?%%%%?!?%?!!!?%!!%!%%%%?%!%??!!!!%!%%%%??%!!!?%%?!!!!!%%!?!%%!!%?%!!%%!!%%!!%!%!%%%!%!?!%%%%??%?%%!?!!!!!???%!%%%%%!!!%%?%%%?%!%%!%!%%??!%!%!!%%?%!???!%%%%%%!!??%?%?%%%%%!??%%?%%%%!?%%%!!%!%!%%!?!!?%!???%!%%?%?%%%!%%%!!?!!%?%%%?%?!!!%!%%%%?!%%!%%%%?!??!%???%%?!%?%%%!!!%%!!%%%%%!%%%%!?!%!%%%!%%!!?!!!%%!!%%?!%%?%?%?!!!%%%!?%%%%%%!%%%?%%%!?%?%%!!%!%?!%%!!%!!%%!%?!!!?!%%?%!%?%??!%%!%%%!!%?!?%%!%%%!%!%!%!!%%%%!!!%!?!?%%%!%!%%%!!%%!!%!%%%?%%%!??%%?%%%!??%?%%%!%%%!?%%!%%!%!%%!!%%!%!%?%!%%%%%%!!?!%%!%%%!%%!?!!?%%%%??!%%?%%!!!%?%%%%%%?%?!%%!?!!!?%?%!%!?%???%%%%%?%????!!%?%!?%%%!%%%??!%!%%%%%!%%?%%!!!%!%%%!?%!%!%%?%%?%?!%%?%!%%!!%?%%%%%%%!%%%%!!!%!%%!%%%%%!?%!%!!%%%!!%!?%%%!??!%!%!%%%!%%!%!!%%%!%!??%!%!!!%!%??!%%%?%%!!!!%%!%%%%%%!!!!%!%!%%!!?%%!%%!%%!?%!!?%%!%!%%%%!!?!!!!%%%%!?%%%%?%!%!!%??!?%!!%!!%!?!?%%??%%%%%?%?!%%%%%!%!%!%%%!!!?!!%?%!?!%%%?%%%!?!!%%%%%%%%??!%??%!!!?!?%%?%%?!%%!%%%%!??!?!%%!%%!%%?%%!?%!!%!!!%!%%?%??!%%!%?%%!?!%%!!!%%%!%!!%!%?%%?%?%??%%!?%??%%!%!!%%%%??!%%!%%!%!??%?!!!%%%%%!%%%!!%%!%??!?!%?%%!%%%%?!%!%%%?%%?%??%!!%%?!%!%!%!%%%%%%?!!!!%%%%%!!?%%%%?!%!!!!%!?%%?!!%%%%%%!%!?%%?%%?%%%%?%%%!%!!%%!?%!%!!!%!!%%!!?!!%?!%!%?!!!!%%!%!%!%?%!%%%%!!?!!%!!!!??%?%!%%?!%%%%%!%?%!%!!%%%%??!%!?%%%%%%!!%%?%!!%?%!!%%!!%%!!!?%%!!%!!%??!%%%?%%??!!?%!!%?%%!%%%%!%%!%%%%%!%!%!%%!%%!!??!%%!?!!%??%!%!!!!??%?!!%%!?%%%!%%!%%%%%!!??%%!?!%!%%!%%%%%!%%!%%!!%%!!%!%%!%%%%!!%!!%!%!%%?%!!%%????!!?%%%!%!%%%?!%?%!?!%!!%!%!?!%%!!!%%?!%%%!!!!%%%!!!%%!%%!!%!!%%%?%!?%%%!?%?%%%%!%%!?!%%%%%%!%%!!%?%%%!?%!%%!!!?%!%!??%!!%!!%%%!%%%%!!%%%!!!!!%!%%!%%!!%%!!%%!!%%%?%!!%%?%%!%%!%!%!%%%!!%!?%%%!%%!%?!%%%%%!%!!%!%%%%%!%%%?!?%%%%!!%%%%%!??!%%%%!?%%%%!!%%?%?%?%!!%%%!%%!!?!%!%%%%?!%%%!%!??%%!%!%!%!%%%%%!%??!%!%!%%%!%!%%?!!%%%!%!!!??!%%!!?%?%??%%?%!%%%!!%%!%%%%%!%%!%%!!?%?%!%%??%%%!%!!%?%!%%??%!?!!%%!!%!%%%%??%%?!!?!!%!!!%!!%%!!!%!%%!%!%%!%%%?%%!!!?%%?%!%%!%!%!!!%?!!?%%?!!!!!%???%%!?!!%%?!!%??%%%%%!!%?%??!%?!!%!?%?!!%?!!?!%?%%?%?%?%?!%!!!!!!%%%!?!%%%?%!??!?!?!!?%?!!%!%%!?%%%%%%%%%!?%!?%!?!%%?!!%%?%!%%%??%%?%?!!!%%%!%%%%!!?!%%!%%%%?%%!!%!%!!??%%!%!!%%!!?%!!?%%?%%%%!%!!%%%%!%!?!!!%%%!!%?!!!%%%%%!!%%?%!!%!%??%%%!%%?%!%%??%??!%%%%%%%?%!?%?!!%?!%%%!%?!%%%!!%%%%!%%??%%%%?%!?%?%!!?!%%%!!%!!%%?%!!?!%?%%!%%!%!!%%%??%%!?%?!?!?%%%%!%%%!%!%%%%!?!%%%%!%%!?%%%?%!!!%%?%%%%%%%%?%!%??%!!%%%%!%?!%%%%!??!%%?!??!!!!%%!!!%%!!!%%%?!%!%%!!%%!%!%?%%%%%%!%?!%%!%?!%!!!?%%%!?!!%!%?%%!?%%%%%??!!!?!!!!%%%!!!!%?%?%!?!%!!?!%!%%?!%?%!!!?!%%!!?%?!%!!%%!%!%%?!??!%!%?!!?%?%%%%%%!!?!%!?%%%?%%%!%%!%?%%%??!!!!%??!!!%?%%%!??%%%%%!?!%%?%%!%%%!%?%!%%!!!%!?!??%?!!!%!!%?%?!!%!%%!%%!!!%%!?%!%%!%?%??%%!!%?!?!?!%?!!%?%%%!%??!!%??%!!!!!%!??%??%!?!%?%%%%??%!%%%%?%?%?!%??%!%%!!?!!!%%%%%%%%?!!!!!!??%!!!!%?!%%!!?%!?!!%?!%!%%%%?%?%?%%!?!%%%%!%!%?%!%!!%!?!?!%!%%%%?!%!%!%%%!%%%!%!%%?%%%!%!%%!%%!!?!!!%%%%?%?!%%%!%!!!?%%!??!?%!!!!%%%%%!!!?!%%%%%!%%%?%%!!!!!%!?%%%?!?%?%%%%!?!!%%!%%!%%!!%!??%?!!%%%!!!!%%%%%%%?!?%?%%???!!?%%?!!%%%%%?%%!%%%!%%!!!!?%%!!?!!%?!!!?%!!!%!!%%%!%!!!!%%%!%%%%!!!%%%!?%!?!?%%%!!!%!%%?!?!!%?%!%??!%!!%!%!!%!%%!%!!!!%%%%%%%%%!%%?%?%!%%%!%!%!?%?%!!%!!%%%?%%!!%%%%%%!!!%!%!!!!%?%%%!%%?!%!%!%%%!%%%%%!!%?!%%!%!%?!%!!%%%!!?!%?!%!%%!%%!%%%!%!?!%%!?%%!!%%%???!?%%?%%?!%!?!!!%%?%%!%%!!%!!%!%%%!!%%%%!%%!%%!%!%!!%!%%!!%%%%%%!%%%!%??%%!!%%!!%%%??%!!%!%%%???%!!%%!%%%%?!?%%%!%%?!%?%!!!!%!%!%?%%!?%!%?%%%%!?!%%%!%!%??!?%!%%?%%??%%!!%%?%!%!%?%???!%%%?%%%!!%%!?%?%%!!!%%%!%%%!!%!%?%?%!!!?%%!%%!%?!!%%!!?%!%??%%%%!%!%%%%%!!!!!??%%?!!!%!%!%%?!%%?%!%%%%%!??!?!%%%??%!!?%%%%!!%!!!!%%???!?%%!%!%%!%!%%!%!!%?!!!?%??!%!!%!!%%%%%!%%%??%?!?!%%%%%???!%%%!%%!?%%%%?!%!?%%%%%%%%!!%?%%!%?!!!!%?!?%%!!%%??!!!%?!%!%%%%%?%%%!!?%?!%%??%%!%?!%!?!%%!!??%???!!%%!%%%!%!%?%%%!%?!!!?!%%!%%!!!%!!%!%%%%%!!!%!!%%!!%?!!%%%%!!?%!?!%??!%!%!%!%%?%!%%%?%%!%?%%%?%%!%??%!%?!%!?%??%%%??!%?%%%!%%%%?!!%%?%%%%%%?!!%%!?%%%%!%!?!!%!!!!%!!!%?%%?%%!!???%!?%%%%?%?%?%?!%%%%%%%!%!%!%%!%%!!!!!%%?%!%%!%!!!!%!%?%%??!?%?!!!!%!%!%!%!%%%?%!%?!?!%%?!%%%%??!%%!%!!?!%%?!%%!!!%!%!!!?%?%?!!!!%%%!%!?!%!??%!!%%%??%%%?!!%!%??%!%%!!%!!%!%!%%!%!?%%%%!%%?!%%%!!%!%?!%!%!!?!%!%%%!!%!%%%!?%!%%%?%%%%?%%?!!!%!!%%?%%?!?!%%%%%%%%!!%%!!?%%%??!!!%!!?!%%%!!??%?%!%%??%?!%%%%%%!%??%%!%!!?!%%%%!?!!!?%%!!%!?%%??!!%%?!%!!!?%?%%%%%%%%!!!!!%%?%%%%?%?!?!!!%%%%%?!%%%!%!%%%%!%!?!?%%!%%!!%!%?%!%?%!!!%!%!!!?%!!!%%%%%%%%!%%!!%%%!?%!!%%%%%%%!%!?!%?!%%%!%?%%%!%!%%%%!?!!%!%%%%%!!?%?%?%%!?!%%!!!%%!?!%!!%!%%%%!%%?!%!!%%?%?%?!!!!%%!!%!!!%?%!%%%%?%!%!?%!%%%%!!%!?!!%!!%!!!%!!!!!%?%?%!?%!?%%!%?%%%%!!%!%?%!!!%!!%%%??!!%?!%!!!!%%!%%?%%!%!%!??%??%%?%!%?!?!%%%!%%%%!!%%!?%%!%%!%%!%%!!%%%%!%??!??%%!!!%%?!!%%%?!%%%??%!%%!!%%!%%%%%%!!%%%%!%!?%%%%%?%?%?%!!!?!!%?!%%%!!??!!!%!!%???!????%%%!!%%%!?!%%!%%%!%!!!%%%!?!%%!!%!%%?!!%?!%%%!%!%%!?%%%%%%!%%%%%?%%!?%%??%?%%%!!???!%!!!?%?!?%?%%%!!%!%?%%%%!%!%!%%%%?%!!?%?!%%%%!?%!%%%%!%!%!%%%!!%!%%%%%?%%%%%%%!!%%!???%!!!?!%!%!!!!%!!%?%%%!%%!%!?!!%?%%!%%%?%!%!%%%%?!%%%%%!%!?!%%%%!%!%%!!%!%%%!!%%%%!%%%!%?!!?!!!?%%!%%!?%!%!%%!%%%%!!!!!%%%!%%%!!!!??!!!?%%??%%!!%%?!%%%??!%%!?!!%%%%%%%%!%!!?%%??!%!?!!!%%?%?!%%?!?!%!?!%!!!%%%%!%?%!!%%!?%!!%%%!?%!%%%%!%!%?!?%!%%%%?%%!%?%%%!?%!%?!!%!%%?%%%%!!?%!%!%??!%%%%%%!!%!!!??!!!%%!%%%!%?%!%%%!%!%!????!%!%%%!?%%!%?!%?!%!?%%%!?!%%%%!%!%%%%!?%!%%?!!?!%%%%%%!%%%%?????!%%!%%!!?!%?%!?!!%%!%%?%!%%!?!%!%%!%!?!!?!!%%%?%!!!!!!!!%%%%%?!%!%%%%%!%%%!!!!%??%%%%!%?!%?%?!!%!?!!%%%%%%!%%%?%%%%!!%%!%%!%?%!!%%!!?!!!!?!%%?%%??%%?%%%??!!%!!!%?!%%%%!!%!%!!%%%%%%%%%%!!%%%?%!%!%!?%%!%!?%!?%%%%%!?%%?!!%!%!%%!!%%%??%%!%%%!%%!!?%%!%!?!%%!%%?!!%%%%!%%!!%?%%?!?%!!!%!%%%%%!!%!!%??!%%?%?!!!%!!?!%%?%%!!!%%%?%?%!?%!%?%!!%??%%%%%%%!%%?%!%%%%%!%?!!!!!?!?%?!!%%?!!!?%!%!!!%?%%?!!%%!%!!!%%%%%!!?%!!!%!!??!!!!%%?%?%%?%!?%%!%%%%%?!!%!!!!%!?%!%?%%!!?%%%%!%!!%%?!!!%?%%!!!!%%!%%!!!%!%!!%!%%%%!!!%%?!?!%??%%%!!??%!!%%%%%%%%!!!%!!%%?%?%%!%!!%!%%%!%!%!?%%%!%%%%%%!??!%!%?!%%!!%!!%%%%%?%%%%?!%%!%%!??!!?%%%%%?%!!%!%%?%?%%%%%%%%!!!?%%%%?!!%?%!%%%%%?%!%!%%!%!%%%%?%%?%!!!%?%?%!??%!!%%!!%?!%!!%!%%%%%!%?!%!%%%!%!%%%!%%%!%%%!%?%%!!!%%!!!!%%!%%%%!%%%?!%%%!!%!%%?%%?!%%?!!!?%!%%%!!%!?!%!!!%?!!%%%!!%%%???%%?%!%?%%%!!%%%!%!!%%%??!%%%!%!?%%%%%%!%%!?%%%%%!!%??%%%!?%!%!%!%%%!!!%%?%%!!?!!!!?%??%%%!%!?%!?%%%%!%!%%%%!%?!!%!!!?%%!%!!!?%!%%%!??!!!?%!%!%%%%%!?%!!!%!??!%!%%?%!?%??%%!%?!?%%%!?!%?%%!%!?%%!??%!%!!%%%%%!!!!!%?%!%%%!!!%!%!!!%?!%!%!?!!!%!?%!%%?!%%!%!!%?!!!!!!%%!!!!%!!?%%%%%%%!!!!%%%%%!!?!%?%%%%%?%%!%%%%%%?%%!%!%!!!%?%%!!%%%%%%%?!%%%!%?!?!%%!%%%?!%?%??%%%!%%%%?!!%%%%%!!%%%!!%%%!?%%!%?!!%%%!%%%%!%%!!%!%?%%?!?%!%!?%%%?!%?!?%%%%%%!!!!%?%%!?!%!!!?%%%!!!!!!?!%%?%%!!%!!??%!!%%!?%?!%%%?!?!!!%!!!%%%!%!%%!%%%!!%%?%%!%!!%%!%%!%%!%?!??%%!%?!?!%%!?!%%!%!?%??%!????!%%!!%?%%%??%?%%%!%!!%%?%!%!%!%!%!!%?!!!!%!!?!??%%%%%%!!!!%!%?!%%%!%%!!!!%??%!%%%%!??!!?%!??!%!?%%?%?%!!?!%%%%?!!%!!%!?!!%%??%%%%!?!?%%%!%!!?%%%?!%%%%?%!!??!!%?%%!%%%%!?!??!?%%!%%%%?%!%%%%??%!%%?%!%?%?%!%?%%%%%%%%%?!%%%!!!!%!%%%?!!!!%!%%?!%%%!%?%%!%%%%%!!!%%!%%%%%%%?%!!!%%%%?%%!%%%%%%%%?%!?!%?!!!%!?!%?!!%%%%%%!?%?%%%?!%%%%%%%!!?%%%%?%?!%%??!!!?!%%!?!%%!!%%%%!!%%%?!?%%!!%%%%%%%%%%?!%!?%!!!%%!%%%%%%%%%%!?%!!!!!!?!%%%!%%!%?%%!?!?!%%%%%?!%?!%%%!!!%%%%!!%?!%!!?!!%!%%%!%?%%!%%!%?!!%%%!!%!%!%%!%%?!?%!?%%!%!%!%?%!%!!?%!%%%!!!!%%?!?!!%?!?%%!!?%%%!%%%%%%!%!?!!%!%%!!%%!%%%!!?%%!%?!!%%%?%!!%%??%%%!!%%!?%??%%!!%!%%%?!%!%%?!%!?!?%%!%%%!!!%%%!%!!!%%%!!%!!?%%%!%%%?%!!?%?%%%!?!%%?%!%%!%?%%??!%?%!!!%!!%?%!??%%%!!%!%!%%!!!!%%?%%!?!%!%!?!%!?%!!%!!%%?%!!!!!?%%!!!!%%%%!%?%???!%%%%%%%%%!?!!%%!%%?%%!??!?%!%?!%!!???%!!%!%!!%!%%!!%%%!%%%%?!!?!%!?%%!!%???!%!!%?%!%%%%?!%%!%%?!%%?!!%!%!%?%%!?!!%!%%!%%?!%%%%%%%%?!!%%!!%%%????!!%%%?%%%!!%%!!????%%%!!%!?!?%!?%%%?%%?%!!!!%%%!%?!%!?%!%!!!%%!%%?%!?!?%%?!???!%%!%%!?%?%?%%%!%?%!%%!%!%!%?%%!%!!%%%?!%!?!!?%!!!%%%?%%%!!%?%%?!%%%%%%!%%%%!%%%!%%%%!?!??%%%%%%%%?%!!?!??%?%?!!%%%%%%%%?%%!?!%!?%%!!%%%?!!!%%!%?%!%%%%!!!?%!%%?%?%%%%%%%?!%%?%%?%%??!?%!%%!?!%%%%%%%%%?%!!?%%%!%!%??%%%%%!?%%%%%!!!%%%!%?!%%%%%%%%%!%%!?!%!%?%!?%!%?!%?%?%%%%!!%%%?%%%%%?!%%???!%%?%%!%%%%?%!%!?%%%!!%%?!?!!!!?!?!%%!%%!!?!%!!!%%?!%!%?!%%?%%%!!%?!!!%%%%%%!!%??!%%!!!!!%?!%%%!%%%%%%%!!%?%!!%%%!!%??!%?%!%%%?!!!%%%!!?!%%!%?%??!%%!%%%?%%%!%!%%?%!%!%!!%?%!%?%%!?%??%??%!?!?%%%!%%?!%!%%%%!?%%?%%%!!!?!%%?%!?%!!%?%?%%?!%%%?%!%?!!%%%%!?%??%%%??!%!???%!!%?!?%%!!!%%!?!!!%%!%%!%%!%?%%%%!?!%!%%%?!%%!!?%?%%!???%%?!%%%%!?!%?%%!%!!?!%%!?!%%!%!%%%!!%!%%!%%??%%%%!%%!%!??%?%%%%!!!?!!%!%%!%%?!!%%%!%%%!!%!???%%!!?%%!%%%%%%%%%!%?!%%%%%!%!%!%!%%!?!!%%?!%%%!%??!!%%?%%?!%%%!%!%?!!%%!!%!!%%??!?%?%!%?%%%!?%%!%!%%?%!%%%%!%%%%!%%!%!%%!!!%%!%!!%%?%%%%%%%%%%?%!?%%%%!??!%%%%%%?%?%%!%%%%%%!?!!%%%!%%%!?%?%!%!!%%%!!!!!!!??!?%?!%!!%%%!%%%??%%%%!%!!%!!!%!%!%?%%%?!%!%%%?%%!%%%%!!!?!!%?!%?%%!!%%!%%?!!%!%!!%%%!%%%?!%!%!%!!?%%%!%!%!?!%%%%%!!%!!%?%%%?!%%!!!!%%%?%%%%!?%??%!%?%?%!!%%%%!%?!!%!?%%%!!?%%?!!%%??!?!%!%!%%?!%!%%%%!????%?!!%!?!!%!%!%!!!%%%%%%!?%?%%!%%!%?%%!%!%%??!!%?!!%%%!%?%?%??!%?%!%%%%%%!!%?%?%!!!%%!!?%%?%%!%!%!!!%?%!!!!%!%%%%??!%%%!%%?%%!%%%%%%?%!%?%!!!!!%%?%?!%?!!???%%?%?!%?%!%%!!%!!!%!??!%%!!!?!%%!!%?%!!!%%%%%!!!?%!%%%%!%%%%%!%!%!!!%!!?%%%!%%%?!%!!%%%%?%%!!!%%%!%?!%!%?!%%%%%!!%??!%%%%!!!!%!?%!%?%?%!%%!!!%!!%?%!!??%%?%!!?!!%?%?%!?!???%%!!?%%!!!%!%%%%%%%%?%!!%?%%%!%%!%!?!%!%?!%%%!%%%!!%!!%%%?!!!%%!?!?%!?!?!?%??!!!%!!%%!!!%%%%%%%%!%%!?%?!%%?%%%!%%%?%?%!!%!??!!!!?%%!%%%%%%%!?!!%%?%!!%!!!?%%%%?%%!!?%!%?%%%%%!%%%%?%%%!?%!?%!!%!!!%%?!%!%%?%%!%%%?%?!!%%%!%%!!%!%%%?%??%!%!%%?!%!!%%!%%!?%!%%%%%?!%%!%%%?%!!%%%%!%%!!%!!%?!?%%?!!!%%!%%%%%!?%!??%%%%%%!!!%?%!%%%%?%%??%!%!%!!%%?!!!%%%!%!?!!%!!!!!%%%%?%??!?%!%%%!%%%!%%%!!!%%!!%?%!%???!!%!%?!%%?%%!??%!!!%?%%%?%?%%!%%%%!%?!%?!%%%!%!!!!%?%?!%!!%!!%%?%%%?!!?%!!%%!%%%%%!%!?%!%%%!?%!%?!!!%!%!%?%?!%!%!!!!?!!!!!%!%?%!%!%?%?!%!%%?%%%%?!!?%%!%%!!%%!!!%?%%!!?%%%%%%%!!!!?!!%%%!!%%!%!%!!%!%%%%%!!%%%!%%%%%!!!%?!!%%%?%%!!%%!%%!?%!%%%%?%%!%%%%%%%!%%%!?!%!%!%??!!%!%%%??!%!%%!%%!%%!%!%%%%%!%%%!%%%!%%%!%!%%?%%%%%%%%!%!!!!%%%%%?!%%%!!%%%%!%%%!??!?!!%%%?%%%%%??!?!%!!%%%%%?%!%%%!!!??!%%?!%???%%%%%!%%!!%!!!%!!%%!!%!!%!?%!!%%%!%!%%%!%%!??!!!%%%!!%!!!%%!!!%!!!%%%%!%!%%%%!%?!%!!!%!!%!%%!%%%!%%!??%?%!%%!%!%%%?!!%%!!!??%%!?!!!?%?%!!!%!!??!%%%%%%?%!?%?!??%%%?!!%!!!!%!%?%!%%!%%??!%!!?%%%?%%%%%%!!%!%!!%??!!?!!!!!%%%!%?%?!?%%!?!%%!!%%%%?!!!??!!!!%!%!%?%!?!!!%%%%!%!!%%%?!%?%!!!!?!%%!%!%!%%%%!?!!!%%%%%%%%%?!%%??!?%%!%%%%!%!%%!!!%%!%?!%%%?!!!!%!%?%%%%!%!%!!?%%%!?%!!?!%%!%%%!!%!%%!%%%%%%%%%?%%%??!%%%?!%%%%%%!%%%!!%%%!?%?%?!!%!%?%?%%!!!%%%?!!??%%%%!%%%!%!%%%?%!%!!%%%?!%%!%?%%!?%%%!!%!!%!!!%%!%%%!%%%%!%%!%!!!!!?%!?%%!%%%?%?%%%!?!%%%!?%!!%%!!%%%!%%!%%?!!!!!%!%??%!%%!!%%!!!?%!!!!%%!!?!!%%!%%!?%!!%%!?!%%%!!%!%!!%%!%%%!?!%%!%!%%!?!?!?%%!%%!!!%%%?!%?!%%%!!%!%!%!%?!%%!%?!?!%!?%%%!!!!?%%!?!%?%%%%??!%%?%??!!?%%%!%%%%!!?%%%!%%%%!%%?%%?!%%!!?%%%%!%%%!?%!%??!?%%?%!%!%%?%%!%!%%%%%%???%??%%%!%%%?!%!%%!%%%%?!%?!%!!%%%%?%%%%%%%?%%%%%%%!?!%!%%%%%!%!%!%?!!!%!%?!%!%?!%!!??!!!!!%!%%%!%?%%%%%!!%!%?!%%!?%!!%!%%%!??!%%!!!!%%?%!!!!!!?!%%!%%!%!%!?%%!?!??!!!?!!%%%?%%%!%%?%%%??%!%!%?%!!?%!!%?%!!!?%%??%%!%%%%?!!%%?%!%!!!?%!!?%!?!!!%!%%!%%%!%!!%%%?%!%!%!?%?!%%!%???%!%?%??!%%!!?!!!!%!!%!!%?%%??%%%%%?!?%%!?%%?%%%?!%%?!%?!!%%?!?%%!?%!%!%%%!?%!%%%?%?!?!?%%!!?!%%!%!%!?%%?%%!%%!?%%?%%?%?!!%!%?%?%!%!!!?%!%%?%%%!%!%!!?!%%?%!%%%?!?%%%%!!%!!?%%??%?%%!%%!%!?%%!!!?!%%!!%%%!?!%!%?!%!?!%%%!!%???!%%%%%?%%%%%%?!%%%%%!%%!!%?!%!!?!%?!%!!%%!?!?!%!?!??%%%%%!%%%?!?%%!%%!?%?!%%!?!%!?!%%%%?!?%!%%%!%%%%?%%?!?!%!?!%%!!%!?!%!%?%%?%%!??!%!%?%!!!!%%??%%!??%%%!?!%%%%%%%%!!%!%!!%%%?!!!%!!!%???%%%%%%!%%!!!%?%!?!!%%%%!!??%!!%!!?%%%!!%????%!%?%!?%%!!!%!??!%%%%%!!?%!???!?%!!!%%%%%?%%!!?%!!!%!!%%?%!%!?!%%%%?%!!!!!?%%!%!%%%!?%!%!%%%!!!%%?!!%?%!%!%!%%!%%!?%?!%%!!!%%%%%%?!!%!!!!%%!%%%%%?%!?%!!!%!!?%!%%!%!%?%%?%%!%?%%!%?%!%?!%!%?%?!!!%?%?%?!%?!???%!%%!%%%!%%%%!%%!!%?%%!!!?%!%?%?%!?!?%%?%!%?%%!%!!%!%?%%!%%%%%%!%%!!!!%?%?!?%%%!!%!!!?%!%!%%%%%?%!!!!!!!!%%?%!!!??%!%?%?!!%%%%!%!%?%%%%!%%!!%%%%%!%!%%%?%%%?!?%%%%%?!%%%%????%%%!!!%%??%??!?%%%%%%%%%%?%%%%!?%%!?%?!?%!%%%%%%!!%%%%%!?%!!!%!?!!?!%%!%%%!?!%!!!%%!?%%%%!!!?%!%!%%%%%%?!!!?%%%!%%%%?%!%%%??%!%!!!%!?%%%%!!%!%%!%!!%!!?%??%%!%%%!%!%%??!!%%!???!!%?%?%!%%%%%!!!%%%%!?!?%%%!%!?%!!!%%%%%%?!!%%!!%%!%!%??!!?!!%!!%%!!%%%%%?!%%!!?!!!%%%%?!??%%%%!?!%%%?!%!%!%?%?!?%%!%%??%!?!%!!%!%%!%!!!!!%?%%%?%%%!%?%!%%%!%!!!%%!!%!%!%%%%?%!!??%%!??!!!%%%%?%!!!?!%%!!%%%%%!??%?%%!%!!!%%%%!!%%%?%?%%%!%!?%%%!!%%%!!???%?%%%%%!%!!?%!!??%%!%?%%%%!%%!!!!%?!!?%%%!%%!!%%%!?%!%%!%!%%%!%%!!?!%!%!%%!!!%%%!?%!!%%!!!!?%%!%!%%!%?%!%!%!%%!%?!%%?!%%%!!%%%!%%!!?!%%??%!%%!?%!!%?%!%%?!%!%!!!%!!%%?%!!?!%!%!!!!%%%!%!!!%????!!!!?!!%!%%!%%%%!%%%%!%%%!%!%?!!%?!%%%?!%%?%%%!%%%?!%%!%!%!%!!%?%%%%?!%!%%!%%?%%%?!!%!%?%%%%%!%!%!%!%!!!%!%%!%%%%%!%?!%!!?!!!%%?!%%%?!!%%?%%%?!%!%!%!!?!%%!%!%!%%%%%%%%%%%!%?!!!%!!?!%%!?!??%%%?%!%%%!%%%!%%%%%%!%%%!%%!!?%!%?%%!!!!%%?!%%%!%!?!?!%!%?!%!!??!?!%%?%%!%!?!%?%%%%%%?%!!!%%!!!%%%?!%%?%%%%!%!%!%!%?!%!%!!!%??%%!%%!%%%%%!%?%!!!%%%%!?%!!!!%%!%%!%??%%%!!!?%!!%!%!!%%!??%%?!?%?%%!%%!!%!!%%%!!!!?!%?%!!!!%!%%%%?%%%?!!%?!%!!%!%%%%%!!%%!!?%%%!%?!!%!%?%%%%%%%?!%!%%!!%!!?%!%!!%!%!!!!%!%!%%?%%%?!%%!??!!!??!!???%%%!!!%%%%%%%!!%%%%!%!%!?!!%%?%%%??%?!%?%%%?%%?%?!%%!%!%!??%!%%??%%%?!?%!%!%!?%?%?!!?%!%!!!%?%!%%!%%%%!%%!!?!!%%?%!%%%%%%???%%!%%%!!%%%%%%!!%?!??%!%!?!!%%!?%!!%%?%%%!%?%!?%!?!!!%%%%%%%%!%!!%!!%!!%!%%%%%!?%?!?%%!%!?!?!%%%!%%%!!?%!??%%%!%%%%!?%%%%%!?%!%??%!%%%?%??%!%?!??!?%?%!!%%%%?!%%!%??%!!%%!%!!%%!!%%!%%%!?%!%?%%%??%!%%%%!%%%%!!?%%%%!?!!?!%?!%!?%!?%%%%%%!!%%%!??%%!%?%!!!%%%?!!??%!!%%!?!%%!%%?%%??%%%%%%!%%%!%%%%%%%%%?%!%%%!%%%!!?!%!%!!%!?%%%?%!!%?!!?!?%!?%!%!?!%%%!!??%%%%!%%!%%%!!%!!!?%???%??!%%%%!%!!%%!%!!%!%?%%%%%%!%%!!%!!!?%%!%%?%!%!!%!%?%?%!%?!%!!%!%%%!!%?%!!%%?%!!??%?!?!!?%%!!%%!%?%%!?%%??%?!!!!%!%%%!%%%?%!%%%!%!?!%!%%!!%%%!?%!%%!!%%??%%!%%!%%%!%%?!%%?%!%%?%!!%%%%?%!!%%!?%!%!%???%?%%%?!!!%%%!%%%%!?%%%!?!%!?%%!%%!?%%!%!%%%?%??%!!%%!%!%??%%%%%%%!%%%!%%%!%%%?%!%!!%%%%!%!%!%!!!!%%%%!??%%?%%%%%%!%!!?!%%%%%!!%%!%?!?!!?!!!?%!!!!!%%!!!?%!?%!%!?%!!%%%??%%!%%%??!!%%%%!?!%%!?!!!%??!%%!%!%%%%%%%!!%%%%!?!%%%%??%?%!%?!!!?%!%?%%?!!%!%?!%%!!%%%%!%%!%%!%%?%!%%!%!!%!!!%?!!??%!!%!!??!%!%!!!%%%%%%%%%?%%%!%%!%%!%%?%!??!%%%%%!%%!?!%%%%!%%%!%!!?%%%?%%?!%!%?!!%?%?%!%%%%%%%?%!!!%%%%%!!?%!%%!%%!!!%?!!%?%%%%%?%%%?!%?!%%?%%!!?!%%%%!%%?!%!!!%%%%%%!%?%%!%%!%?!%?%%%?%!%%%%?!%%?%?%%!%%%??%%!%%!!!%!!!%!!%??%!?!%??%%?!%!%!!?%!!%%%%%!%%%!%%%%!!!%%%%??!!!%!%%!%%??%!!%?!?%%%%%!%%%%!!!%!?!%??%!!?%%%%%%!%%??!!%%%%!%?%%%%%!%%%!!!?%!!%%?!%!??!?!!?!!%%!%!!!%!%%!?%%!%!%!%%?%%%!!%%!!??!%!!%!!%%%%??!?%%?!?%??%%?!%!%?%%!%!!!!!%?!?!%!%!!%%%!!!%!!!%%!?%!!!%%!!!!%%%%%%%%!!%!%%!%%%!%%!?%!?!!%!!%%%!%%%%!%%%%!?!%??!!%%?%??%%!?!%!%?!%%%%%%%%%!??%%?%?%!%!%!!%!%?%?%?!!%!!%%!%%!%?%?!?!!?%%!?!!%%%%%!%%%%?%?%!!%!%?%%%%!??%!!?%%%%%%%?!!%?%%%%%!?!?%!%!!?%%%!??%%%!%%!%%!?!!%?%%!?%%%!%?%?!?%%??!!!%%!?%!%%%!%%%!%%!%?!?%!?%%%%%?!%?!%%!!%%!?%!!%!!%!?%%%!%%%%!!%%!!?%%%%%!%%??%!%%%!%%%%%%%!%??%!%%??!?%%%%%!!!%!?%%!?%??!%%%!%?!%%!%%?%%%%!!!?!!?%%%!%?%%%?%!%%%!%%%%!%!%%%%%%%%%?%?%%!%!%!!?%%%!!%%%??%???%??%?%%%%%%%!?!!%%??!%%!%!%%?%!%%%%%%%!%%%%?%!%?%???!?!??!%!%?%%%!%?%!%%%%!!!!!%%!%!%%!%!%%%%%!%%!!?!!%?!!%%%%%%!%%!?!%%!%%%%%!?!%%%!!!%?%%!!%??%%???%%!%?%!!%%?%%?%%%%%%!%!?!%%%%!%%!%%!%%%!?!!%!!!!!%%!%?%?!%!%%!?%?%%%%!%!%%!%?%!?%%!%?!!!%%!!%%!%!%%?%%%!%!!?%%%%?%%!%!!%%?!%!!!!%?!%%%%?%!!%%%%!!%??%!%%%?%%!%%%%%%%%%%!%%%%!%!!%%%!!%!!!?!%!!!%?%!!?%%!%%?%%!!?%%%?!%!%!%%%??%%!!?%!!!%?%!%%%%%%!!%%!!%!?%?!%!?!%!%!!!!!%!!%%!%%!!??!%%!%%!%!%!?!%!?%%!!??%%?%!%!%!!%!%!!?%%%%!!!%!!!%%%%?!!%%?%%?%!?%!!!!?%%%%%?!!!%??%%%!!%%!?%%!?!!!!!%%%?%%?%%%!!!!?%%!??%%!!!?!?%%%!%!%%!%%%%%!?%?%%!%?%?!%%!%%%!%%%!?%%%!%!!%%%%%%%%%%!!?%?!!?!?!!??!!%%!??!!%%%%!!?%%!%!?!%!%?%%%!%!!%%%!!%!%!%?!?%!%!%??!%?!%%%!!%!!%%%?!!%%%!!%!!%!%%!!%!!!%!?!%!%!?%%?%!%%%!%?%!%%!%!?%?%???%!%!!?%%!%%?%%!?%!%!%%%%??%%!!!%%??!!%%?%%!%!%!!%%%!%?%!?!%!%%%%!%?%%%%!%!%%!%%%%!%!%%%%?!!%%%!%!%%!!?!!!!%!%%?%%%!%%%!%%!%%?%%!!%%?%!%%%%!%%%!%%%%%%?!!%%%%?!??!?%!%%%!!%!%!%%?!%%?!!%%%?!!?%!!?%%!%!?%!%!!!!%%%!!!%%%%!%!%%!!%!!%!%%!?%!!!!%%%%%!%%%?!!!!!%?!%!%%%!!%%%%!%%%!?%?%!!!??%!!%%%%%%?!!%%%%!?!!%??%!?!?%%!?!%%!?!%!%?!!%%%?%!%?!%?!?!?%%%%%%%%?!!!%%!!?%!%!!%?%%%!%?%%%%%!%%%%??%%%!!!!!%!%%%?!%%%%!?!!%%?!!%!%%!%%?%%!%%%%%%%!%!!%%%%%?%!%!!?!%%??!!!%!?%%?%!!%?!!%?%%%?%%%%%!%!!!%?%%?%!!!!%?!%%%%!%%%%?%%!!??!?%!?%%?%%%%%%!!%!%%%!!%!!%!%%!%!?!%%!%!%%!?!%!?!!%%%!%%%!!%!%?!%!!???%%%%%?%%%%%%%?!!?%%??!%%%?%%%!%%!?%?!!%!%?%!?%!%!%%%!%!%%?%%!?!%!%!%?%%?!%!%?%!!!?!!!%%%%?%?!!!%%%%!?!%%%%%!!%!!?!!???!%%?%?%?%!%!!%%??!!!?!?%%%%%!!!!%%%%!%!%%%?%!%?%!!!%%%!!?!%!!%%!!%%!!%?!!!!%?%!!?%!!%?!?!%!%!!!?%%%%%%%%!%!%%!%!%%!%%!??%%%??!!%%!%%%?!??%%!%!%%!!%%?!%?%%!??!!!%!!%%?%!%??%!?%?%%?!%%?%%??!%%%?!!!%%%%%!?%!%!%%%%%%%??%!%%??!%%!%!%!?!!?!?!%%?!?%?%%!!%?%?!%%???%!%%%%?!%!!%%!%!!!!%!!!%!%%!%!%?%%!%!!%!?!!%%!!%!%!%?!?!?!?!%%%!%!%%!%%!!%?!!!!%%!%%?!?!??!!%%??%%?!!?%%!?!%%%!%?%%%%%?%!?%!!!!!%?!!!?!%!!!%%%%%%?!%!%%%!%?!%!%%?%%%%!%!!%!!??%%%%!!%%%%%!!??%?%%!%%%%!%!?%%!%?!!%%!!?!%%!%!!%%%!%%!%%!!%!!%!!%%%!!!?%!!%!!?!%!!!%%!?%%%%?%%!%%%%%%%%%!!%%!!?%?!!!!%%?%?%%%%?!!?%%%!%!%!!%%%!!%%??%%%%!!%%%%!!?!%%%%!!!?%%?%!%!!%?%!%?!%%%%!%!%%%%%!!!%?%%%%!!!%!%!!%!?%?%!!!??!%%%%%%!%!%%%%%%%!%%%%%%?%?%%?!%%?%%!%%%%%!?!%%!%?!!%?!!%?%!!?%%!!%%%!!%%!!%%?%%%!!!!%%!?%%%?!!%%%%%!%?%!%!%!?%%!?%!%%%!%%%%%%??%%!%%%!%%%!!%!?!%!%!%!%!!%%!!%%?!!!!%!!%??%!?!?%!!?%?%??%%%%!!!%!%%%%%?%!!!??%%!%?%!%%%!%!%?!!!!!%%!!%?!?%!%!!!?!?%%!?%%%%?%%?!?%?!?!%%!?%!%!!%?%%%%!!!?%%%!?%%%%!?%%%?%%!%!!?%?%%%%%%?%!!!%%%?%!!?%%%%%%%!%%!%!!%?%!!!!%??%%!!%?!%%%%!%!%!!?%%%!%%??%?!!%?%!?%?!%!!%%%!?!%!?%%%!!!!!%%!%!%%%%%%!?%!?!!%??%?!!!!!!?%%!%%!??%%%%!?!!%%!%?%%!%!?!%!!%%?%!!%%%!!?!!%!!!?%!%%%!%???%%?%!?!%%??%?!!??!!!%%%%%%!%%!?%%%?!?%%%!!?!%%%%!%%?!!%%%%%!!%%?%!!!%%%!%!%%!%%!!%!!!%?%?!%!!%%%!?!%%!%!!!!?%!!!!%%!%!!?%%%%!%%%%%%!%%%%!!%!%%%%%%!!%!%!%%?!!%?%!%%!?%%%%%!%!%%?%%%%!!!%!%??!%!!%%!!!%!%%%?%!!!?%%%%%!%?!!%%!%%%!?!!%?%%!??%%?!%%!!!!!%%???!%!%%%!!%%%%%!%%%%!%!%!%?!!?%%%!%!!!%!%!%%!%%?!%%?%!!!%%!%%%!%!!%!?!%%!%!%!??!?!%%%!?!%!!%%%?!%!%%%%%%!!!!%%%%%%%%!%%?%%!!!%%!!%%%%%!%%???!!!!%%!%!%?%?!%%!!!?%%!?%%?%%?!!%%!%%!!%%%!!%%%%!!%%%?!%%%!%%!%!?!%?%%%%%%%%!%%?%?%?%??%!%%??!%?%%%!?%!!?%%%!%!?%%%%%?%!!%???!%!!%%?!%??%!%?%!!!%!!%!%??%%%!?!%%!%%%%?%!%?!!%!%!%!%%%%%!??%%?%%%%!!!%!%%%!?%?%!?%%!?%%?%%%!!!%!%??!!%??!!!?%%%!!!%%!%!%%%%!!!!%%!%%!!%%%%!?!!%%!??%%?!!%!??!%%%%%%!%!!!%%?!?!%?!!!%!%!%?%%%%%!%%%!%!!%%%?!%?!%%%%%%!%!%%%?!%%!!??%!%!!!%!!%?!%?%%!%%?!%!?!%!!!%%%%%%!%%%!!%!!%%%!??!!%!!?!%??%%%%!!%%!!%!%!!!%%!%%?!!!%%%?!%%?%%%%%!!%%%%%!!%?%!!!%!!!!!%!%%!!!%%%%%%!?%!!%!%?!!!!?%%?!%%!%!!!!%%%%!?!!%%%%!!%??%!%?%?!!!?%%!%%!!%?%!!!%!????%!?!!%%!!!%?!!!%%?%!%!!%%%?%!!%!%%%%??%!?%??%!%%%?%!%!!%?%%%%%%?!!%%!!%?%!%?!?%!?!?%!!%!!!!!%!%%%%?%%!%?%%%?%%%%!!%%%!!%!!!%%!%!?%%%?%?!!!!??%%%??%%?%!!!%%??!%!?%!%%?%%!%%%%!?%%!%?%!!???%%%%%!%!%%%?!%!!%??!%%!!%!%%!?!!%???!!%%%%!!??!!%%!?%%!!!%%%!?%%%%%!%%%%%%!!%%%!!!?%!%%%%?%!%%!%%?%%%!%%!%?!?%!%%?%!%%%!%%%%%!%?%%!%?%!%!?%!!%!!%%%%%%%!!?!%%%?!%%!!%!!!%%??%%!%%!!!%!%!!!!!?%!%%%!%%%%%%%%!%%%?%%%!%!%!%%%%%?%%?%?%%%%%!%%%!%%%%!!%!!%%?%!%%%%%?%%%%%%%!%?%?%%%%%%%%%%%?%!%?%!?%%!%%!??%!?%!%%%%%!%%%!!%!%?%?!?!%!!?!!%!?%%!%%!?%%?%%!??!!%!?%!%%!%%??%!%%?%%??!?%%%!!%?!?%?!?%%%%%%%?!%%%%%?!%!?%!%%!%%!%!?%%%%!%%!!!?!?%!!%%?!%!%%%!%%!%%!%%!!!%?%!%!%%%?%%%?!?!!!!?%?!%%!%?%%%!???!%?!%%%%!!%?%!??%%%!!?%!%!%%%%!%%%%!%%!!%%!!%!!%%%!%!?%??%%%%%%!%%?%%%%%!?!!%!!%%!%!%%%!%%!?%%!!!?!%%%%%!%%!?!?!%%%!?%%%!?%!%!%%!?!?!%!!??%?%%???!?!??!!%!%?%!?%%!!%%!%!!%%!!??%!%%!?!!!%?!%%?%%!%?!!!!%%%?%%?%?%%!%%%%?%%%%%!!%%!!!%%?!?!!%!%?%%%%%%%%%%%!%%!!!%!%%%!%%?%%!%%!%%%%!%%?!!!%%%%%?!%?!?%???%%!!%%!%%!!!%?!!%%%?!%%?!!%%?!!%!%?%!?!?!%%%%!!%!!%?!%!!!%%!%!%%?!%?!!?%%%!%%%!??%!!%%?%??%!!!!%%!%%%%!%%%%%!!!!%%?!!!%!?%!%%??!!%%!%?%!%%??%%?%!%%%%%!?%!?%%?!!%%%!%!%!%?%%?!!!!%!%%!%%%!%%%!%%%%!%%%?!!!%%!!%%!%!%%?!!%?!!!%!%%%!%!%!!%%?%!%%%%!!%??!!?!%?!!?!!!!!!!%%%!?!!!!!%%?!!!%%?!%!%%!%!!%%!?%%!%?%!%!%%%?%%!!%!%%%!!%%!!!?%?%%!%%%%%!!!!!!%?%%?%%!!%%%!%!!!?%!%?!%?%%!%%!??!!!!!%%%!%%%%%!!!!?%%%!?!?%?!%???!%%!%!%?!%%?%%?%%%%%!%?%%%??!?%%%!%%!!%!%%%%?!?%%?!!?%?!%%?!!%%%!!%%%%%!?!%?%?!!%!!%!%!%%%!!%!%!%%??!!%!?!!!?!!??!?%!!%%%%%?%%!%!%%??%%!!%%%?!!%!%%%%%%!%!%!%%%%%%%%%%!%%?!%!%!%!!%?!!%%%%%?%?%!!%%!%%!%%%%!?!!!!!%%!%%!!?%%%%?!!!%!?!%%%!?!%!%%%??%!?!%?!!?!!%!%!!%!%%%%%%%?!!%!!%?%!%?%!%?%!%%?!%!%?%!%!!%%%%%!%%?%!!%%%%!%?%!%%!?%?!%%%!%!%%!!%%!!!%%%%%%%!%!%%?!!?%!!%%%%%?%%%%!%%%!!!%!%!!?%%%!!%!%%%!??!%%!!%?%%%!!!%?!?%%%?!%?%%?!%%!%%!?!!%??!%%%!!?%%!%%??!!%%!!%%%%!!!??!!%!%%!%!!!%%%!%!%?!%%!!??!%%%%%%!%!%??%!!!%!!?!%?%!%%%?!%%!%!!!?%%!!%!%%!?%!%!?!!?%???%%%!?%%%!%%%??%%%!%%%%?!!!!%?!%!%%?%!%?!%%%?%!%%!!%!%%%??%!%%%?%%%?%!%%%!%%%!?%?%!!!!?!?!%%!%?!%!?!??!%%?%!%%%!?%!%%!%!%%%!%!?%%%!!!%!!?!%?!!!?!?%%%%%%!?%!%?%!!!%?%!%%%?!%!??!??%%?%?%%!?%%%!!!%%%!%!%!%%??%%??!!%%!%%%!%!%%?%!!!%!!!%!%?!!%%%?%%%!?%%!!!!!!%!!!!%%%?!%?!%??!!!!!!!?%%%%!?%%%!?%!%%%!!%%!%!%%!!!!%%??!%!%?%!%%%%%%%?%%%%!%!%%??%!?%%!!!?%%?%??%!%%%%!!?!?%%?%%%%%!!!%!!?%!!?%%%%!!!%?%%%%%!%%!!!?%%%?!%!?%!!%!!%%?%%!!%%%!%%?%%%%%%%!!%!%?%%%!!?!?!%!%!%%!!%%?!?!!%%%%?%!%?%!?!!!!!%%!!%!!!%%%!!%!%?%?%!%%%%?!!!%%%!!%!!!%?!!!!!%%%!%!?!%%!!?!%%!!!!?%%!%!%!%!?%%?!!%!%?%!%!?!%!%!?%%!%?!%!%?!%%%%%%%%%%!%?!%?!%?%%?%!%?!%%%?!?!?%?%%%??%%%%!!%%%%%!%??%!%?%%!!!%%%%!%%%!%!!!%!?%%!%%%%%%%!%%%!!?!%?!??!%%?!!?%!!!%%%!!%%%%%%!%!!%!%%!%!%!!%?%!!%%!%%%?%%%%!?!%%?%?!?!%%%!%%%?!?!%?%%!!%?!%?%%?%%?!!%!%?!!%%%!!!%!%!?%%%%%%!%???!%%%!?%?!%!%%???%%!!%%%%!%!!?%%%%!%%?%%%!%%%!!!!%!!%%%!%?%!?%%%%%%!!%%%?!%%?%%%?%!!%%?!%%!%?%!%!%?!%?%%?%!!!?%!%!%!!%%%%?!%%%?!!!?!%%!!%!%!%%!%??!!!?!%%!%%%!%??!!??!%!?%%%?%%%%??%%?!%%%!?%%%!?%%%%%!!%!!!?%!%%!!%!!%?%!!%%%%!!!!!%%%?!%?%!%!!%!??!%%%!!?%%!%%!!!?%%%!!%!!%!!!%%!%!%%%%?%!!%%%%!%%?%%%!!%%%%!?%?%?%!?%%?%%%%%!!!%%%!!!!?%%%!%!!?%%%%?%!%%%!?!?%%%!!?%!!%?%!!!%?%%?!%%!%%?%??%!?%!%!%?%?!%!%%%%???%!!%!!!!%%%%!?%%?%!!%!?%%%%%!!?%?!%!%?%!!!!!%?%%%%!!!%!%!%!%%%!!!!%%%!%!%!?%%!!%%%%%%!%!?%?!!%%!%!%%%%!%%%%!!%%!%!!%!%%!??!%%?!%%!%!%%%%%%%!%?!%%%!?!%??!?!%%%?%!%%%%!!?!!%%%%%?%!%!%%%%!?%%?!%%%%!???!%!%?!!%?!!!%%%%??!%%%%!%!%%%%!%%%%%%%%!!??!%%!%!!%%%!%%%!!?%%%%%%!%!%!?%%%%?%%%!!!!%!!?%!%!?!%%!%%%!%!!%%!%%%!%%%%%%%%?%!?!!%!!?!%!?%!%!!??%%!!%%%%!!%%%!!%%?!!%!?%!?%!%!???%!%!%%!%%!!%%!%%%%%%%?%!?%!!%!!!%?%%%%!!?%!!??!%!!%%%%%%???%!?%!%%!%%!?%%!%%%%!!?!!!%!%%!%?%!??%%%!?!%%%?!%%%%?%!%%%!!?!%%%%!!!!??!??!%%%!%%%!%%?!!%!?!%%%???!%?!%%!!%?!%%??%%?!%!%%%!!%!%%%%%%%!?%%%%!%%!%%??!%?%??!%?%%%%%!!%%?%%!?!%%%!%%%%%!!!%!!?%?!?%!%%!%?!!%%!%%%%!!!!%%!%%%!%%!!??%!!!%%%%!?%!%?!%!%!%%%%!!?%!%?%%!%%!%%?!!%%!%!!%?!!!!!!%?%%%??!%%%!!!%%%%!?!!%%%!!!%%!%!%!%%!%!%%%?%%!%%??%%?%%%?%!!!%%!%%!??!?%%%%??!%!%%!!%??!%%%!!%%%%!?%!?!!!%%!?%%%%!%%%%!%%?!!!?%%?!!%%%!%%%%%!!%%?%!%%??!?%?%%!!%!!?!!!?!!!!!%%!%%!?!%%%%%%%%!%!%%%%%%!!?!?!!%%%?%%%%%%!%%?!???%%?%%!%!%%%!!!%!%!%%%%?%%%!%??!%%%%%%%%!%%%!?%%%%%?%?!%%!%?%!%%%%%%%%?%%!?!%?!%%??!%%%%!%!%?%?%!%%!%?%???%?%%%%%%?%%%!%%%?%%%?%!!!%?%%??%?!?!%?!%%%%!%?%!!%%%!%!%%%!%%??%?!?%%!?!!?!%%%%!!%%%?!%%!?%?%!%?!%%!%!%%%!?%!?%!%!%%?!%%%%?!%%%%%??!%%!%!%%%%%?!?!!%!%%%%%%%%!!?!%!?%%!!??!%%?%%%%??%%!%!%?%?%!%%?%%%!?%!%?%!!%!!!%!%??%%%%?%%%%%%%?%%!%%!%%!%%!%%!!!%%%%!?!%%!!?!!%!!%%!?%!%!%%%!%?!%!%!!!??!!!%%?%%!%?!?%!%!%!%!!%%!%%%!!%?%!!%!%%!%%!?%!%%!?!%?%?!?%!%%%%?%!?!%?%?%!%!!%!%%%?%??%!%%!?%%?%!?!?!?%!!!!!%%%%%!%%!!!!!%!!!%%!!%%%%??!!!!%?!%%!!%%%%%!%!?!!%!%%!%!?!%!%%!%?!%!?%!%%%?%%?%%?%%!?!!%!?%%?%%%%?!%%!?%!!!!%?!%%%%!!%!!%%!%%!?!!%!%??!%!%%!%?%%!%!%?%%!%%?%%!?!%%%?%%!!?%%%?%?%!%!%?!?%%%!%?%!%%%?%%!%?%%!?%%!%%%%!?%?%?!%%%%%%!%%?%!!?%!%!!!?!%!!%!%!%!%%%%!!!!??%?!%!%%%!?%%%%??%%%!%!!%!%%?%?!!%%!?!!!%!?%%?%??!!%%?!%!%%%!?%?%?%%%%!!!!%%!%!!%?!%?%!!%!%?%?!%%!?%!%?%%%?!%?%%!%%!%%!!!%%!!%%!!!%????%!%%!!!%!%!%??%%!!%!!??%?%??!%!%%!%%%!!!!%?%%!?%?%!!%%?!%!%%!%!?!%%?%!%%%!%!%!!?%??%!%?!%%!!%%!%%!?%!!%%!!%!!%%%%%!%!%!!%%%!!%!%%?%!!?!%??%%!%!?%%!!%??!%%?!%%%!%!!%%%%%!%!!?%!!%!?!%?%%%%!?!!??!%%%!%%%!%!!%%?%%?!%%!%!%!%!???%?%!%%%!!%!!%!%!%%%%!%%%%!!!!%%%!!!?%!?%%?!!%%%!!%%%?!%?!!??%%%??!!%%%%%%?%%!?%%%!?!%!%%%%?%!!%%!!%%%??!%!%?!%%?%!%%%?%%%?%!?%%%!%%%!%?%%%%%%??!%%%%%%%%!%!%%!%%%%!?%%%%!%?!%!%!??!!%%%%%!?%?%%??%!!%!!!%%%%?!%!%!!?%%!!%%%!!%%%?%!%%?%!%?%%%!%%%!!%?%%!%%!%%!?%!!!?!?%%?!!%%%!??%%%!%?%%!%?%!!%%!%!?!!%%?%%!!%!%%!%%!%!%??!%%%%%!?%%!%!%%%!!??!!%?!!%%!%!!!?%%?%!%%!!%!%?!!%%?%%%!!%%!%!%%?%!%!%%?%%?%??%!!%!!%%%%?%!%?%!%%!!??!!!%!!?%?%!?!%%%%!%%%?%?%%!%??!!%%!?%%%%%%%%%%!%!?!!%!%!!!!%??%!%!%!%%%%%%!%%!%!?%?%!%%%%%!%%%!?!%%%%!%!?!%%%!?%%%?!?%!%%!%!%?!!!%?!%%%%?!!%??%!???!%!%%%?!!%%!%%?!!?!%!%%!%%%?%%%%%??!!!%?!%%?!!%!%%%!%%%?%%???%??!%%%?%%!%!!??!%!%%!?!%!%?%?%?%%%??!!!%%?%%?%!!!%%%!?%%?%%%??!!%?%%%!%!%!%%%!%%%%!!?!%%%!!%!%?!??%!!!!!%%!%%?!!?%%%?%!?%%!%?!??%!!%%?!%%!%%%!??%!!!%!%!%%?%%%%%?!?%!!!%%%?%!%%??!%%?!%%!%%%%?%?%%!%!!!!%?!!?%!?!!?%!!%!%?!%%%%%?%?!%!!%%%%!%!!?%%!!%!?%!!%%?!!%%??%!?!%???!%!?%!!%%%%!%?%%??!!%%%?!%%!?!%%!%%!%%%!%%?!%!%!!!%?%%%%!%%!%%!%%?%!!?!%%%!%?%%%!%%%!%%!!%!!!!!!%%%%%%%%%?!%%%%?!%!!%%%??%!%?%%!?%%!!!%!%%!%!%%!%!!%%!%%!!%%%%%???%%%!%!%%%!%%?!?!!%??!!!%!%?!?%%%!?%%%%?%%%!%%%%?%%!%%!%!%%%!!%%!!%%!???%%??!%%%!!?!!%!!!!%!!%?!?!%%?%?!%?%%!!%?!%%!%%%!!%!%!%%%!!!!%%%?!%%%%%!%!%%%%%?%%!%!%!!!!!?%%%!%%%!!!%%%?!%%!%%%%!!%?%!%!%%%%!%%%%!!%%?%!%%%!!%%%%?!?!%%!%?!%%!?%?%%?%%?%%%?%!!!??!?%%!?%%??!%%%%%!!!%?%%%!%%%!?!%%!%!?!%!%??%%%?!%%!%%%%%%?%%%%!!!%%?%!%%%!%%!?%?!??%%%%!!%!!??%?????%!%%!!%%%!%!!!%%?!%!!%!%?!!!%?%%%%%%%???%!!?%%!%%%!%%%%?%%?????%?%%%!%%%!!%%?!%%%!!?!%%?%%%%%%?%??%%%!!!%!%%%%%%%?%?%%%%%%!%??!!!%%!?%!%%?%!%?!!%%!%%%!%%!%%%%!?%?!!?%%!%?!%!%%?%%!%!!%%!?!?!!%!%!%!?%!!!%?!!!%%!!!%%%!?!?%?%!!%!!!??!%%%%?%%%%!?%!%!!%%?!%!%%%!%!%%%%?%%%!?!%!?!%%%%%%?%!%%?!!??!?!%%%!%!?!%!%?!!??%%!%!%%!%!%!%%!!!%%?!!%!%!%!!%!!%!!%!!?!%?!?%%!!%%?!!!%%?%!!%?%%!%?%!%!!!%%!%%!%%!%?!%%!%%%%!?%?%!!%%!!%!!?%%%%%!!%!!!%%!?!???%%!%!!?!%?!%!%!?%!%!%!%!!%!%%%%%%%!?%?!?%!%%%%!%%!!%!%!?%%!?%!%?!?%%%!%%%?%%!%!%%%%?%%%%!?%%%?!%%%%!!?%!!%!!?%%%%!!%!!!%%%!%%%!%%!?%%%?!!%%?%!%%%??!%??%!!!%%%!%?!!%%?%?%?!%!%!?%?%%%%%%?!!!?%%?%?%%%!%!%%%%%%!%%!%%%%%?!!?!!%!!%!?%?!?%!?%!?%%%??%!!!%!?%%!?!!%%%!!%%%%!%%%%?!!!%%!?!%??!?!!?%%!%%!%?!%?%!%!?!!?%!!!%%!?!!%%!%!%%%!%%%%%%%%%!%%!?%%%!?%%?%?!%??%%%!%%%%?!%!??%!%%!!%!!%%%%!%!!?!%!%!%!%%!%?!%%!!%%%?!%!!%!%%%!!!%%%??%%!%?%!%%!!%?!!%?%%!%!!%?%!!?%%?%%%%?%%%!!%%!%!%%!%!!!%%?!!!!%?%?!%?!!%!%!%!%%!!%!?%%!%!!%%%!%%?!?%!!?%!!!!?%?!%??%%%??%!!%!%%%%%%?%!%%%%%!!?%!%%?!%!%%%%!!%%%%!%!?%%!?!%%?%%%%!!%?!??!!!%%%!!?!%!!!!%%%?!%%%!!%?!%%%%!?%%%%%%%!%%%%%!!!%%%%%??!%%!!%%%?!%?!!%!!?%%?%!!%?%%!%???!%%?!%%?!%?%?!!!%!?!%!%!%%?!!%%?%%%%!!%?%%%?%!!!?%%%!!%%!%%!%?!%%?!%?!!!!!%!%?%?!%!?%%%!%%?%%%!%?!!%%%%%%!%!!%%%%!%!%!%%%%!%%%%%%?%!!?!%?%%%%%%%%?%!!%%%%!%?%%!%%??!%?%%%!!%%%!%%?%%%?%%?%!%%!%%?%%!!!!%!%%???%?!!%%!%%!%?%?%%!!%%%%??!%!??!%%!%!!!!%!%!%!?%!!?%!%!%!%%%%%%!?!!!%!%!!?!%%?%?%??!%!???!!%!%!?%%!?!%%%%!%!!!%??!%%%?%%%!!?%%%%!?!?!%!%%%%?%%?%%!%%%?%!!?%!%?%?%%!?%!%!%%!%?!%%%?!%%!%%%!%%%%%!%%%%!%%%!%%%%%!!!!%??%?%?%!?!%!%?!!!%%%!%%!%!%!!%!!%!%%!%!!%%%??%%%%%?!%%!%%%%%%%!!%%?!%!%!?!%%%%?%%%%?%!!!%!!%%!!%%%%!%?%%!??%?%%%!%%!%!!%%%%?%%%?%?%!!!!%%%!%%%%!%%%!%%!%%?%?%%!%!!!%!!%%!%%%%?!?%%!%%??%%!??%%!%%!!%%%%!!!?%%%!%%%!!!%%?!?%!?!!%!%%!!%?%%%%%%!%!!?%!!%%!!!%%!%!%!!%%%!%??%!%!!%%!!?!%!%%%?%%%!%?!!%?%!%!!%%%%!%!!?%%?%!%%%%%%!%!%?!%%?!%%%%%%%!%!%!!%%!!?%?%%?!!!%%%%%%%?!?%?%%%%!%?%?%!!?%%%%%!!?%?%%%?%%%!!%%%%!%!%%%!!!%%%!?%%!!!!?!%?!?!!!!??%%%%%%!%?%!!%%!?%!?!!!%!?!?%%!%!%!%!%%%?!!!%%!%!%%!%!!%!%!%!%!?%?%!%!!%%%!%%%!%!%%!???!%%%%!%!!%!%%%%?%%%%!!%%?%%%%!%??%!%%%%!%!?%%%!%%!?!!!!!%%%???%%?%%%%!!%!?!%?!%!%%!%%%!%?!%%%%%!!%!!?!?%%!!?%%%%!%!!!%%%!%!%!%%??!%!?%!?!%!%%!%?!%!%%%%%%%%!%%?!!?!?!%!%!%?!!!%%%!%%?%%!%%%%!%%%!%!!!%?%?%%?!%!?%??%??!?%%?%!%%!%?%??!!%%%?!!%!%%%%!!!!%??!%?!!!!%%!!%%!!!?!!%%%!%%?%?%!?%%!%!??%%?!?!%%%!%%!!!%%!!!%?%%%%!%!!%%%!!!!%?!%%%!%!!!%%%!?%!?%!%%%%!%%%%!!%!%?%???!%%!%%!%!%%%%%%%?%!?!!!%!!%%%?%!!%%%%!%?!!?%!%%!!!?!%%!%%!%%!!!?%?%%!?%!%%%??%!?%?%%!?!!%?%!?%%%!%%!%!!%!%!?%?!%!!%%%!!%%%%!?%!??%%%%%?!%%!%%!!!%%!%!%%%!?!%!%!%%%?%?%%%%?%%?%!%%%!%?%%%%?%?%?!!?!!%?!!!!%%%%!%!%%!%!!?%?%%!!!!%%%!%?%%!%!?!!?%?%%%%!%!%!!%!!%%!!%!?!!!!%%?%%!%??%%?!!%%%%%?!%%%%!!!%%%!%%%!%%!%%%%%!%?!%%%%%??%!%!!%!%%!%!%%%%%?!!%%?%!%!!!%%?%!?!%?%!!!!!!!!?%%!%!%%%%%%?%%%??%%%%%!%%%%!%!%!?%?%!%%!%!%!%!%%?%??!%!%%?%!%%%?!%%%!%%!!%%%%%%!!?%?%%%!%%%???%%%!?!%!?%?!!?%%%!!?%%%%?!??%%!%%?%!??!!?%%%?%!%%??%!?%!?%!!!%!!%!?!%??%!!%!!%??%%%%!%%!!?!!?%?%????%??!?!%%%%%!%!%%%%%!!%!!???!%%%%%%?!%!?%%!%!!%%%%%!%!!%!%!!%%%!!%!%!?%%!%!!%%%%%!?%%!%%?!?!!%?%%!%%?%%%!?%!?%%%!!!?%%%!%%?%?%!!%%?!%%!?!%?%??!!%!%!%?!!%!!%%%%%?%%?!!%%!!%?%%%!%!?!??!%%%!%!%%!!!%!?%!%!%%%!!!%%!!%?%!%!%?%!?%%?%%??!!!%!%%%%??!%!!!%?%?%%%%?!%!%%!%%%%?!!!%?%!%%!!?%%%!?!%!!%!%%%%%%!%%%%%%!!??%!?%%??%%!%???%%?!?%%!%%?%%???!!%%!!??!?%!?!%%%!%%%!%??%?%%??%!%!%??%%%%!%!%?!!%%%%%%???!%%%%%%!%%%%%?%!%%!%?%%%?!%%%%%%!?!!%!%%?%?%%!%!%!%?!%?%?!%!%%%%?%%!%!!%!%!%%%%%%%%!!!%!!!?%!!!!%%%%!!%%!%%???%!!%?!%?!?%?%%%?!???!!%%?%?!%!??%%!!?!%!%%%!!%?%?!%%%?%%!%%%%!?%!%%!%?!%!?!%%!?%%?!%%!!!?!%!??!!%!%%!!%?!%%%%!%?%%%?%!%%%!?!!%!!!%?!%?!!?%%%?!%%!%%!?!%%%%!%%?!%!!%%%%%!!%%%!!?!%%!%%%!!%%%??!!%!?%%?%%%?!%!!%?%!%!%%!%%!!%?%!%%%??!%!%!%!!%%??!?!%!!%%!%%?%!%%!!%!%%!!!!?!%!%!%%%%?!!%!%%%%%??%%%?!%%%?%!%%%!!!%!!%%%!%?!!!%%!%?%?%!!?%%!!??!%!%?%?%%!%%?%?%%?%%!%%!%%!??%%%%%!!!%%!!%!?%!?%?%?%!%%?!?%!???%!%!?!%%?!%%??%%?!%%%!%%%%?%%!%?%?%!?%?!!%?!!%!%!!!%?!!??%%%%%%%%%?!%!%%?%!!?%?!!%%!%?%?!!!?%%%?%%%!?!???!%!!?%!%%!%%!!!!?!%?!!!!!%?!%!!%?%?%%%%%!%?%%?!?%%%!??%%%%%!??%%!!!!%?%%%?%?!?%%!%?%!%??!%%%%??!%%%%%!%%%?!%%%!!!%?%!%?%%!%!!!%%?%%?%%%%%%%%%%!!?!!!%%!!%%!%!!%?%!%!!!?%!%?%!%!!!%%??%%%!%%!!%%%%%%%%%!%!%???!??%%?%%%%!?%!%%!%%%?!?%?!!!!%!%%?!!?%%%?!%%!%%%!%%!??!%!??%%%%%%%%%%?%!%!!%!%%?%%%%%%%%%%!!?!!!%!%!!%?!%%?%!??%%?!!%?!!!!!%!%%!%!!?%%%%%%?!%%%??%?!?!%?!?!?%!?%!%%%%%%%%%%%%?!%%?%%%!%!%%%?!??%!!%!%%%??%%%%%!!%%!%%%?!?%!?%%!!%!?!?%%!%!?%%!!%%%%%!%!!!!%?!!!%!%%!?%!%%!!!%!!?!?%%!%%%!!!!%%%%??%!!%%??!!%!?%%!%%!%%%%!!?!%?%%%%?%!!!!%!%?%%%%!%!!%!%?%!%!!?!!%%%%?!!%?%!?!%!%!%%%%?%!!?%%!%!!%%!%%%%!%!!?!!!!%%?%!%?%!%%?!%!?%%%!!%!!%!%%?!%?%%!%!!%%%!?%!!%!%?%?%%!?%%!%!!!%!%%%%%%!%%%!%%?!%!?!?%?%%?!%%!!!%!%%!%!!%!?!?!!%%%!!!!%?%!!!!%%%!%%%%%!%%%!%!%%%%%?!!!%?%!?%%%??%%%??%!%?%%%%%%%!%%!%?%%%!%!?!!%?%!!%%%%%%%?%%%!??%??%%%%??%!%!?!%%%?%%!?%?!%!!%?!!!!!%%%!%%!!%?!%!!%!?%??%?%!!!%%%?!%%!%!%???!%%!%%?%!%%!!!!%???%%?%!%!!%%?!%!!!!!%%%!!%%!%?%%%%%!!?!?%!%!!%%%!%!%!?%!%%%%??!!%%%!%!%?!?!%!!%%%!?!!%!!%!?%%??!%%???%!%?%!%%?!!%%!%%%!!%%%!%?!!!%%!%!%!%!%%!!%%!%%%!?!%%?%?%%!%%!????%%%!%!!?%!%!!%%?!!!%?%%?%%!%%%!%!%%%%!??%%%%%%%%?%?!!%!%%%?%!?!%??!%?%!!%%?%!?!!%%!!!%%!?%%%!!?!?!%!!!!%?%!%!%%?%!?!%!!%%%%%%%?%?!!%?%%!!?!!%?!%%%??!!%%?!%!!%%?%%%!!!????!%%%%%%%%!%!!%%!%?%%%%!!%%?!!%!!%%%?%%%!!%!%%!%!?%!%!?%%%!?%?%!!?!?%?%%%%?%%!!%%!%%!%!!?!%%!%!%%%%!%%%?%%%??%!!!!?%!?%%%%%!!%%?!!!%?%!%!?%!%!%?!%%%?!%??%?%!?%%%!!!!%?!%%!??%%?%!!%%%%%!!%%!!!%!%??%%%!?%%%%%!!%%%%%!%!%%!!%!?%?%%%!!??%%%!%!%?!%%%?%%%%%%%%??!%%%%?!?%!!!?!!%%?%%?%%!%?%!?%?%%!%!%%!%%%%%!%!!!?%!!!!!!!%%%%!????!!!!!%%!!!!%!%!?!!%%%%%%!??%!!?%%?!!!%!%?!%!%?%!%!%%!%%%!%%??%!%?%!!?%%%%%??!!%%!%%%%%!%%%?%!%!%%!%?%%%?%?%?%?!%%%!%!%%?%?!%%%%%??!%%%%%%%%%%%!?%%!!!!%!!%%!%!%!%%??%%?%%!??!%%%%?!%%?%??!%?!%!%%!??!%%!%!!%%!?%%?!!%%!!!?!!!%!!%!?!!!%!%%?%!!!%%%%%!!%?%%?%%??%%!%%?%!?!%?!%%%!%%%%!%!%?%%?%!%!%%!%%%%%%%%%%!!%!!%?%!!!%%!!%%?%!%!%%!%??!!!%!%%!?%!%%?!?!!%?!!!?!%!?!!!%!!?%%?!%!%?%!%%%%%%!%%%%%?%%!%%%%%!%%!%!!%!!%%%?!?!%%?%%!%?%?%!!%!!?!%??%%%!!?!!!?!?!%%?!%?!!%?%%?%%!%%!%%%!%!%%??!!%%?%%%!%!!%%!!%!!%!%?!!!%!%!%?!?!%%!%%!%%%%%%!%!%%!!??%%?%??%%!%%%%!?%%%!!%%?%?%?!!%!!%%%%%%%?%%?%%!!%!?%!!%%%!%!%%!!%!%%!%%%%?!?%%%!?%!!%%?%%!%%%%%%!!?%%%!!%%!%!?!%!%!%%%%%%?%?!?%%%!%!!?!%!!%??!%%%?%?%%%!!?%!!??%%%%%?%%!%%%%?!!?!!%%!!%?%%?!!!%%%!%%!?%!!!?%!!!%??%%!%%%%%%%!%!%%%%!%%?%!%%!%%%%!?%%%?%?%%!%!!!%%?%%!%%%%%%%%%%%??!%%!%%%!!!!!!!%!%!%!%?%!!%%!!%%%%%%?!%!%?%!?%??!?%%%%%!!%!?%%!??%%!%%!%%?%%!!%%%?%?!!?%%%?%%%???%!%%%%?!!%!%%%%%!!%?%%!%!%%%%!%%%!%%%!%%?%!!!%???%%!%%!?%!!%!%!!%!%!%!%!!%!?%!?%%%%!!%%%!!!%!?%%?%!!!%%!!!%%!??%%%?%!%%!!%%?!%%?%%%%%?%%??%!%?!%%%%!%?!!%?%%%??!%!!?!!%%%!%?!!%%%%%%?!%!%!%!!%!%?!%%!?%%!%!?!!??%!%?!!%!%?%%??!!%!%%!%%%%%??!!!!??!%%?%%!%%%!%!!!%!%!%!%?%!%%%%%%%%%!%!%%%!?%%%?%?%!?%!%%!%%!%%%%?%%%%%%??%%%%!!!!%??%%!!%!%%%%%!!!%%%?!?!!!%!%!!?!%%?%!%%%?%%%%!!%%%!%%!!%?%%!!!%!%%%!!!%!%!%!%%%!%%%%%%%!%%!!!!!%?%!?!!%%%?%!!%%!!%%?%%!%%?!%%%%%%!!!!%!%%%?!%??%?!?%%!?%%%%?%!%%!?!!%??%!%!%!%%%!!%!%!?%!%?%%%%?%%%!%?%%%?%!%%?%!!!%%!?%%%%%%%%%!%!%%%!?%!!?!!%%%%%!%!!??%!%?!%%%!!?!%%%%%!?%?!!!%%!%!!?%%?!%%!%!?!%!?%!%%?!%%%!%%%%!!%!%%%!%%%!?%!%%!%%!!%%?!%%%?!%!%%%%%!%!%!?%!!?%%%%!!%?%%!!%?!%%!%%%%%%!??!!!%!?%%?%!!!?%%%%%?!?%%!!%%%%!!%%%%%!!!%!!%!!!%%!!!!%!!!?%%!%%?%!%%!%!%!%?!!!%%!!!?%??!?!!%%?!%!%%!%?%!%%%%?%?!!%?!!%%%%!?!%%%%%!%%%%%?%%!?!?%%%%!%%??%%!!%?%?!!%%?%!?!!%?%%%!?%%%?%%%!?%%%!%%%%??%%%!%%%%!%%%%%!%%!%!!%!!!%%%?!?%%!%!??%%%%!!%!!!?%%!%??%%!!%??!%%%!!!!!!!%%%!%%%%!%!%%%!%!!?!%%%%%!%!!!%%!?!!?%!??%?%%!%?%!%%%%!???!%%!%!?%%%?%!%%!!%!?%!%?%%%!!%!%!!!%!?!%%%%%!%%%%?%%!!%!%%!??%%%!??%%%?%?!?%%!?%%!%%!%%%%!%!!!%%!!!%!!%%?!%%%%%!!%?!!%!!?%%!!????!?%%%%%!%%!%!%%%!%!%???!?%%?!?%%!!!%!!%!%?%%!!%%%%!?%?%?!%!%!%!%!%%?!%%%!%!%%%?%?!?%%%%%?%!!?%%%!%??%%!%!!!!%!!?!!%%!!!%%!%%%%!!?%%?%%%!%?!%?%%%%!%%%%%?%!?!%%!!%%?!?!!%?%?%%%%?%%%%%!%%%%%%?%!!%!%%%%%?%!%!%!!%!!%%!%%%%!%???!%!??%%!!%%?!%%?!!!%%?%?%%!%%%%!!%%%!%%%!?!%%??%!?%!%!?%!%!%%!?%!?!%%!%!%?!!!!!!?%?!%!!%!!%%!!!%?%%??!?!!!%%%%!%%?!!%?%%!%%!%!%%!?!!%?%%%?%%%%%!!%%%!%?%%!!?%%%??%%%%!%%%?%%%!!!%%%!%!!%%%?%%%!%%%%?!%?%!%!%!%%%%?%!%%%?%!!%%!%?%%!!!%%!%%%%?%!%%%%%!%%%?!!!!%%%%%%??%%!!%%???!!?%%?!?%?%?!?!%?%%!!%%%%!?%%?%%%%%%!%!%?!%%!%%%%!!%?!!?%!!!%!?%!!%%!!%!!?!%!!?!%%%!%%%%%%%%%%!!?%%%!!!%%?%%%?!!?%?%!%%%%%!!?%%%%%?%?%%%%%%!!%%!%?%!?!%!!!!!!%%%!?%%?%%%!%!%%!!%??%%%!!!%%%%%%?!%?%?%%?%!!%?!?%%!%?%%??%%%%%!%%%!%%!%%?%%!?%%%%!%?!!%%!?!%!!!??%%%!!%%!%%!?!?%%!%!%%%?%??%??!!%?%%?!!!%%??!!%!!%!!%!%%%!!?!%%?!!%%!!!%!!%%%!!??%!!%!??%?%?%%??%%!??!%!?!%!?%%?!%!??!!!?!!%!!%%?%?!%???!!%?!%%?%%??%?%!%%%?!%%%!!%%%%!%!!%%!%%%%%%!%!%!!%%%!%%%%!??%%!%%%?%!?!%%!!!?%?%!?!!%%!%!!?%!?!!%%%%%?!!?!!!?!!!?!%!%!!??%%%%%%%%%!%?!%?%%?%!%!?!%!%%%!!%!!?%?!%!%?%%%%%??!%%?%%!!%%%%!?!%??!%%%!!?!%%!%?!%%%?%?!!%%!%%%?!%?%%!!%!%!%?%%%!%!!%!%%!!!%%!!%%%%%%!!?%!%?!?%!!%!!!%%%%%?%!?%%!%!%???!%??!!%%!!?!%!%!?!!%!%!%%!%%!!%%%%?!!%??!%%!!%%%?!?%!!?%%%%%%%%!!%!!%%%!?%%!%%!?%!%%%?%%%%!%!!%%%%!!!!%%!%!%??%!!!!%%%!!!%%?!!%!!?!%%?!!?%!%?!%!?!!!?%??!?!%!!!%??!%%%?%!!%%%%%%%%!%!%%%?%%!!%!%!?%!%%%%!!%?%?!!%!%%?%!!%!?%%!!!!%!!??!%%!?!?%!%%!%%%!?!%!?%%!?%!?%%%?%?!!%?%?%%?%?!%!%!%?!!%!%!%!!%!%?!!?%%%!!!!?%?%%!%!?%!!?%%%%!!??%%%%%%%!?%!?%!%?!%%%%?%?!!%!!%%%?%%!!%%!?%%!!%!!?%!%%%%!!%%!%?!%?%!%!%!!%%%!%%?%%!%????%!%%?!%!%%%%%%%!%!%%?%%!%%%%%%!!!!%?!%%!%?%%!%%!???%%%%!!!?%!%??%%!?!%%?!!!?!?%%!%%%!%?%%!!%%%?%!%?!??%%%!%?!?!%!%!!%!??%%%!!?!?!%%%%!%%%?!?!!%!?%?%%!%%?!!%?%%%!%?%?!??!?!%%%%%%%!%?%!?%!!?%%%%%?%!%!!%%?%%%%!!!!!!%%%!%%!!%!!%!%!!%!!%%%%%!%%?%%%!?!??!%%%!!%%%?!%%?!?!%?!!!!??!%%%?!%%%%%!%!!%!%!%!%?!%%%?????!!?!!!??%%?!?!!!%%?%!!!%?!%!!!!!%%!!%%!!%?%!%!%%!!!%!!%%!!!!!!%%!!%%%!!!%?%!!%??!%%!%%%%!!?%!!%%%!!!?%%!%%%%!%!%?%!!?%!%!!?%?!%!!%?%%%%%!%!!!%%%%!%?!!%!!?%?%%!%!?%?%?%%?!%!%%!%%!!%!?!!??!!!?!!??%%%%%!!???%?%??!%%%%?%%!%%%!!!%!!!%!%%!!%%%%%%!!%!!?%?!%!!!!!%%!?!%!?%%%%!!%!!%%%?!?%!!%?!%?!!%%%!!%!?%%!!%!!!%%!?!%%%%?%!?%!%?!%%%!%%!%?%%%!!%??%!%?!!%?!%?!?!%!%!?!!%!%%%%%?%%%!!%!%!%%!%%%%?!!%%?%!!!!%%!!%!%!!!%!%!%!%!%%%%%%%!?%!%%!!?%%%!!!%%?%!??%%!%!%?!%%!%?%!%%!!!%%!?!%%%%!%!%%%!%!%%%%%?%%%!%%!%%??%%?%%!?!??%%%%!!%?!!%%%!%%!!%??!%%!%??!!%?!!%!!!%!?!!!?%!!??%!%%%!?!?%!%!%%?!%%%!%%!!?%!%%%%!%%?!!%!!%%?!!!%%!!?%%%?%%%!%?%%??!!?!%%%!!?%%?!%!!?!%!?!?!%%%%?%%?!%%!%?!!!%?!%!!!%%%%!!%%?!??%%%!?%%?%%?%!%%%!%!!!!!%%%?%%?%%!%!?%!%%%!%%%!%!!%!!!%%%%%!%%%!!%?!%%!!!%!?!%!%%%!!!!%!%%?!?%%?%%!!%%%%%%!%%!%!%?%!!%!!%!%%?%%!?!!!%!%!!!??!%!%%%!?%!!%%%!!%!!%?%%%!%%%%%%!!!%?%!%%!!%!%%!!%%%%!%%%!%%%%%?%%?!??%%!%%%%%!%%!%!%?%?%%!!%!%!%?%%%%%%!%%%%%%%%!!%%!%!%?%%%!?%!!%%%%%%%!!%%!%?!%?!%%!?%%%%%!%!%%!?%!%%?!%?%!!!%%%%%%?!?!%%!%%%%%%!!!?%?%%%%%!%%%?%!%%%%!!!%%!%?%%!!!?%%???!?%!!%?!%%?%?%%?!%%?%%!%!%?%!!%?%%??!%!?%!!?%%!%%!%!!!%?%%%%!!?%!%!%!%%!!!!?%!!%!%!%!!?!??%?%%!%!%%!?%%%%!%?%?!?!%%%%%!%?%?%!!!!?!%%%??!%%%!?!!!%?!??!!!!%?%!%?%!!!!%%%!!??%%!?!?!%%??!!%?%%!%%!%!!!!%!?%!%!!!%%%%!?!%?!%!%!!!%!!?!%!%??%%?!%!??%%?%%%%%%%%%%%%!%%?!!%%%!!%%%%%%!!!!%!%!%!%!%!%!!%%?%%??%!?%?%%?%!!!!%!%!%%?!!?!!%%%%?!!!!!%!???%%%%%%!?%!?%?%%?%??%%!!!%%?!%%%??%!%!%!%!!!!!?%!%%!!!%%%%%!%?%!!??%%?!%?!!!%!!!%%%%!!!%!%!%%!%%%!!%!!?%%?!!%?!%!!%?!!%%%!%!?!!%%!%?!%?%?%!!%%!%%!!?!?!%%%%%%?%%%!?%?%%?%??!%%%?%%%?%%%!!%!!!%%?%?%%!?%?%!!%%!!!!%%!%%%%?%!%%?%%?%?%!%!?%!%%%%%%%!%!?%!!!%?%!!%?!!!!%!%%%!!%%%??%%%%%?%!!?!!%?!!%!?!!%?%!!%%%%!%?%%%%!%%%!%?%!!%%%%%!!!!%%%%!!%?!!!%%?%!!!!!%%%%%!?!!%%!??%%%%%%!%%!%!!!%!%%%%!!%%%!%%%?%!%?%!%%?%%%%%%??!!!%%!%%?%!%!%!%!!!?!!!%%%!!%%%%??!%!%%!%!!?!!!??%%!?%!!%!%???!!!!?%?%?!%?!%%!!!%%?!!%?!%%%?!??%!!!?!!%?!!??%!%!%!!%!!%%%%%%%!%%%%!!%!%!%!%%%!!!%%!!!%!%?%!!%!!!%!!%?%%!?!%!????!??%%%%%!%?%%?!%?%%%%???%%!%%%?%%!%%%?%%!?!!%%%%????%!!?!%!%%?%%?!%?!?%%%%%!%%%%%?%!!??%%%!?%%!%%%!%%?%%!!%?%?!%?!%!!%!?%!!%%?%%%%??%!%%!%%!!%%%%%%!%!%%%!%!%!%%%%?%!!%%!%%?%?!?!%!%%%!%?%%%%!?!%%%??!?!!!?!?%%%%%%%%%!%%%!!%%?%!%%%%?%??%%!%!!%!?%?%?%%%%!%%%?!%%%!%?%!%!%!!%?!!%%%%!?%!!!%???%%!!?%!%?%%!%?%%%!%!!?%!%??%%%!%%%%!%?%?!%%%?%!!%%!%???%%%%!!%?%%???!%!!%?%%%?%%%?%!?!%%%%%%!%!!!%!?!?%%%!%!%%%?!%%!!%%%!!%%!%%%%%%?%%%%!%%%?%%!%%%%%!%?%!%??%?!%!!!!%!%!!!?!%!!%!!!%%%!%%%!!%?!?%?!%%!%!%%%?%%%%?!!%??%%!%%%%??%!!%!!%!%%%!!%%!!?%!!%%%%!!???!%%?!%%%%%!!!!%%%!%!%!??%?%%!!%%%!?!??!%?!!!%%?%!!%%%?%?!%%%%%!!!%%%%!!%%%!%%%%??%!!%!%!?%%%%???!%!!!??!%%!!%%%!%?%%%!!%%!%%%!!!%?%%%%?%!!?!?%%%!!?%?!!!?!!%!?%?!!%%!%%?%!!%%!%%%%%%%%?%%%!%!!%!%!%!%!%%!!!??%%?!??%?%??%%?%%%!%!!%??%!%%%%!%!!%%%%%!?%%%%%!%?!%%!?!%?%?%%!!%%!!%!!!%%?%!%!!!!!%!%!%%?!%%?%!??%!!%%?%?%%?%!%!?!!?!%%!!%%%%%!%?!?%%%%?!%%!!%?!%%!?!!%!?%!%!!%!%%!%?%!!!!!%%??%!%!%%!%%%?%%!%!%%?%%!%!??%%?%%!!!?!%!%%%!%%%%%!!%%!%!%?%??!%!!%??%%?%!!!!%!%!%%!!%!%%!%!!!%%%?!%%!????!!%?!%%%%!!!%%!!!%!%%%!%??%%%!!!%!%%%!!%%%?%%!?!!?%%%%!?%%?%%?%%!%%%%!!%%!%%!%!%%?%%%%??%%?%!%!%?!!%?!!%!%?%!?%%!%%?!%%?%?%!%%!?%%%!?%%!?!%!?%!!?%?%%?%!%%%!!!%???!%?%%!!%%!%!%!!%!??%?!%?!%?!%%?%!%%?!?%%!%!%%??%%?%!%?!%%?%??!%!%%%!%%!%%%?!?%!?%%!!!%!%%%!!!%%%%%!?%%?%%?!%%%%!!%%%%?!!%!%!%%%!!%!%!%%?%%%%!?%!%?!!%?!?%%?!!%!%!%!?!?%!%!!??%?!!%%%%%%!???!!!%!%%%!!!%?%%%????%!%!!%!!%%%%??%%?!%?!%%%!?%%!%%?!?!!!%!?%!??%!%?%%!!%%!!%%!%%??!%!%%!%!!%%%!%!%!!%%%%%??!%%!%%%??%%%%!!!!%?!!!?????%%!!%%%%%%!?!!?!%%!%%?!%!%%%!?%?%!?%%%%%%!!?!%%!%!!?%!%!!%!%?!%!!?%%!%?%%%%!!?!?!!%!%%%!%?%%%!%!%%%!%%!%???%%!%!!%%?%!%!%!!%!%!!%?!!%!?%%%!%??%%!!%%?%?!?%!%!%%%?%!!?%!%%%!%%??%!%%%%%!%!????!%!?%!%%?%%?%%!%!%%!%!%!?%!%%%%%%%%%%%%%?%%%%!%%%!%!!!%%?!%%!%?!%??%??%?%%!%%%%%??!!%%%%%?%%%!!???!!%%%!%!!!%%%%!%?!!%%!?%!%%??!%%!?%%%?!%%?%!%!%!%?%%%%!%?%!!!%!!?!%%%!%!%%!%!!!%!?%!%!%%!!%%!%!!%%?%!?%%%%%!%!!?%?!%%%?%%%%%?!%??!%%!%%%%%%%?!!!?%!!!%%?%?%?%!!!%%!%!%%%!%!!?%%%%?%!%?%%%%%!!!%!?!%%%%?%%!%%%%!%!%???!?%%%%!!%%!%%!!!%!!%!!?%%?%!!%!%%!%%!%%!!?!!!!%!!%%%!!!%!!%!%?!%%%!!!%%!%%?!%%?%!!%%?!%!!?!??%?%%!%?%!%?!!%%%%!%%!%!%?%?!%??!!%!?!%!%%%%!%!%%%%!!!!!%%%!!?!%%!!%%?!!!?!%%!%?!!%%!%%!%%!!%%%%%%%%!%?%?%%!%!!%!?%!%??!%%!!?%%!%%!%!%%%%%!!!!?%%!%!%!%!?%%!?%!%%%!%%!!!?%!%!%%?!???%!%!???%!?%!!!%?!%%%%%?%%!!??%!%!%%%!%?%?!!!!%!!%%%%%!%%%!!!!%!%?%!%!%!%%%!!!?!!%?!?%!!%!??!!%%!?%%?%!!%??!%%%%%?%?!%%%?%!%?!%!%!!%?!!%!%%!%%%%!%!!%!?!????!%?%%!%%?!%%%?%!!?%%%!%!!%!!%%%%!!%%%%%%%!%%%%!!%?%!%!?!%?%?!!%%%?%%%!%!?%!%%%%?!%%!!?%%%!!%?!%!!?!%!%?%%?%%%!!%!!%!!?!?%%!?%%!?!?%!!!%!%%%%?%%%!%!!!%?!%!!%%%?%!%%?%!%!?%%%%%!?%!%!!!!%?!?%%!%%?!%?%%%?%%?%?!%?!!!!%!!%!!%!%!?!%!?!%!%%!?%%%%?%!%%?!?%%%%!%%!!!%!!!?%!?!%??%%%%!!%%%%!%!?!!?!??%?%?%?!!!?%%?%%!!%!%%!?!!%!%!?%%!%!!%!%%!?%%%!!!%!%??%?%??%!!!?!!!%!!!%!%%%%?%%%!?%?!!%%!!???!%%%!%!!%%%!??!%%%?%!%?%?!?!%%%?!!%%??%?%?%!!%%!?!%!!%%%%?%!%!?!%%%!?%?%!?%!%%?!%%%%%%%%!%!!%%!!!%!!?!!!%!%!?%%!!%%%%!%%!%%%!!!%%!!%!%!%??!??%!!%?%%!%?!%%?%%?!%!!%%%%!?%%!%??%!%!!%%%!?%??%%?%??!%%%?%!%!%%%?!%!!%%??%%%%!%%?!%?%!%!!%%?%%%?!!!!%%%%%?%%?%?%%%%!!?!?!!%%%?%!%%!%%%!?!!!!%!%!%%%!%?%%!%!%%%%%!!!!%!!%%%%!%%!?%%%??!%!!!%?!%%%%!!%!%!%!%?%%!?%%%%%!%??%%!!%!?!%?!%%!%!!%!%%!?!!!%%%%!?%%?%%%%!?%%%!%%?%%???!!%!??%!%%%%!%!!!!?!%!%?!%%?!!%!%%%?!%!?%%?%%!!?%!%!%?%?%???%%%%%?%?%%?%%%%?%%%%%!%!!%%!!!%!%!!%!%?%%%!%%%!!%!!?%%?%%%%?!%!?%%%%%?%!!%!??!%!%%%???%%%%?%%%?!%%%!%%%%%!%!?%%%%!?!%?%%!?%%%!%!!%?%!%!!!%?!%%%%%%!!%??%%!?%!?%!%%%%!!!%%%%!!?%%%%!%!%%!?%%?%%!!!!%%?%%%!%%!?!%%!?%%?%%!%!?%!!??%!!??!!%?!!%!%??%%!!%%%%!%??!!%?!%%?%!%!%%%%!?!%??%%!%?%!%!!%%!!%!!!%!?!%%!%!%?%%!?!!%?%?%?%?!%%?%!?%%%!!%?!%%%!%??!?%%?%%???%!%%%%!%%!?%%!%%%%!%?!%!!%?!?!%%!%%%?%!!%%%%%!!???%!%%!!!!?!%%!!%!%!%!?!!%%%!!!!%%?%?%%%%%%!!%%%!?%%%!%??%?%?%%%!?!%!%!%%!%!%%%!%%!!%%!%!!%?!?%?%%!?!%%%%!?%%%!!?%!?%%%?%!!%%!%%%!%%%?!%!?!%%!%%!%?!?%%%%!!!!%!!%%??%%%!?%!!!!?%!!%%%%?!%%!%?%%!!???%%%%??%?!!!%%%%!%!%!%!%%%%%%?%!?!!%%!!!%??!%??%%!!?!%!%!%%!%%!!??!!%?!%%?!%!?!?%!%!?%??%%%!%%?!?%??!!%%!%%%!%?%%%!?!%%%?%%%!%%%%!!%!%?????!%%!!!!%?%!%%%?%!!%%%!?%!%%%%%%%??!?!%?!!%%!!%!?%%%!%!%%%%!%!%!%?%???%%!%!!!!?%%%!!%!!%?!?%%!!%?!%??!%%!!?%%!!%%!!%!?!%!%?%%?%?!%!%?%?%%%!?!%%!!%%?%%!!%!!%%%!!?%?%%!!%!%%%?!%!!%!%?%?%?!%%%%%??%??%%!?!!%%%!!!%%?%%%!!%%!%!%%%!%!%%%%!%%?!%%!%!!%!!?!!?%%!!%!%%!!!!!!%?%%%%?!%!!!?%%!%???!?%%%?%!%!!%?%%%!!!%!%?%!%%%%??%%%!!%%%!%%?!%!%??!!!%?!%%%%%??%!%%!!!!!?%%!?!?%%%!%?%!!%!%%%!!!!%!%%!%%!?!!!?%!%%?%%%?!%%?!%?%%%!%?%%%%?%!%!?!%!%!%!?!%!!%%%?%?%%%%!%%?%!%%%??!%!%!?%?!!??!%!?!!!%!?!!%?%%!%%%%%!!!%!!!%%%?!!!%?!%%%!%%%!%%!!%!!%?!!???!!!%%%%?%??%%%!%%!%?%%?%?!!!%!!!%!%%?%?!%??%%!??!?%?%?%!%!%!%!%!?!!%%%?!!%%%%!%%%???!!???%%?%!??!%!%!!%!!%%!!!?%!%%!!%%%%%?%%%%%???%%!%?%!??%!!%%!%!?%!!??%!%%!!%?%!!%!!%%!%?%??!?%%!%%!%!!%%%?%!!%!??%%%%%%%%!!!!%!%%?%!!!%!%?%%!!%?%%!!%%%!!?!%%!!!%%%%%??!%!%%!!!%%%!!?!??%?%!!!!%!%!%%%%?%%%%!!%%%!!?%?%%??%%%!?%%?%%!%%!!%?!%??!%??%%!%!%%%!%!?%%%!!%%%!!!%?%?!?!%%!!%%!!%!!!%%!!!%!!%%??%%?!?%?%!!!!!%!%!%%!?!%%?%!!%%?%%!!!%?!!!%?!!!?%!!!%?!?!%%%!??!??%%%%?!!?!!%%??%%%%%%%!!%%%%%!!%%?%%%?%%!!?%!%?%%!!%!!?!!%%%%%?!?%!?!!!%!%?%%!%!!!%!%!!%?!!%?%!!?%!%%%%!%??!%!%?%%!%%!%?!%%!%%%!%??%!%?%??!?!!!%!!!?%%%!!!?%!!%%!?!??%%%%!?%%!!?!?!?%!!%%%!!!!!!%!!%!?%?!!%!!?!%?!!!%%%??!%%%!%%%%!!%%!%!!%%!%?!%!?%%?!??!%%!!%!!!!%%!!%?!!!!!%%%!%%%!!%%!?%!%%!!!?!%?%!!???%?%%%%%%%?!%%%%%?!!%!!%??%%?%!!%!%!%%%?%%!%%!%?!!%!%!%%?!%!%%%%%?%?!?%!%?%%!%%%!%%?!!!???%%%!%%%%?%%!!!!%?!%%!?%!%!%%!%!?!%%!!%!!?%!%!%%?%!%%%!!!?%%!%%%%?!?%!%%%%%%!%%%!%?%!%!!%??!?!!%%%%!%%%%%%!%?!?%!!%!%%%!!!!%!??!!?%%!?%?!%!?%?%!%!!%%%!%?%??!%%!%!%%%%!%!!%%!%!%!%%!!!%%!%%!%%%!!%%?%%%%%!?!?!!?!!%%!!%!!%%%!%!%%!!%%??!?!?!%!%!?%?%!?!?!!%%?!?%%%!%%%!??%%%%%?%?!%%%?%%%!?%%%!?!!%!%%?%%??%%!%!!?!!!!!%!!!?%?%%!?!%%%%%%%?%!%!?%%!%%?%%%%%?!%!!%!%%%%!!%%%%%%%%%!!%%%%%!!!!%%?!%!?%%!!!?%%!!%?!!%!!!%!!%?%?!?!%?!!%%%!%?!!!%??%%%!!%?!%%!%%%??%!%%!!%?!!?!!?!%!%%?%%!%?%%%%!!!%!%%%!!%?%%%%%!!!%!%!%%??%?!%?!%%%%%!%!%%%!?%!%!!%!%%%%!%?%%!!?!?%!?!%!%?%?!%%%%%?!!%!%!%!?%%?!!??!%!%%!%!%!%?!??%%!!!%%%%%!%!?%%%%%!%!?%?!%%%%%%%%?%%!%%!%?%%%%%%%%%!%%%%?%!?%%?!%%%!%?!!?%%??%!%%%?!%%!!!!%%%%%!%!%!?!%%%%%%%%%!%?%!!?%%?!%?!%%!?%%?%?%!?%%%?%%%%%%!%%%!?!!?!!!?%?%%!?%!!%??!!%?!%%?%!%?!%%?!%%!!%%%!%!!%!?%!%%!?%?%%?!%?!??%%!?%?!!%?%?%%%!%!?!?!%%%%!!!!%%%!%%!%%?%!!%!?%!%%%!%!!%%!%%!%!!%!?!%%%!!%%!!%!%!!%%%%%?%%%%!!%%?!?%%??%!%%%%%?%%%%%%%%%!?!%!%%%!!!??%%!%!!%%%??%%%%?%%%%?%?%%%?%%!%%!!%%!%%!!%%%%%?%!%?%??%%!%!!!%?%%!%!%?%%!!?!%!?!!?%!%%!!%!?!!!%!????!%%%?%%!%!%%!%%!!?%?%%%%%?!!%%%?%%%%?!!!!?%!%!%%!!%??!%!%%!%?%!?%!?%!!!%%!?!%%%%?%!!!!!?%%!%!!%%%%!!%%%?%%%!%!??!%?!!%?%%%%%!!%%!!!%!?!%!%!%?%!%%%%%%!%%?%?%!!!???!!%%%%%??!?%!???%!!%%?%!!!?!!?%!%%!%!%?%!%!?!?!!%!?%!!?!%%%!!!!%%?%!%%%%!%!%%!%!%%?!%!!%%%!!!?%%!%%%%%%!!!%!%%?%!?%%?%!!%??!!%!%%?!!!?%!!%!?%%??!%!%%!!%?%%%%%?%%%%%!!!%%!?!%?!!?%!?%%!%!%%%!%!%!!?%%!!%%!%%%%%%?!%?!%?%!%%!%!%!%?%%!!!!?%%!!!!?%?!!!%?%!!!%%?%%%%%%!!?!?%%!%!!!!!?!%%%!%%!%%%%%!%%?%%?!!!!%%!%%!??%%?%%%!%%!!!!%%!%!!%!!%!!!%%%%!???!%%!%!!%%%?!!%?!%%%!%%!!%!%%!!%!?%??!??%!??!!%?%%!!!%%%?%%?!?%?!??!?!!!?%!%%!%%%%!%%%!%%%%%!?%%%!!%%%??%%!?%!%!%%!%?!!!%!%?!%%%%%%%%%?!%%!%!%?%%!!!%!%!%%%?!%%!%%??!%!!%%!!%%?!!%%!%%!?!%%?%!%%!%%%%%!%%!!%!!?%!!?!!!?!%!!%%!%%!!!?%?%!%?!%?%!!%%!%!!%!%%%%%%%!!%!!%!!!%?!%%%!!!%%%%!!%%%%!%!!!!%!%!%%%%%!!!!!!%?%%!?!%!%!%%%!%?!%???!%!!!?%%!!!?%%!%%!?%!!!?!?%!??%%%!%!!!%!!!?!!%%!%!!!%%%%%!?%%%%%!?%%!%?!%!%%%%%%!!!%!!?%%%%%%!!!%%!!!%!%!?!%%!!!%!!%!!!%%%!!?%?%!%%%%%%!%!?!%%!?%?!!%%!%?%%%%!!%%??!!!%!?%%??%%%!!?!!!?%%%?%%!!?%%%%!%!??%!%!%%?!?%%%%!%%%!%%%?%???!%!!%%?!%%%!%%!%%%!%?%!!??%?%%%!%%%?!%%?!!%%!?%!?%%!!%%%%%%!!!%%!%?%%!!?%%%%!%!%%!%!!%!?%%!?%%%%%%!?!%!!%?%!%!%%%%!%?%%!%%!%%!%%%!!?%%%%%%%!!?%!%?%%?%%%%!?%!%?%!%%%%%%%%!!%%%?!%%%%%%?%!!%%%%%!?!??%!??????!%?!!?!!%!?%%!%%%%?!%%!%!%%%!%?%!!?%!!?%%%%%%%!?%%!%%%?%%%!!%%%%!!%%!%!!%%%%%!?%!%??!%%%%%%?!%!%%!!%!??!%?!!!%!%?%%!%%%?!%%!?%%!%?%!!%?!!%!!%?!%!!?%?%%%!%%!!!%!??%!%!!!%%%%!!%?!!%?%!%%%%%!%%!%!%%%%!%%%!?!!%???%%%%?%%?%%%%%%?%!%%!!%%%%%!%!%%%%%%%%%!%!%!%!?%%%!%!%!%?!%!!?%%%!%%%!%%?!%%!%?%%%%?!%!%!!%%%%%?%%%%%??%?!%!%%%?%%?!%!%%?!!!?!?%%?%!%%!%%!%%%!%!%%!%%!%!?%!!!!%???!%%%!??%%!?%%%!!%%%%%%!%!!?%%%!?%%?%%?!%!%?%!!%%%!!!%%%%%?%%?!!!?%%?!?!%%!%!!%?!%%%!%%?!!%%%%!!!!%%!%!??%%%%%%%!?%?%?!%!?!%%%%!!!?!%!%%?!%%?%!?%!!%?%!%%!%%!?!?%%%%%%!?%%!%%%%%%!??!?!%%!!!!?!%!!?%?%%%!%%%%!%%!!!!%%!%%?%?!?!!??!%%!%!%!%%%%!?%??!%%!%!!?!!!%!%%!!!%%%%?%!?!%!%!%%%!%!??!!!%%%??%?%%%%!?!%%%!!%!?!%%!%!!%%%%%!%!%%%!?%%%%?%%!%%!!!?%!%?%%%%!?%%%%!%!%%?%%%!%?!%%??%?%%%!!%%%%%%%!!!!%?!?!!!%!?%%!%%%%%?%%!%%!%?!%%?%%%!%?%%!!%%?%!??%%%%%?!%%?%?!%%%%?!%!!?!!!!%!!!%%!!%%%%!%%!%%!?%!%%%!%!!%!!!%!?%?%%!??%!!%!%?%!!%%?%%%%%%!%!%!!%%%%%??!%?!!?%!%%%%%%%?!?%!%!%!%?!!!%%%?!%?!%!%!!%!?!%!%%?!!!!%!?%%?%%!%!?%?%%%?%!!%%%?%%%!%%%%?%!??%!%!??%%?%!!!%???%%%%%%?%!%!%%%%?!!!?%!%%%%%%%%!!!!!%%!?!!?%%?!!?!%%%%%%%!%%?%?%!%%%!%%!?%%?!%%%!!%%!%?%!%!!%%%%%%%!!?!%%!?%%%%!?%!!!!!%!?!!%?!%!!%%%?!?%!!?%%%!%%%%%!%%%%!?%%!!!?%!%%!!%!!!!?%%???!%%%%!!?%!!%%!?%?%!?%%%%%!!%%%?!%%!!%!%?!?%%%%%?!!!?%%%?!%%??!%%?!%!!%%%%?%%%%!%!?!!%?!!!?%?%!%%?!?!%%!!!?!%!%!!%?%!??%%!%%!%?!%??!%!%!!!%%?%%!%%??!!!!%%!?%!!!!!%!%%%%?%%%!!!%!%?!!%%?%?!%!?%!?%%%!%%%?!!%!!%!%%%%?%%!%!!%%!!!%%?%?%%??!?!!%!??!%!%?!!!%%!?!%%%!!%?%%?%%%%%%%%!?%%%!%!!!!%%!?!!%!%?!!%%!?%%!!%!%%!%?!?!?%%?%?!%%!!%!%%%%%%?%!%%!%%!?%%%%%?%!%%%%!%!%%%!?%%%!%!%!!%%%%%%%%%%%%!!%?!%%%%%!%%%!%%%??!??%%%%?!%%!?!!!!%!%%%%?%%!!?!!%%%%%?!?%?%!!%!?!%?%%?%%%%%!!%%%%%%!%%?%%?%%!?%!%!%%%?%%!%%%??!%%?%?%!%%!!%?%%%!!!!%%%%!!%!!!!?%%%%%?!%%??!!!%!%?%!%!?%!??%?!%?!!!!%%%!!%%%%%?!%%!%?%%%?%!?%?!!%?%!!?%?%%%!%%%?!%%%%?!%%%!!?!!%!?!?!!%!%%%!%%??%%!%!!!%%!%?!%!%?%!?!?!%%%?%!%%!%!%%%%!%!?%%%!!%%!!?%!%%?%%!?%%!?%%?%?%%%%%%%?%!!!!%!%!%!!?%%!%!!!!%??%%!!%%?%!!!%!%!%%%%%!!%!!%%!%?!%%!?%%!!!%??!!%%%!!%%!!%%!%!!?!!!%%%!!%%!%%%!!%%!!!%%!%%%!%!!%%?%%!%%!?%?%?%%?%?%!!%%%!?!%%%??%%!%!%!!%?!%%?%%%%?%?!!%?!!%%%???!!!??%!?%%!?%!?%!%??%%!?!!!!!%?%%%%%!!?%!%!%!!%%!?!%!%%?!%%!%%%%?%!%%%!%?%%%%%??!!?%%!!%%%%%%%%%%!?!!%!!!%?%??%%!?!?%!??%%?%!!%%%?%?%%%!!%%%!?%??%%!%%!%%!%?%!!%!!%!%%%%%%??%!?%%?!!%!??%%!!%%%!!!?%!!?%%%?%?%?!%%!?!?%%!%%%!!%?!%!%%?!!%!%%%??%%!%%!%%%%%%%!?%%!?%!??!!%!?%%%%%!%%!%%??%!%%%%%!!%%%!%%%%%%!?%%?%%?!%%%!%%?%!%?!%?!!%!!!%!%??%%?%%%%%%!%!%!!%!%!%??%!%%%!%%!!%!!!!!%!%?!%%!%?!%%%%!!?%!!%%!?%!%?!%%!%?!!?!%?%%!%%%%!??%!!%%!%%?%!?%!!!!!%???!%%%!??%%!%%%?!!!!%?%%!!!%%%%%%?!%?%!!%%%!?%%?%!%?%%??!!!!%??%!?%%%?!?%%%!!!?!%%%?!%!%%?%!%?%%%%%?%??!!%!!%?%%%?!!%!%!?%%!?!%!?!!?!%%!%%%%%%%?!%!%%%!!%!%%%?!!%%%!!%!%!?%%?%!%!!??!%%%!%!??%%%%%!!!%!%!!%!!%!!%%?%%%!%!%!%??!!??%!%%%%!%%!%?!!%%!%!!%?%%%%!?%!!%%!%!!!%%%%!?%%%!%!%!%!%?%%%!!?%!?%!!??%?!%%%%!!%!!%%%%!%%!%%!!%%!%%?%%%%?%!%!%%!%?%?!%%!?!!?%%?%%!??%%%?%!!%?%?%%%!%?%%!%?!!!!!%%?%%!!!%%%?%!!%%%%?!%%!!%!%%%!!!!?%??%%%%?!%?!%%!!?%%%?%!!!!!%!?%!!?%!%!%%%%%??%!!!%!%%%%!%!!?%!!%%%%!!???%%%%?%!%%%?%%%%%%%??!%%!%!!%??%!%%!%%!!%%%%%%%%!!%%%!%%%%%%%!%%!%!!%%!%!!?!!!%%%%!%%!%!%%!%%?%%?%%%!!%!%?!!%!!!%!!%!!!%%%!??%%?!!!!%?!!!?!%!!%!?%?!!%?%!!!!%??%%%?%!%%%!!!%%!??%!%%!!!?%%?!%?%?%!!%?!!!?%%!%!?%!%?!?%%!?!!!!!%!?%%%%%!!%%?%?%%!%!%%!%%%!!!%?%%%?%?%%%%%%%%%!%?%%%?%%%!%!%%%%%!!!%%%%%%%%?%%%%!%!!??%%%%%!!%%!!%%%!!?%!??!%%!%!%!!!%%?!%!%%%!%!%!??!%!?!%%%!%%%%%%%??!!%%!??!%%%!!!%!!%!!!!%??%!%%!%!%%?%!?!!%!%%?!%%?%%?!%!!?%??!%%!?%%?%??!%!!%%%!%!?%!!!?!!%!?%!%!?!%%%%%%!!!?!!%!!?%%?!%%%%%%?!%%!!!!!%%?%%%!!?!%%!%!%%!!%!%?!%%%!%%%!?!%%?%%%?!%?%!!??!%%!%%%%%%!!?!%%!%%?%!%%%!!!%!?%!!%%!%!%!%%%%!%?!?%?%?%!%%!%!!!!%%%!!!?%%%%%!!%%!%!%%%%??%%!%%%!%!!!%%%?%!?!%!%!!%!%%%%!?!%%!%%%%%!?!!%!!!!?!!?!%%%?%!!%!%%!%!!%!!!%%%%!!?!?!!!?%%%%%!%?%!%%!%%!!?%!!%?%%%!%%!!%!%??%?%%!%%?!%%!%?!?!%?%!%%%%%%!!%?!!%%!%!?%%!%%%%!!!!%%%!?%%%%!!%%!!%%!%%%%!!%!%%??!?%%%%%%%!?%?%%?!%%%%%%!%%%?%!?!??%!!!!%%!%%!!%!%!!!!!%%?%!!%?%%?!%!!%!%%%%!%%%%??%%%!!%%%!%!%!!%%%?%%!?%!??%!%%!%??!!%!%!%!!%!%?%%??%%!%?!%%%%!!%%!?%!??%!!%%!%%!!??%%!%%?%?%!%?%!%?!!?%!?%%%!!%!!!%%!%?!?????%!!%%%!%!!%%%%%%???!%%??%%?!!%!!%!?%%%%?%?!!%%%?%%!!%!%!%?%!!%%!!!%!?!!!%!%?!!!%%%%%%!%!%!%?%!!%??!%%??%%!?%%%%?!!!?!?!%%!??%?!!%!!%!!%%??!%%!????%%?!!%?!!%%%!%!%!!!%!!!%%%!!??!!!%?!%%%!!%?!%%%%%%%%!!!!!!!%!%?!%%!?%?!!!%!%!%%!%???%?!%!!%?%!%%!!%%%!%%!!!%!!%!!%%?%??%!?!?%?%%%!!!%?%%?%%%!%%%!!%%!%!!%!!%%!%%%?%%%%%%!%%%%!!!%%%%!?%%%!?%!??%?%%%!!%!%?!?%%%?%!?!%%!!%%%!%!%%%?!!!%%%%%%%%?%%!%%%%!%%%?%!!%%?!%%%?%%!%%%?!!??!%!%?%!?!?%%!%?%!%%??!%%%!%%!%?!!!?!%%%%!!%?%!!?%!!%%%%?%!!%%!?%%?%%!!!%!%?%!%?!?!?%!!%??%????!%%!%!%?%??%%?!?%!!%!!!%!%%!?%!%%!%!%%%!?!!!%%%!!%%!!%%%?!%??!%?%%!!?!!%%!%!%?!!%!!!????%?%?%!!!%?%%!??!??!?%?!%?%!!%??!%%!!!?%%?%%??!%!!!?%%!!?%%%%?%!!%?%%?%!%!%%?%%%%?!%!%!%%%?%%!%%%?%!!!!?%%!!%%?!!%!!%%!%?%%!%%!!%%??!%!%%%%?!!%?!%!??!?%!?!!?%?%?%?%%%%!!%!!%!!!!%!%%!%!%%%!?%!%%%!!%%!%%?%%%!%%%!!%!!!%?!%%%!!!%%%%!%%%%?%%!??%%%!%%%%%%?%?!%%%%?%?!!!?!%%?%?%%%%!!?!!%?!%%%%!!%%%%%!!%!%!!%!%!!%%?!%!%%??%!%!!!!%!%%!%%!%!?%?!!!%%!%!!%%%%!?%?%!!!?!%!!%!%?%!%%%%!%%?%?%?!!?!%%%%??!!?!!!!%!%!%%%%?%!!!%!!%%%?!!?%%?!!%!??%%!%%%??!%?%!!!!!!%!%!!?%!%!%!?%??%?%%!?%%%%%%!%%%%!%%!!%!%?%!!%!!%%!!%%%!?%?%%!%?!%!%?%??!?!%%%%!?%?!?!?%!!%!!!!!%%%%%!!!?%%%!%!%%%%%?!!!!%%!!%%!%%%%!%?%%%!!!?%??%!%%?!!!!!%!%%%%!%%%!!!%?!%!%!%!%!!%!%%!?%!?!%%!%?!!%!%!?%?%??%!?%?!%%%%?%%%%??%!%%%%%%!%!%%%%?%%%%%?%%%?%%%!%%!%!!!!%?%%!%%%?!!%!!!%%%%?%%!%!!?%!%!%!!!%!!!%!!%!%!?%!%%!?%%??!%%?!%?!!%?!!?%%%??%%%??%%%!!!!!?%%%%%??!%?%%%%!!!!??%%%%!%!%?%!?!?!?%!%%?%?%%!!!!%%%%!%!!!%%??%%!%!%!%!%%?!!%!!!!%%!%?%%%!!%%!?%!%%!!%!%!!%%%!!%?%%%!%%%!!%%!!!!%!%?%!%%?!%%?!?!!!%!%!??!%!!!%%!%%%%!!%!!%%!%%%%%%%?!!!!%%%%%!?%!?%?!%%%!%%!%!%%%%%!%%%%!!%!?%!!!!?%%?%!%%%?%%!!!%%?%?!!%!!%%%%%?%?!%!%%%%%!?%%%?%!%%???%%%!%!!?!?!!!%!!!%%!%?%%!!%%%%%!%?%!!!%!%%%!?%%?%!%%%!%%!?%!!!!%!!!%?%%!%%!%%%%%%??!!%?!%!!!!%%%%%?!%%!%%!%?%%!%!%%!%%!!%!!%%?%!%%!!!!?!!%!%%%%%!%?!!%!?%%%?!?!!%?!!%%!!%!%%!%%!%!%%%%!%%!%!%%?%???!%%%??%%!%!??%%!?%?%%!!%!!!?!!!!!%%%%!?%!%?%%%%%%%%?%%%%???!?%%%!%!%%!%%!%%%%!!%!%%?!!%!%!!%!!%%!%%!%!%?!!!!%!%!%%%?%!%!%?!%%%%%?%?!%%%!%%?!%??%%!%??%?%!?%!!%%!%!%%%%%!?!!%%!?%%!?!!!%!%?!%%!%!%%%%!%?!?%%?%!%%%%%%?!%!%%%!!%??%%!%%%??!%%!%%!%%%!!%!!!%%%%!!%!%!!!%?!!?!%?!??%?!%??!%%%%%!?%?!%%!!%!!%%%%!?%!%%%%%!%%??%!%%!!%?%%%%%?!%%??%?!?!!%%?!?!%!!%%%%%%??%!!%%!!%%%%!%%!!%%!%!%!%!!!!!!%%!%!%%%!%%!?!%%%%%!%!%??%!%!%!!!%!%!%?%%%%?%??!!%?!!??!!%%%!!!!!!!%?%!?%%%!%%!%%%!%!%?%!%%%?!?%%%%!!%!!%??!%?%?%%!%%!%!%?%%!%%%??%!!%%!%!%!!%%%!%%%%!!%%%%%?%!?%%!!!?%?!?%%!%?%%!%??%?%%%%%!!!!%!%!%%?!?!%%%%?%??!!!!%%?%!%!!%!%%!!%%?!%%!%%%%!%%%!%!?%%%!%?%%%?%!%%%?%!?!!%%!!?%%!!%!!%!!!!%!%?%%%%%%%%?%!!%??%%%%?!%!!?!%%%!??%?%!%%!!%!!!!%%%!%?%!!!%%!!!%%?%%?%%%!%%?%%!%!?%%%%!!!??!%%!%!%!!!%!%!!%%%!%%!%!?!??%%%?%!!%!%?%%%!%%??!!%%%%!!!%%%%%%%!%%!?%%%?%?!!%?%%%!%%!%%%%%!!%%%?%!%%%??%%%%?!%?!?%%%%!!%!%???%?%%!%??!!%!%!%%!%!%%%%%!?!%%?%%?%!!?%%%?!%!%!%?%!%%!?%!%%?!!%!?%!!%!%%??!%?%%%%!!!%?!%!!%%?%?%%%??%!%%%%!!%%%!%%?!!%%?!?!??!!??%%%%%?!%%%%!!!%!!%!%!!%%%%%!!%%%!?%%!%!%%%!%!!!!%?!!%!%?%%%?!!%%%%%?!%!%?%%%!%?%%?!!%!%!%%%%!!%?!?%!%%%!%!%%%!%?%!!!!%!?!%!!%%%%%?%!!!?%?%?!%%!!%?!!%!!%%%?%!%!!%%%!%!%%!?%%!%%%?%%%!!%!!%%!%!?%?!%%!%%!%%%%!%?!%%!%?%%%%%%%%!%%!%%?%%%!!%%%?%!!%%?!?!%%%!!%!%!!%%%%%%%!?%!%?!!%?%!??%%%%!!%!%%?!%?%%?%%%%%!%?%!!?!%%%%!!!%?!??%%%%!%??%%%%%?!%%%%%%?!!!%!%%%%?!%%!!?!!%?!%!%?!?%%%?%%!%!%%!!!%%!?%%??!!!%%%%?%!%%!!?!%%!!?%%%%!?!!?%!!%!?%?!%%!?%%!%%!%!!!?!!!%!?!%%?!%%%%%%!!%!%%!%!!!%!%!%%%%%%?%!%%%?!%%!%!?%!!%??!%!!!%%!??%!%%%!!!%%!%%?!%??%%%??%%%!%%%%%!!%%!%!%!%!%!?%%%?%%%!%?%?!?%%?!%?!%!??!%!%!?!!%?%!%%!!!!%%%?!%%%%%!%!%!!!%???%!%!%%??%!%%%%!%%%!%??%%!%%%%?%%!%%%%?%%%?%?%?!!?%%%%!%%!%!%%%?!%???!?%%!%%??%!?%!%%!%?%%!%%!?%%%!!%!%!!!?%%!?%!?%?%%%%?!%%!?!%?%?!!!!%?!%!!!%!%%%!%%!%?%%%?%%?%%?%?%%%%%%?%!???%!%%!?%!%!%%??!!%??!%!%!%%%%!!%%!%!%%!??%!?!%%?!!!%%%%%!%!%!%?%%???%??%%!?%%%%??%%!!%%%!!!%?%?!%!!%!??%!!!%!!%?%%%%%!%%!%%!!%%%?%%?!!%!!%?%!!!?!%?%%%??%%!!%%%!%!%!?%?!%!%??!!!!%%????!%%%%?!%%?%!%!%%%%%!!!!!%?!!?!!%??!!!?%%!%!!!!!!?%%%!%!!?!%!%%%%%!%!?%!%%%!%%%?%%%%%%%!%!!%!%?%%%!%?!!%!%?!!?!%!!!!!%?%%%%%!%!!%!%%?%!%%?!!%!%?%!%!!%%?%%?!?!%?!!%!?!!%!%%!%?%!%!%%%??%!%%?%%%%%%!!!!%%%%%!%%%?%??%%?%%!!%%!%%!!??!%%!%!!!%!!!!!!!%%%!?%%%??%?%%%%%%%?!!%%?%!%%!?%%!%!!%%%%%%%%!%!!%%!!!%%%??!%!!?!?%%%%!!?%?!!%?!?!%%?%%!%%%%%!!%!%!?%!?%%%%!%!?%!?!%%%%!?!%%!!!?%!!!?%%!?%!!?!%%%!%!%%?!!?%?%%%%!%!%%%?!?!%%?%%%?%??%%?%!%?%%%%?%!%?!!%!%%?!?%%!!%%!%%!!%!?%%?%%%?%!%!!%%%%!?%%%%?!%?%??!%!!!%!!!%!!%%%!%!?%!%%!%!%!%!!!?!!%%%!%%!%?%?!%?%!%!%%%%?!?%%%!?%%??%!?%?%%??!%%!%?%%%%!??%!!!%?%%!!!?!?%!%%%!!%?%%%%!!??%%%%%%??!?%!%%%%%%%%?%%%%%%!!%?!%?%%%%!?%!?%!!!!%%!%!?%%!?%!%?%!!?%!%!%%%!%?!?%!%%?%?%%%!!!%!%%%!!!%%???%%!%%!!!%%%!!%?!%%!%!!%!!%!?!%!!?%?%%%!%!%%!?!%%%%!!%%%%%!!??%%%%!%%!?!?%%%%!%%!%!%!!!%!%!%%?%?%%!!%%!%%%%!?!!%?!?%%!!%!%!%??%%%%!?%%%?!!%!!!!?!%!%??!?!!%?%!!?!%??%!!%%%!!!%%!!%%%!!?!???%%!!%%!!!%%!%!%%!%%%!!!!?!%?!!!!%%%!%%%%?!%%%?!%%?!!%!%%%%?!!!!%%!!?%!!?%%%!%%%?!!!%%!%!%%%%%!%?!%??!!%!!%?!!!?%!%!!?!%!!%%%!!!%%%?%?%%!!%%!%??!!!%?%%%!%??%%!!!%?%%%?%?!%?%!!??!?%%!%!?!!%?!%%!%%%%!%!!!?!%%!%%?%%%?%!%%!!%%!%!!!!?%!%?!%?%%!!!%?!%?%?%%%%%%%%!%%?%%%!%%%%%!??%%!%%%?%!%!?%%?%!!%!?%%%?!!?%%%!?!%%!!%%?!!!%%%!!!?%%!%!%!!?%%!%%%%%!?%%%%!!%%%??!!!!!%?%?!!?%%%%!!%%%!?%%!%!%%%?%%!!%!%%!!??!%!?%!?%!!%!!%!?!??!!!%%!%?!!!!??!%!%%%%%%%!%%!%!%!%%%?%%!?%!%%?!!?%?!!%!!%%%%%!!%%%%%%!?!%%%?%?%!%%%!%%!%%%!!%%%%%!%?%%??%%%??!%%%%!%%%!%%%%!!!%?%%%!%%!%%%!?%%%%%%!%%!!%%%%!%%!!%%%?%%!!%!%%!%%%?!!%%%%!%%%%%%%%%!%!%!!%%%%%%%%!!?%?%%%%!%%!%!%%%!?!%%!?%%%!??%%%!%!???!%%%?%%%%%?%%%?%%!%!%%%%%%!!!?%%%?!%!%%%%%%!%!!%!%%%%%!%?!!%%%!!!??%%%%%%!%??%%%%%%!%%?%!%%%?%%%!%%%!!%?%!%!!%?%%!!%!?%!?%%!!%!%?%%!!!?%!!%%%!!?%!!%%%!!%%%?!!%%!?%%%%%%!!%!?%!!%!!?%?%%?%%%%???%!%%%%!?!?%%%%%%%%%!!?!?%?!%%?%?%!%?%!%%!%%?%?%!!%!?!!%?!%%!%%%%%%?%?!!!??!%%%?!%%%%%%!?%%?!?%!?!%%%!%!%%%%!!%!%!%%!%!%!!?%?%!%%?%!!%?%%!%%%%!!%%!?%!%%!!?!!!!?%%%!%%%?%%!%%%!?!?!%%!!%%%!!??!!!!%%%%?%%%%%%%%!!%%%!!!%%!%%!%!%%%!%!!%%%%%?!%!!?%%?%!?%?%%?!!%%%%%?!?!%%%%!%%!%%%%%!%%!%%%%??!%!%%%%!%%!%%%%!??%%%%!%%%%%?!%%!!%%!%!!!!%!%%%?%?%!%!%!%?%%!%!%%%%%%%!%%!%%!?!!%%!%%!!%%!!!!!?!!%%%???!%%!%!%?!!?%%%%%!%%%%%%%%%%?!!%%%!!%%!%%!!??%!!????%?%%%%??%%!!!%!!!?!!!???%!%!!%!%%%%!%?!!?%!%%!!?%%!!%??!%!%%!%?%%?%%?%%%%%?!%!%!!%!%%!?!?%!!!!%%!!%?!!!%%%!%!%!%%%!%%?%%?%!%%!!%!%!%%%?%??%!!!%%!!%!%%%!%%!%%%?%!!%%?!%%!%%!!!%??!%%?%!!!!?%%!%??%!!!%?!%%%?%%?%%%%!%!%%!!%!?!%!!!!%!%%%%??%%!!?!%?%%%!%?%!?%!?!%%%%!!%??%%!%%!?%!!%%??%!%?%%%%?%%%!!?!%%??!%!!%!%%!!%%%%!?!%%!!!%%%%%!%%!%%!%%!%!!%?%!?%!%!%%!%%%!%!%%%!!!?!%%??%%!%%?!%!%?!!?!??%!%!??%!%%%%%!!%%!%%%!!!%%!!%?%?%%%!%??!%%%??%%!!%%?%%!%%%%!!!!%!%%!?%%%?%%%%?%!!!%!%!%%%!%!%!!%!?%!!%%!%%!%%!%!?%%%!?%%%!!%%%!%!%!?%?%%%?%%%??%%%%??%%?!?!%%%!%%%?%%%%%!!%!%%%!!!!?%%%!!%%%%%%??!%!!!%%%!%%%!!%!%!%%!?!%!?%?!!!%!%?%!?!%?%%!!?%!!??!!%?!?%%%!%!!%!?%!%%%!?!!%%!%%!%%%%%%!%!!?!?!%%%!!!%%%%!?%?!!?!!?!%?%%%!%!%?!?%%?%%!%%%!%!!%%?%%%!!%!%%%%?%!??%%%!%%%%!!%!%%!?!%%!%%%%%%%??%!!!%!??!!%%%%!%!%%!!!!!%%%%%!!%?%%!!%!!%!%?%%%%%!%?!!%?%%%%!%!!%%!!!??!!%%%%!%%%!!!%%???%%%?!?%%%!!%!%???%%!%??!!%!%!%%!%?%!%!!%!%!%%?!!%?%%!%%%%%?!?%%?%%!!!%%!!%%?%!??%%!%?!%%!!%%!!%!!!?!%%?!!!!!%%%!%%!!!!%?%?%!%???%!%!%%%%%%!!%?%?!%!?%%%!%%!%%%!?%!%%%%!!%%!!%%%%%%!!%%%!%?%%%!%?%%?!%!!%?!%%!?!%%!%%%%??!%!!!!%%%%%!!%!!%!%!?%%?!%%%%%!!!%%%!?%%!%%???%?%%?!!%!!%%!!?%%%?!%%%%!!%!??%!%!%%%!%?%?%%%%%!%?!%!%%!%!!%%%!%%?%!%%?!!!!?%%???%%!%%%%%!??!%%%%!%?!!%%%%%?%?!!!!?!%%?%??!%!!!?%!%%%?!!!%%?%?%%%%%!!%%!!!%%?%%%%%%?%!%%!%!!%%!?%%%!!!%!%!%!%%%%%!!!!%??!%%!%%!!%%!%!%!!!%%%%%!%?%?!!!??%!%%!%%%%%%%%%!!%!!%?%%%!?%%?%?!!!%%!%?!%!!!!%%?%!%%%?!?!!!?!?%%!?!??%?!?%%%%%%??%!%!%?%!!%%!!%!%!?%?%%%%?%?%!?%?!?!!?%?%%%%??%??%!??!%?%?%!!!%%!%!%!%????%%%%%?!!%%!!!%%?!%%!%%!!!!?%!%?%!%%%%!!%%%%!?%!%%!!%%%?!!%!!%!!%%%%%%%%%?%!?!!?%%!!%%!!%%?%%!!%%!?!!!%%!?%%%%!!%!%!!!%%?%!%%%%%%!%%%%!%%!?!%%!??%!!?!!%!%!%!?!%!!!!!!%%!?%%?%%?%!!%!!%%!%!!%?%%%%!%!%!%!!!%?%%%?%%%??%%%!?!??!%!!%%?!%%%!!%!%?!!!%!!!!!%%!%!%%!?!?!!%%%?%%%%!%%?!??!?%!!%!%%%??%!%%?%%%!%!%%!??!!%?%!!%!%%?%%%%%%%%%%!!!??%?!!%%%???%!%%%%!%!?!!!!?%?%%%!%%%!?%%?!!%%?!!%!%?!%%%%%%%%%!!?%%%%?%??%%%%?%?%%%!%??%%!%%!%?!?%%?%%??%%%!%%%%%%%?!!!?!!%%?!!?%!%!!%%%?%%%?%!%!%!??%?!?!%%!%???%%%%!!!%!%%%?!%%%%%%!%%%?!!!!%??!%%%!!%!!!!!%%?!?!?!?%%%!?%!%%!%!?%%!?%?%%%%%%!?%!%%%%?%?!?%!!%!%!%%%%%!!%%???%!%%!%%?%!%!%!!%!!!%%?%!%?%!!%%%!%!!!%?%%%%!%%%%%%%%%!%!?%!%%%%!%%%!%%%%?????!%%%%%!?!%??%!%!%%!!!!?%!!!?%%?%%%!!%!%%!!%?%!%!%!%%??!%!%%%!%!%%!%%%%!%%%??!%?!%%!?%%%%?!!%!%%%!!%?!!%!??%!%?%!%!!%!%?%!!!!!!%%%!%!!%%%%%%!%%%%!%%%!%!??%?%!?!??%%%%%%!%!!??%!%!?!%!%%%?%!%!%!!!!!?%!%%%%%!%?%!%%%!!?%?!!%%?%!%%?%?%!%?%!?%%!%!%%?%%!%%!%%%%!?%?%%?!%%?%?!%!?%%!??%??!%?%!?!?!!!??!%?%%?%%%%?!%??%?!!%!%?%!%!%?%?!%!!%%%!!!%%!%%!!%%%!%%%!!%!!%!%!!%!%?!%%?%?!%%!%!?!!?!!%%!!?%%%%%??!%%!%%%!??!%?!!%%%%%?!!%?!%!!!%%%!??%%!%%%%!!!!%%?!%!!?%?%!!!!!!!%%%?!!!!%!!?%%?!!!!??%%%!%!%%%%!!?%?%!???!?!!%%!%!?!!!%%%!?%%!?%!%!!!%?!!!%%?!%%%!%?!%?%!%!%!!?%%!%!??%%%!%?!%%?!?!%!%?%!%%?!%%!%%%??%%!!%%?%!%??!!?!%!%???%!%%!%%?!!%!!%!!%%!%%?%?%%%%%!%!%%%!%?%?%?%%%%?!!!%?%!?!%%??%%??!%?%!%?%%!%%?%%%%%!!!!%?!%!%!!?%?%?!!!?!!!%%%%?%!!%?!%%!%%%%!!!%?!!?!!?!!%%%!%!%%%%%!!!%!%%%%%!%!%!!%%%?!!?!%%%%%%!%%!%%%%?%%!%%!!%!%%%%?%%%%?%%!?%!?%%??%??%%%!%?%?%!%!?%!%%%!!%%?%%%%!!?!%?!%%%%!%%?!%!?!%%!%%%!%%!!!%%%!!%%%%!!!!%%%%?!!%?%!%!%%%!!%!!%!%%%%%!%%%%!!!%%!?%!%%?%%%%?!%%?%!%%%%%%!%?!?%%%%!%!%!!%%!%?%%!%?%?%!?!%!%!?%!!!?%%%%%%!%%?%!%!!%%%%%%%%!!?!%!%!%!!%!!!!%%!%%?%?%!!%%!%!%!!%%%%!??!%%%%%!!?%!%?%%%%?%!%!%%!%%%%?%%!!%%%!!?%%%!?%!??%?!%!!%!!%%?%!%%%?!?%%%%%!%%%%%!!!%?!%!%%%%%%?%%%!!%?!!!!!!?%?%%!!%%!?!?!?!!??%%%%%!%%!%%%%!!%!%%%?%!?%%!%!%%?!!?!?%!?%!%!%%%!%%?%%%?%%%?%%%!!%!%!%!%%%!????!%%%%!%%!!%?!%%!!%?%%!?!%%!%!%?!%%!%%%??!%!%!!%%%?%?%!%%%%%!?!%%?!%%%%!%!!?!%?!!!%!!!!%!%!!!!%!%%%%?%???!%%!%!?%%?%!%%%%!!%%!?!%%??%!!!?!%!?!%%!%%!%!%%%!%!!!%?%%?%?%!%%%!!!!%%!!%%%%?!!!!%?%!?%%%!%%??%!???%!%%%%?!!%%%!%%?%%!%%%!%%%?!%%!!%%%%%%!%?%!%!!!%!%%!??%?!?%!%?%%!%!%!?!?%!?%%!?!!!?%?%%!%%%%!%?%!!%!!???%%!!%%!!%!%%!%%%!!?%%%!%%?!%%!%%%?%!!!%%%%%!%%%%%%%%!%!%%%%%%%%!%?!!%%%!%!%!%%!!!!%%%%??!!!!%!%?!%!!?%%?!?%!%!!%?%!%!!%%%?%%?%%!!%!%!!!!%%%%?%%%%!!%!?%%?!!%%!!%%%%%%!%%!%!%!%!%%!%%?%?%%%%%%%!%!%!?!?%%%%%%%%%%%%!!%%?%?%!!%%%%%%%%%!%%!%%!!!%%!!%%%%%%%%!??%!??!%%!!!%%%%%%?%%!%????%%%%%!%?%!!!%!!%?!%!%??%!!%%%?!%!??%!%%%%%%?!!!%!%!%!!!?%%%%!%%!%%%%!%!?!%?!!?!?%!!%%%!%%%%!%!?%%%!%!%%?!!%%!%!!!!??%%%!%!%%!%!!!%!?!%?!?!!%%%%!!%!?!!!%%!%?%%!%%!!?%%%%%!!?!%%?%%!!%!!?%!!?%!?%%%!%?%!!?%!?%%%!?%%%%?!%?!%%%??!%%%!%%%%%?!!!?!%%%!%%%?%%!%!?!!!?%%!!%!?%%%?!!%?%??%%%?%%!%?!%%!%%!!?!!!%%?%%!!%%!??%!?%!%!%%!?%!!%%!!!?!%%!!!%!%!!!!%??%??!%!%!!!%!%%%%!!!!%?!??%!%!%!%?!%%%!%%%%%%?%%!%!%!%%!?!%%!!%!!!%%!%%!%%!?!%%%!%!%%%%%!%!!!!?!?%%?%!%?%!!?!%??%??%!?!%%!?!!!!%%%%!!%%%%%?!%!%?!!%%?!!%%%?%%%??!!%!!?!%?!!%!?%!%??!?%%%!%%%%?%!%%%%!?%??%%???!%?%?%%%%%!?%!%??%%%%?!%?!!!%!!?!?!!!!%?%%%!!?!%%%%!%!!%%!%!%%?%!%!!%?!%!!!%%?!%%%?!!!%%%!!%%%!%!%%%%!?%?%%%%%%%%%%!?!!!!!!?!?%!?%%!?%!?%!%??%%%%!!%!!%?%!!!%!!%%%!?%?%?%%?!!?!%%!!%%%%!!%%%!!!%%!%?!%%%!%%%!%%%??%?!%!%?!%!%%!%?%%%!!%%%%!%%?!!%?%!!%?!%%%%%%???!!%?%%?!%%%%?!%%?%%%%!!%%!%%%!%%%%!%%%%%%%%%!!%!%?!!%!%%%?%!%%%%?%?!%%!%!%!%!!%%%%!!%%%!%%%%!!%%!!?!%%%?!!%!?%%%%!?%%%!?%!%?!!?%!%%!!!%?%?!!!%%!%!!!!??%?%%%%%!?%?!!%!%%!?!???!%%!%!?!%%%!%!%!%%%!%%!%!%%!!%!%!%!?%%!%?%%!!?!!%%%?!%%%%?%?!%!?%%?%!%!?%!%??%!%%%!!?!%%!?!!%%%!%!!!%%?!%?!%?!%%!!!!%!%%!!%?%?!%!!!!?%%%%%%%?%!%%%!%%!!%%!%%%!%!!%%!%%%?%%%?%%%?%?%??!!!!%%%!%%%%?!!%?!%?!?%!??%!!?%!?!!?%%%%%%%!!?!!?%%?????!%%?%!%%!%%!??%%!!%?%!%%?%?%%!!!%!%!!?!?!%%%%?%!?%%!%?!%!%!%%!%%!!!%%%!!%%!?%%%!!!!!!%!!?!%!!%?%!!!%!?!?!%%?%!?%%%%%%%?!!!!!%!!!?!?%!?%%%%!!%%!!!%!?%%%%%%!!%!?%!?%%%!?!%!?%%%%?%!!!!!!%%%%%!!!!%!!%%%?%%%%%!%%%%%?%%!%!%?%%!%%?!!%%%%?%%%?!!!!%!%!!%%!!!??%%%%!!%%!!?!%?%!%!?%!%%!%%%?%?%!??%%?%?%%?!!%%!!!%%%%%!%!%?%%%%!%??%%!!?%!!%%??!%!!!?!%%%?%?%!!!?%!!?!?%?!%%!!%?%!%%!!?!!!?!%!!%!%?!?%%%%?%%!%!!!%%!?%%%%?!%%%??!%%%%%!!??!%%??%%??%!!%!%!%!%%!%%!!!%!%%!%%!%%%%?!?%!%?%!%%%!?%%%?!%%!%?%!!!%%%%%?%%%%!?%%!!?!%??%!?%?!!%%!%!%!?%!%%%!%%!!!?!%!!!%%?%?!!%?!%!%%%%?!%%?!%!%!?%?!?!!?!!!?%%%!%%!???!%!%?!%%%??%?!!!?%!%%?!%%%%%!!!!!!!?%%%%%%%?!??!??!!?!%!%%!%%!?%%!!!!%?!%%%%??%?!%%!%!!%%%%%%%%?%?!!%?!!!%!%!!?%%!!%%!%!%!%?!!%?%%%%!%?%!?%!!!%%!%%%?%?%%!!%%%!%%!!??%!?!?%%%!%%%%%%%!%%!%!%!!!?%%%!%%%%%!!%%%!%%%%!!%%!?%?%?%!!%%?????!!!%%??%!%?%%%%!!!!%%%?!!?%%!!!!?!%!%?%?%?%%!%%%%%!!??%?!%%%%!%??!?%%%%%%%!%?!!!?%%%!!!%!%%!!%%?!%%!%%%!%%%%!?%%!%!!!%!%%!!!!!?%%%%%!!!!%%!%%!!%%%!!%%%!?!%%!%??%%%?!?!%%%!!%!%%%%%!%%%??!%%?!%%!%%?%%%!???%!!%%%!!!!!%%!%%!%%?%%%?%????%%?%?%!?%?!!?%!!%!%%?%%?!?%?%%%!!%!%!%%%!!!%%!!!?!%%!%%!!%%?!!%!!!!%!%??!%!!%%%!!%%!%%??%!%%!%%%!!?%%%!%!!?!%?!?!!!%?%!?%!%%%?%%%!??!!!!!?%!%%?!%!%!!?!%!%?!%%!%%%%%?%?%%%?!?!!?%%%%%%!%!%!!!?%%?%?%!!%%?!!!%?!%%%?!!????%%%%%!%%%%%!%%%?%%%!?%!!!%!%%!%!%%%%??%%!!!%%!!%%%!!!??%%%%!?!%!?%%%%??%%%?!%%?%%%?%%%%%?!%%%!%%?%!!!??%%%%%%!%!%!%%%%??%%!?%%%!%%!%%!!!!%%%%%%%!!?%!!%%%%%!!!!!!%%%%%?!%!%%%%!%%?!!%?!!!?!%%%!%%?!!!%!%!!!?%??%?!!!?%%%%%%%!?%%%!%!!%!%!%!!!%%%!%%%%%%?%%%%%%!%%!%%!!!%!%%%%?!?!%%!%!?%?!???%?%%%%!%?%%!%!%?%%%%!%!%?%%!%!%??!!!%%?%%!%%!!%%?%!%%!!%!%?%?%!!%!!%!!%!!!!%%!%!????%!!%%%%!!%?!!%!%?%%%%%%!!%?%%!%%%!%%%%?%%%!%%%!?!%!%%%!%??!%!%!%%!%!%!%%!%!%%!!%!%%!!??%!!%!%%?!%%%%?%?%%!!?!?!!%%?!%%%%%!%!!%!!%!%!!!%%%%%%%%%!%!!!%%?%%%%?%!!%%!!%%%?%%%!!%%??%!%%%%%%??!?!!%%%%%!%%%!!!!%%%%%%%!%%%!?%?%%%%!%!?%%%%!!%!!%%%%%%!%%%!!!!?%%%%%!%?!!!?!%?%!%%%%!%?%!?%?%?%%%?%%%!%%!!!!%!!%??!%%!!!!%!!?%%?%?%!?%%!?!%?%!!!!!%%!%%!%!%%%!%!%!!!!??%?%?!??%?!%!%?%%?!!!%!%%?%!%!%!%!!!?%%!!%%%!!?%?%%!%%!%%%%%?%%?%%%%%?!%?!!!%!%!!%!%!%%??!!%%%!?!%!!%%%!%%!!%%!%!%%!%%!?%%%!?!?!%%!!!%?!?%%!%%%??!%!!!???%!??%%!%?!%%%?%?!%%???%!%!%?%??%%%?!%%!%!%%%!??%%!!%?%%%%%%%?%%%!%%%!%!!!!!?!?%%!!%!!%%%%%?%?%%%%%%!!!%%%%!%%??!!%!!%?%!!%%!%!!??%%%?%%?%!!!%!%!!!%%?%!%%%%!%!%%!%%%%%%!%!%%!%%%%!%%%%!?!!%%!%?%%!%%!!%!!%!!!??%%!?%????!%!!%%!%?!%?!%%%%%%%!%%%%?!!%%%%%?%%!!!!!%%!!!!%%%%!!!%%%?%!%%!?%%%%?!?!!%!%%%%?%%%!!%!!!%%%!!!!!%!!%!?%%%%%%%%!?!%%????!%%%%?%%!?!?!?%%%%?%!%?%%%?!%%%%%%%%%%!!%%!?%%?%%?%%%%%!!%%?%?%?%!!%%!!?%%!?!%!%%?%??!?%%!%!%!%%!!?%!%%?!!!%?%!!!%!%?!!%!%%%!%!%!?!!!!%?%%%%%!?!??!%?!%%%!%!%!!%%?%?%%??%??!%%%!!???%%%%%!%%!?!%%%?%!%?%!?%!%%!!?%!%%?!!?%!!%%!%%!%!%%!%%!%!?!%?!?!?%!%!?%!%!!%!%!%!?!!!%%!%%%%%%!!!%!%!!!%%?!%%%%%!%!%!!%%!!?%!%?%%!%%%!%!?!!%?!%%%!!!%?!%!!!%%%?%!%!%%%?%%%%%%%%!%%!!!%!?%%!%!%%!%%!!%!!%%%!%%!!%!%%?%!!?%?!?%%%?%?%%%!%%!!!!%%!%!%!!!!%!%%!?%!%%%%?%!?!!!??!%%!%!!%%!%%%%%%%%%%!!%%%%%%%!!!%?%?!?%%!%%!!!!!?!%!!!!%!?%!!?%%?!%!?%!!%!%%%%!%?%!!?!!?%%?%!!%!!!!!!!%???%!!!%%%%%%!%!%!%!%!%!%!?!%?!?%!%!!!%?!?!!%%!%!%%%%%!%%%!?%%%%?%%?%%%!?%%%%!!%!%?!?!!%%?????!!%??%%!%!?!?%%?!%%?%!%%!%%!!%%%?!!%%%%?%!%%?%%%%%%%!!!%%%?%%%!!%!%!!!%!%%!%?!%%?%!%%!%%%!%%%!!!%%?%!%%!%!%%!!!?!!%%%%%%%%%%!%!!%%%%%%%%%%!%?!%%!%%%!?!?%%%!%%%%?%%!%?%!!!?%!%%%%?!%?%!%!?!!%!%%%%%%!%%%?%!!?%%!%?!?!??%%%!!%%%!%%??!%?%%!!%?%!%!!!%!??!?%%!!?%%%%?%!??%%!%%%!?%%!?!%%%%!%!%%%?%?%!%!%%%!%?%!!?%%!%%!%%?%%%%%%?!%%?%?%%!!?!!!%%!??%?%!?!!!%?%!%!%%%%%%%%%?%!??%!!?%%%??!!?%?%%%%%!%%%%?!?%!?%%!!%%!%???%!??%%!%!%%?%%!%%%??%%?%%%%?!%!!%%%%%%!%%%!!!!!%%?%!%%!!%%%%!%!%!!%!!!?!%?%%%!!%???!%?!%%!?!%%?%%%!%%%!%?%!!%%%%!%%!%%%%%%!%?%?!%!!?%!!%%%!!??%%%?%%!%?!!%!%%%!?%%%?!!%!%!!%%%%%!%%!!%%!%!?%%%%!!%?!%!!%%?!?%!%!?%?%%%%!!!%!%%?%%%%!%%!!%%!???!!!%%!%!?%%%%!?%%?!%!%%!!?!?%%?%!!%%%%%%!!%%!%%%%!%??!%%%%!%?!!%%%?%!%!?%%?%!%!!?%%!%%!!%%!?!!?%%%%%%!%%%%%?!!?%!%??%!!%!%!%!%%%?%?%%%%%!?!?%!!%%%%%!%?%%%%!%%%%%%%%%%!%%%%?!?%??%%!?%%%!!!!?%%%!%!%%?!??%!%%%%%%!?%!!!!!!%!%!%%!!?%!%%?%%!%%%%%%!?%%??%!!%?%%!?!%?%!!!!!!?!!!?????%%?%!%!%%!%?!!?%%%%%?!!!%!%%%?%???!?%%!%?%?%?%%!?!!?%?%!!%%!?%%%!%%!?%%?!!!%!%%%%%?%%%%!!!?%!!!!?%%%%%?!!%!%!%?%?%%?%%%%!!!!%%%?%!!!%!!%%%!%%%%%%?!%%!%!!%!!!?%?!!!%%%%%%?%%!?%%!!%%?%???!!?%!%%%?%!!??%%!!!!%%!!!%!%!%!%!%!%%%!%%!!%!!!??!!%%!!%%!!%%!%?!!!%%!%!!!!%%!!!%!!?%%%%??!!%%%%%%!%!?%!!!???!%%%!%!!!%!%!%?!!!%!!??%%!!?!%%!!!%%%??!!!%?!?%!!%%%!%!%%%%!!%%?%!%?!%%!!?!?!%??%?!%!%%%!?%!!%%%?!?%??%%%%!%!!%!%%!??!%%!%%%%%%%!?!!%%%%%%%%%%%%%!%!?%%%%!%!???%%%?%?%?%!!!%%%%%%%%%!%%!%%%%%%?!%%!!%!?%%%%!%%%!!!%%!%?!%%%!!?!!%%%??%%?%!%%??!%?!%?%!?%%??!%%?!?%%!%!%!!!!!%%!!?%!%%!!?!?!%!%%!%%%%%?!!%%!?%!%%%%!?!!%%!%%?%!%!!!%!%?%%!%%%%!!%%?%!%!%!%%!!!%?%!?%%%!%%!!!%?%!!!%%%%!%%%!!!?!!!%!!%?%%!%%?%%?!%??%?%%%%%!!!%?!%%!!?%!?!!!%%%!%%!%%%???!%%!%?%%%?%??%??!!!!?%!%!!%%!%%!?!%!!?%%%!%%!!!%%%%%%%%%?%!!%%!%%%??%!!!!%!%%!!%%?%%!!??!%!?!!%%!!%!%%!!%%%!!!%!%!%!!%%?%?%%%!?%!!?%?!%?%%%!!%%!!%?%!%%!?!!%%!%%%!!%!!%!?!%%?%%!!!!%%?%!!%%%??!%%!!%%%?%%!!?!%%?!%%!?%!!?%%!!!%%%??!%%%%?%?%%%!%%%!%!!!%%%%!%%?%!?!%!!?%?%%!%%%%?%?!%!%%!%%!%%%%%%%%?%!?%!!!%%%??!%!??%!!!??!%%%%%%%!%%!!!?%%%%%!%?%!%?%%?!%??%?%%%%?%%%!!%%%??%!%%!!%!?!!%%%!%%?!%!?!!%!%?%?!!!%!%!?!?%!?!!%%%??%%%%%!?!%%!%%%%?%%%!!%!%%%?%%!!?%!%!!%%%!!%%?!!!?!%?%%%!!!!!%%%!!%%?!%?!!!%!!?%%%%?!!?!!%%%!!%%!!!%?!???!%%?%%!??%%?%?!!%%!?%?!%%?!!%%?%!%??%%%?!!??%!%!!!%?%%!?!%%%%%%%%!%%!%!%!!%%%%%??%%??!%%!?%%%!%!!%%%%%!%!%!%%%!%%?!!%%!%%?!!%%!!%!!!!!%%?%%%!!%!!?!!%!%%%!!%%%%%!%%%%!?%%%%?!!!!?%%?%!%!!?%%%!???!?%!?%%?%!%%?%!?%%!!!?!%!!%%!%%%%!!%%%?!%!?!!!?%!%!%!?!%!%%%?!%!%%%%%%??!?!?!?!%!%!%!!%?!%%%%%!%?%!%!%!%?%?!?!%!%%!%??%?!?!?%%??!%!%?!!%%%%!??%%%%%!!!?!%%!%?%!%?!!%%%!!?%?!%!?%%?!!%!!!%?%%?%!?!%%?!?!%?%?!%!%%?%%?%!%?%%!%%!!!?!!!!?%???%%!!!???%%%%%?%!!%!%%%!!%!!%%!%!%%?!%%!!%%%!%!%!%%%?%!%%?%!?%!%%%%!%!?%%%%%!%%!!%%!%?%%%!!??!%%!%%%%!!!!%%????!%%??%%%%?%%%%%%!!!%!%!!%??!?%!%!?%!%%!%!%%?!%%%%!!%???!%!!?!%!?%%!%%?%!%%%!%?%!%%!??!%!?!%!%%!%!%!!%?%%!?%???%%%%?%!%!%?!%!?%!%!!!%%!%?%%%!!%!?!!%%%!%%%%%%%%!?%%%!%!%!%%%?%!%%%%!%%?!!?%!%!%!!%%!%%%!??%?%!%%%%%??!%?%?%%!%%!!!%?%%?%!!!%%%%!%!%!%?!%%!%?!%%!?%%!!?!%!%!?!%%%%%!%%!!?%!?!?!??!%%!%?!%?%%%%?%%%!!%?%%!!?%??!%?%%%!%!%%%!%?%%?!%!?!!%%!!%%%!?!%?%!%?%?%%?!%?!%!!!%!%%%?%%!???%!!?%%%%%%!!%%!!?!%%!%!%!!?!!%%!%%%?!%%!%%!%%!%%!%!?%!%!!%%%%%%!%%%!%%%%%%%%%%?%%!!%%%!!!!?!%%%!!!%!%!%%!!!!%!%?!%!%!!%!%?%%?!%%!%!%%%!?%!!!?%%?!!%%%%%%%%%?!%%%%%!!!%?!%%%%%%!!%!?!?%?!?!%%%!%%%??!%%%%!!?!?!%%!%!%!%?%%!%%%?!!!%%!?%!!!?!?%%%%?%%?!%%%!%!!!!%!!!%%%?%%!!%%!?!%%%%!%?!!%!!%%%%!!?%!?%%?%%%%%!!%%!%%!%%%%!!?!?%%%%%%??!%%%?%!%%!%%!!?%%%%??!%%??!%%!?!%%?!!%!!%%?!%%!?!?!?!%!%!%!?!!?!!?%%%!?%%%%%!%%%!!?!%!!%!!%!!%?%%?%?%!?%?!%%%%%?%?!%??%?!%!%%?!!!%!%%!%?%!%!%?%%!%%!%!!%!%!!??%%!!%%?%%!!!%!%!?!?%!?!%!%%!!%!!!!%%%%??%?!%%?%%!!!!%%!?%%!!!%!!%?%%%?!%%!%%!%%!!%!%?!?!%?%%!%%?!%%??!%%!%%%!%?%%?!!%!%%!!%!%%%%!!!!!%?!!%%%?%%!%%%%?!?!%?%%%!%?!%!!%%!%%%?!!%%%%?%!%%?!%%%%?%%%!?!!%%!!%%!%!!!!%%%!%%!??%%?%%!?%%%%!!?%%%%%%%!%%!!%!%!!%%%%?%%!%?%?%!!!!?%%!%%!!!%%!%%%%!?!!!!!%??%?!!!!?!%!?%%%?%?%%!!!?%!%%!%?!?!!%%%!?!!!?%%?!!%!%?%%!!!?!!!!%!!%??%!!!!?%%!%?!%!?%?!!??%!%!!%%!!%?%!%%!?!%%!%!%%%%%%!%!!%!!%?%!!?%%?!%%?!%?%%!%!%%%%??!!%%!%?%?!!%!%!%%%!!%%!%?%%!!!!%!?%?!?%%%!?!%%!%!%%%!!!%!%?%??%%?%?!!!%??!%!%??!%?%%!?%?%!%%!!?!???%%%!!%%%%!%%!!%%!!???%%%%!%!%%!!?%?%?%!??%%%%!%%?!%%%%%%%%%%%!%!!!?!%%!??!!!%!%%%!!!!!?%?!!!!%%!!%!!%%%%%!%%!%%!!?%!?!%!%!??!!!%%%!%?%%%??%%!%?!?%!%!?%??%%!!?%!?!%?!%?%%!%%!?!!%?!%%%%??%??!??!!!!%%%%%%?%?!%%?!%%!?!%%!?%!%!%!%?%!%%!!%%!%!!%%%%?!%!%%%%%!%!%%!%!%%??%%%%!%%%!%!%!!?%?%??%?%!%!%!%!%%%!?%!!%!%!!!!%%%!%!!%%%%%%%%?!%%%?%?!!?!%%%??%!%%!!%%?%!%%!!!%!!%%!!%!!%%!%!?!?%%%?%%%!!%%%!!!!%!!?%%%%!%%%%?%!%%%!%%!!!?!%%!%?%!?%!!%?%%%%%!%%%%?%%%?%?!%%!?!%%?%!%%!%%!?%%%!%%!%!%!?%%%?%!!%!!%%!%!!!%!%!%?!%%??!%?!%%!?%!?%%%!%?!%%%%??!%?!%!%%!%%!%!%%!?!?%!?%%!%%!!!%%%%%?!!%?%!%?%!%!%??%!%!%!%!?!!!!%%?%%?%%?%%%%%%!%%?!?%!!%!%!!??%!!%%!%!%%%%!!%!!!%?!??!%!!%%%?%%!%%%%?%?!%!!!!?!%?!%%%%%%%%%%%%%%??%?!!%??%%?%%%%%%!?!%?%%!%%!!%!%!%!%!!%!!%!%!!%%%?%%?!!!?!?%%!!?%!!%!%?!!?%!!%?%%?%!%!%?%%%?%%!%?%!!!?!%%!%%%!!???%%%?%%%!!%%%%%%!!!!%!!%!%%?%%!%%!%??%%%??%%%?%!!!!%!!%!%!!!%%?!%%%%!%%!%%%%%!?!?!!%?%%%%%%??%%!!%?!?%!%?%!?%%%%%!?%!%?%%!%%%%%%!!!!!!?%!?%!!!%!?%%%?!?!%?%!!%%!%%!!%?!%!%!%!!!!%!%!%!%!%!%!%%!!!!%%%%?%?!%!!%!?!!!!?%??%!!%%??%%!!!!?!!%??!%%!?%!?!!!%!?!!!%!?!???!%!%!%%%%%%%??!?!%%%?%?%!%%%%%%%%%%%?!!!%?%!!%%%!%%!!?%!!!!%?!%%%%%%!!!%%!%?%!!???%%%%%%?!%%%%%%!!%%%%%%%!!?%%%!%%!%!%??!!!%??%!?%%%!!%%?%%!%%%%%??%%%%%!!%%%?!!%!!%%!%%%?%!!!?%!%?%%!%%%!!%%%?!!%!%!%!??!!%?!?%%%!!!%%!%!!?%%%!!?%%!!!!%!%!%?!%?%%%!?%%!!!?%%!!%!?%%%!!%!!?%!%!!%?%!?%?%!??!??%%!?!!%!!!?%!%%!%%%!!%%!!%?!%?%%!!%%%!!%!%!!%?!%!?!!?%%%!!%!%%!%%?!%%!%?%%!?!!%%?!!?%!!%!%!?%!%%!%?%!%%!!?%?!%%%!!%!!%%!%!!?!?%!!?%!????%%%!!%!%!%!%%??!?!!%!%!%?%%!%%%!%%!!?%%%%?!%%%?%!%?%%%%%%!!%%!!?!%%!%?%!%?%!!%%!%!%%!%%!%%!!???%!?!%%%%%%!!%%!?%%!!%%%%!%!%?%?%!%%%!%!%%???!%!!%%!%%!%!!%!%?!!%??!%!%%!?!%!!!%%%?!?%!?%%!?%%?!%!%?!!!!?!!%!%%!%%!%!%!!%%!!!%?%!!!?!%%%%!%%!%%!?!!!?%!%%%!!%!%%!%?%%%!%!!!!!!%%%%%%!?!%!%%%!!?!!%%%%?!?%%%?%?%%?!%!!!%%%?%?!%%!?!!!%%!?%%!%!?%?!%?%?%%%!%%?!%%%!%?%%%%%%%?%!!?%%%%!%%!!!?!%?%!%?!%!%%!%%!%%%%!?%!!%?%%%%%!!!%%%!%!??%%%%?!%!!%??!%!!%!?!?%%%%!%?%%!!%%%!%!!?%%%%%??%!%!!!????!!!!!!!?!%!%!!%%?%%%%%%?!?%!%!%?%!%!!%?!?%%%!%!%%%%?!!%%%%%?!!!%%!%%?!%%!!%%%!%%?%%?!!%%!!!!%!%%!?!%!!?%?%!!%??%%%%%%%!%!%!!%!%!%?%!%!%??!?%%%%%!%?%!%%!%!%?!!!!%!!!!?!!%!%%%%?%?!%??%?%%%%%%!%?%!!%%!%%!%%%!!%%?!%?%%%!%!%%%%%!%!%%%%%%?%%%!%%?!%!%?%!%%!!?%?!!!!?!%%%!?%%!%%%!%%%%?%%%%%??!!!%%!!!!%%%%!!?!%%?%%!?%!%!%!%!%%!!?%%%!!!!!%%??!%%?%%%?!?%?!%!%%??!%%%%%!?%!!%?!?%!!%!%%%%%!%%%%%?!%%%!!%!!%?!?%%?%?!!%?!?%!%%%%%%!%!%!%%?!!%??%?%%!!!%?%??%%!??%%!%%%?%%!%%!%%%%%!%?%%!%?%%!!%?!%!!%!!%?%%%?!%!%%%%%!%%!%?%%%%?%%!!!%!!%?%?%!!%!%%%%?%!%!!!%%?%%!?%%!%??!!%%!!%?!!!!%%%%?!?%%?%%!%%%!%!%?!%!?!%%%%!%!!!!%!%!%?%?%!%??%?%%!?%%!?!!%!%!%%%%!%%%%!%%%!!%!?!!?%%!!%%!%%%%?%%?!%?%?!%!!%?!%?%?%%%!%!%!?%%%%%%%!!%%???%%!!?%!!!%%!%%%%!%?!!!!%!!%%?%!!%%%!%!!!!%%!%!%%!!?%!!%?%!?%%?%%%??%?%%%%!%%%!%%!%%!%?%%!%%%!!%!??!!!%%!%!??%%!%?!%%!%!!%!!%%%!?!!%!??%%?%%%!%!%%%%%%???!%%%%%?%%%%%!%%!!!%%!!%!%%!!%?!!!!%%%!%!%%%%!%%%%%%?%%!!%?!%?!%!%%?!!%%?!%!!??%!%!%?%%%!%?!?%!!%%!!!?%!?!%%?%?!%!!%%!%!%!%%?!%!!!%%!%%!!!!!%!%%!%%!%%!!!%%%%?!?!%!%%!!%%%%!%!!!%%!%%?!%!%!?!!%%!%%!!!!!%%%??%%!%!%%%%!!!?!%%%!%%%!%?!!!%!%!%%?%%%%!%%%%%%!?%%%!%%!%%%%%!?!!!!%%??!?%?!%!!!%%%!%%?%!?%?!%!!%!%?%?%!!???!%!!!%%%!%!%!!%%!!?%?!!?%!?!?%%!%!!%!%%%!?%%!%%!!%!%%%%%!%%?%%!!!!%!!!??%!?!%!%%%!%%?%%!%%!!%%%%%!?%%%?!%!!%%!!%!!%!%%%!%!%?%%!%%%%%?!?!%!%%%!%%%%%??!!%%%%!%%%%!%!%?!??%%%%?!!%%?%%!%?%!?!?%!?%%?!?%!?!!%!%%!?!%%!!!%!!?!%%%!!??!%!!%%%!!%!?%%?!?%!%?%!%?%!%!!%!%!%%!%%!%?!%!%!!%!!!!%%!%!?%%%!%%!%!!%?%%%%%%!!%!%%?!%!!%!%%!%%%!!!%!%!%%?%!%!%%%!?%?!%%??%!?%?!%?%!!%!%!!%%%?%%?%%%!%!%%%%%!%%%%%%!!%?%!%%%!%%!?!%%%%%%%%!%?!%!!%!?%%%!%?!!!???!%%%%!!%%!%%%?%!!%??%%?!??!?%!%?!!%??%%!!%!!%!??!%!!!%%%!???%?%%?%%!!??!??!!!%%%%%!?!%!%%!%!!%%%!?%!%!%?%?%!!!?%?!!%%!!%!%!%!??!%%%!?%%?!!!!!%%?!??%!!!!!!!%%%?%%%%%%%!%%%%%!!%%?%!%!!%!!%!%%%%!?!?!%!%??!!%%%%!!!%!%!!!%%%%%%%!%%!!%%!%?!%%!!!%%!!%??%?%%%%%!!??!%%%%%%?%%%%%%?%?%%!!%?%%%?%?!!??%%!%%%!?%%!!%!!%?!!%!%%%?%!?%%??!?%%?%!%!%%%%%?!%!%?%%?!?%%!?!%%!!?!!%%%%!!!?%?%?%!%?%!%!%%!%!?!%?!!!!??%%%?%!!!?!??%!%?%%%%!?!!!!%%%%%%%!%!%?%%%?%%!%?!%%!!?%%!!%%%%!%%!?!!?!%%!%%%%%?%%?%%!%%!%%?%%!!?%!!!%!%%?!%!%!%%!??%%%!!!?!%%?%%%!%%%%!%??%%!%!!%?%%!!%!?!%!%?!%!!%!?!%!%!%%%!!?!%%%?%!!%%?!%!%?!!%!!%?%%%%%%!?%%!?%%%%%!?!!?!?%!!%!%!!!!???!%%%?%%%??%%%?!%!?!!%??!!!%%%%!%??!%%%!!%?%%%!!!!!!%%?%!?%!!!%?!%%?%?%??%%%%%!!!%?!?%%!%??%?!!%%%%!%!!%!%?%??%!%??%!%!%?!!!!%!%!%%?%%??!%!!%%%%%%!%!%!?%!!%!!%%?%%%!%!?!%?%%!%%?%!!!!!!!!%%%%%%%%%%%?%!%%!%%??%%%!%?%%?%?%%%%!!%%%%%!%!%??!!?!!%%!?!%%!??%!%?%%%%!%!%%%%?%%?%%!!?!%!%%%%!%%%!%?%?!%!?!??%%!!%%%!%%!!!%?!%?!!?%?%!%%%%%!??%?!%%!?!%%!%%!?!%%%%%!!?!%?%%!%%%!?!!?%!!!!?%!%%%!?%!?%!!?%!%!!?!%%%%!%%?!!!%%?%%!?%%%%%!%%%!%?%%!%%%!?%!!!!%%!!?%!%%!%%%%%%!%%%%!%%?%%?%%%%!!?%!!%%?%?%?!?%%?%?!%?%!!%!%%!%!%!%%%%%%!%!?!%!%!%%%!!%!%%%%%%!%?!%%%!!%!!!%?!!!!!!%?%%%%!%%%%%?!!!%?%%%!%%??%%%!!%%!%!!%!%!%?%!%!%%!?%!%!%%%!%%%%!%?!%%!!?!%%%?%%!%%?!%?%%%%%%%%!?!%?%%!%!!%??%!?%!%?%!%!%!!%?%%%?%!%%?%%?%?%??%%?!!%%%%%!%?%%%?%??!%!!!%!%%%?%!!!%%%%!!%?%!%!%%%!???%%%%%%??%%!!%%?!%!!%%!%!?%!%?%!%%!!?%!%!?%%!!!%!!%%%%!?%?%?%!%%%!%!%%%?%!!%%%%%!!%%%%!??!%%%%%%%?!?!%%!!%%%!%!?%!%!?!%?%?!!!%%%%!?!%%%!%!!?%!%%!%!!%!%%!!%!?%!!?%?%%?%!%%?%%%?!?!!??%!%?%%?!??!%%%?%?!%%!%!!%!%!!!%!??!%??%%%!%%%%%%%%?%!!%!?!%%!?%%!%%%?!%?%%%%%?%?!!!!%%?%%%%%%%!!!%%!%%!??!%%!%%!%%?%?!%%?%%%%!%%%%%%?%%%%%!!%!%%?%%%!!??%!%!!%?!%!?!!%!%?!%!%!%%!?!?!%!%%!%!%?%%%!%!!%!!%%!!%!%%%!%%%!?%%%%%!!%!%!%!!?%!%%!%%!%!%%%!??%%%%?!%!!!!%%%?%%%%%%%%!%?!!%%!!?!%%%%!%%?%!!%%!%?%!!?!!%!!?%!!!%!!!%!%!%!%%?%%!%%%!!%%%%%%%?!%?%%!!!!!%%!%%!%?%%%?%%!?%%?!!?%%!%%?%%!?%%!%?!%!%%??!%!%%%?!!%!!?!%??%%?!%!%!!%%%??!!!%!!??%?!%%!?!%!%%!!?!?%%%?!%?%?%%%%%%!?%%!%%%!!%?!%%%!!%%?%%!!?%%!!?!%!!%%%?%!?%!!%?%%??!%%!!?%%%?%??!!%%%%%%%%%%!!!%!%%%%!%!!%?%%?%?%%!!%%!%%%!%?%%?%?!!?!%%%?%?%%?%?!!%%%!!!%%%!%?!?%%%!%?%%??!%%!!%%??%!?!%%?%%!?!!%!!?%%%?%!%?%%%%%!?!!!%!?%%?%%!%%%%%%%?%%!%!!%!!?!%%!?%%!?%%!%!%%!!!%%!%!%!??!%!%?!%%?!%!!%%%%%%%!%%%?!?%%%%?!!?!?%!%%%?!?!%?!?%!!!!!%%!%%!!!??%!!%%!?%%?%?!%?%%%!?%??!!?%%%%?!%%!%!%!!!?%?%??%!%%%?!?%%%%??%%!?%%?%%!%%%!!%%!%!%%%?%%%%!%?%!!!%!%??%%%%%?%!%%???!!???%%%!?!!!%%!!%%%%!%!!%%?%%%??%?%!%!!%%%%%%!!!%%%%!!!%!!!!!%%?!%!?%%%%?%%%!%%!!!%%?!%!%!!!%%%?!!%%!%%%%%!%!%?%%%??%?%!!%%!!%!%%!%!!%%%%%!!!?%!!!?!%!!%%%%%%!%!!!%%%%?!%%%?%!?%!!%%%%%?!?!%%%!!!!!!?%!%%!!??!!!%%%%%%!!?%!?!?!%!%!%!?%%!!!%!%?%!!?%??!?!??!!!!%%!!?%%%%?!!%!%!!%%?!%%!!?%?!%?!%!%%!%%%?%???%%!?%!%?%!%%!%%!%!?%%%%!!%%?%!!%?!%!%!%!%?%%!%?!%%!%!!?%!?%%%%%!%%!%!%?%%!???!!!!??%?!!!%!%?%?%?!!%??%%!%%!%%!!%%??%%%!!%%%!%!?????%%%%%%!%?%!%!?!!%!%!!%?%%%!%?%%?%?%%%!?%%?%!%%!!??!%?!!!%%?%?!%%%%!??%!%%?%!%?!?!!!%!?%%%%!!!?!!?!????%%!%!??!%%!!%%%%%!?%!??%??!!!%!%!?%?!!%%%%?%%!%%!%%%!%%!%%?!?%!!%%!!!!!%!!%%%?%!?%?%!%?%??!%!%!%??%?!%!!?%!%%%%!!%!%?%!%?!%%!%?%?%%%!%%!?!?%!%?%?%!!%%%%?!!%?%%%!%%!!!%!!?%%%!%???%%?%%%%%!%!%%%%!%%%!%%%!%!!%%?!%?%!%%!!?!!!?%%!!!!!?!!%!%!%%!!!?%!!!!%!%?%!!!%%?%!%%%%!?%!!%%%!%!?%%!!%!!%%!%%%%%!?%%!!%%%%!!?%%%%!%!%%?%!%%%??!%??%%%%%?%!!?!%!%!%%!%!!%!%!!!%!%!%?%!%%!!%%%%!?!%!%%%!?!%%!%%%%%?%?%!!%?%!%!!!%!%%?!!!??!%!%?%%!%!!%!!?%?%%??!%!%%%%!!%!??%?%%!!?%!%%!%?%%%!%%?%!!%%!!!%!%!%!%%!%!%%!%%%!%!!?!!?!%!!%!!%!?%?!%!!!!%!!?%!??%%%!%%%%%!%!!?%%!%!!%!!?%??%??!!!?%?%%!%%%%%!%?!!%?%%!%?%!!%!%!!?%%???%%!!?%%%%!%%!!%!!%!??%%?!!??!%%%%%?%%%%?%%%%%%!!%!%%%%%%%?!?%%!?!%%?%!%!%%%%%!%%?%!!%!?!%%!!%%%%%!!!?!!??!?%%?%%%%!%!!!!%!%%!?%%%!?%!%!%%%!?%%%%!%?!?%%!!!?!!!?!!%%%?%!%%!?%%!%%?%%%!?%!!%%!%%%%%!%%?%%%%!!%%!%!%!%?%!%!!!?%!!%%!%%?!%%%!%?!?%!%%%%!%!%%!!!%!%%%!%%!%%%%!!!%!??!!%%%%%!%%%%%!?%?%!!?%!%%%!!%?%%%??!%%%???!%%%?%%%?%%%%!!%%%%!%%%?!%!!?%%!%!!%!!!!%?!!!????!!!%%%%!!%%!%%%%!!?%%%!%%!!?!%?!!%!%%%%%%%%%%%!%?%%?%??!!!%%%?!!%!%%!%!%%%%%%%%!!%%%!!%?%!%??%!%%%!%%%%!!%%!?%%%%?!%%%%%%%%%!%?%??!%?%%?%%!%%?%!%%!%?%%%!%??!%???!%?%!!%?%!%!%%!?!%???%%%%!%!%?%!%!?!?!%%%%%?!?%!%%%?%!!%!%%!!?!%%%?!%%?!%!%%??%!%!%%!%%?%?%%%!!%!!%%?!!%?%%%%!!%%%%?!?!??%%%!!?!%!!!%%!!%%%%?%?%?%!%%!%??%?!!?%!%%!!%%!?%%!%!!%!%%???!%!%%%%%%%!?%??%%%%?!!!%%%%%%%!!!%?%%!??!!%!!?!?!?%%!%%?!??%%%?%%%%%%!%%%%?%%!!%%%%%%%!??%!!!??%%%!???%%!%??%!!%??!!%!!!?!%!%!%%!!!%%%%?!!?!%!!?%%!!%?%%!!!!?!!%%%%%!!!!%%%!%!?!?!%!!!%%!!%%!?!%%!%%%%%!%%%%!%%!!%%!%!%%!?!!!!%%%%?%%??%?!%?%%?%!%???!%%?%?%!%!?%%!?%%?%??!%%?%?!!%?%?%%%?!??%%??%?!!%%%!%!?%%!!%!?!%?%%%%!%%?!%%%%!%!?%!?%!%%%!%%%?!!!?!%?%!%%%!%%%%%!%%%!%!!%!!?!?%%%%!%%?%??%!?%%?%%?!%%!?%!%?%!%%%?%%?%?%%%%!%???%?!!!%%%%%!%!!%%%!?!%!??%!%?%%%!!%%%???!%%%!?!%!???%%?!%?!%%%%!!!??%?%?!!!!%!?!?!%?%?%!%?%%!?!!%!?!!%?%!%%!?!!?%%!%?%%!%%%%%%%%!!!?%!!%%%!?!%%!%%%!%%!!%?%!?!!!%%%!?%%%?!%%%!%!!?%!%?%%%%!?!!%!?!%!%!%?!!!?%%!%%!!%??%!%!%%!!!?!%%??!%!%%!%%??!??%%%%?%%%%%!%!!!%??!%%%%%!!!!?%!%?!?%!%!!!!?%!!%?%!%%%%%%%%!!%!?%?%%%%%?!%!!!!%%%!!!?%!%!%?%%!%%%?%%!!%?%!%%%%%%!!?!??%!!%%%?%%%%%%%%%!%?%!!%!%%?!%%%%!!%!%?%%%!%??%%%!?%!%%?%%%?%!%?%%%?%!?%%!!%!%%%%!%%!!%?!%!!%%!!%!%%!%!!%!!!%%%%%!?!!!!!%%%?%?%?!%!!?%!%%!%%%?%?!%%?!%%?%!%!?%!!%%!%!!%!%!%%!!%%!!!%!?!!%!??%!%%?!%?%!?%!!?%%%%!!?!%%!%!%%%%?!!%!%%%?%%!%%%!%%?%?!%%%!!!!%?!!%%?%?!?!!!!!%%%%!%??!%?%!%%%%%%%%%%?!%!!%%!?!!!!!%!%!!%%!!?%?%??%%%%%!%%%%%??%!%%!%%!%%%%!!%?!!!%!?%%%!%%?%!!!?%!!%%!%!%!!!%??!%!%!?%%!%%%%%!%%!%!!?%!!!%??%!%!?%!!%!!!?%%!!!?!!?%!?%!??%!!%?!?%!%%%!%%%%!!!%!%!%!%?%!!%%!?%%%??!!???%!%%%%!!%%%%!%?%!%!%!?%%?%%!%%!?%%!????!?%%%%%%!!%%??!%%%?!%?!!%!%%?!%%%%!%%!%?%?%%!!!!!%%?%%?%!%%!!!!?%?!%%?%??%!%!%%%!%!!%!%%%%!!!%!%%%%?!!!%%?!!%%%%%%%!!!%?%!%%%%!%%!?!!!%%%%?%!%?%%!!!?!%!%!%?!%%!!%%?%%!!%!!%!%%%%!%%!!%!%%!!!%!%?!!!!%%%%%!!?%%%?%!%!!!%!?%!?!%%!!!%!%?%%!%!!%?%%%%!?!%%!??!!!!%%?%!%%!!!?%%!%!!%!??!%%!!?%%%!%%!!??!%%!?%!!%%%%%%!%%?%%?!?%%%!%!%%%?%??!%%!?!%?!%%%!%%!%%?!!!!!?%%??%!!!%?%%%%?!?%%!%?%%!!?%?%%%?!!????!!%!%%%%?%!%?%!!%!????%%!%?%%%%??%!!!%!!%!!!?!!!%%?!%!?%?%?%!!!%%%??!?%!%%?!%%%%!%%%%!!%!?%%%%%%%%%!!???%?%%%!!?!?%%?!%!!%!!%%%%?%?!!!!!%%%%!!!!!!%%!%!%%?%%%%%%!!?!%!?!?%!!!!?!!!??!!%%?%%%%!%%!%?!!?!????%%!%!%%!%%%!?!%!%%%%!%!%!%%!%!%?!!%%%%!?!%%%!%!%!?%%!?%?%%%%%%?%%??%%%%!!!!%!?%%%%%?%%%!%%?%!%?!!!%!%!?!!%%%!!%?!%?%%%%%%!%!%!%%%%%%!!!!%%!%!???%!!%%!?!!%%%%%?%!%!%%%!%!?%%?%%%!%%!?%%??%??%%%!%?%!!!%!%%%%?%?%%!%!%!%?%%%%%??!%?!%!%!!??!!%!%!?%%!%%!!%!!%!%%%!?!%%??%!?!!%?!%%?%!!!%%!!!%%!%%!%%%!???%!%?%!%!%?%!%!!!%%%!%!%%?%!%%!%%%%%!!!%%%%%!?%!%?%!%!%%!%%%?%%?!%%!%%?%!%!%!!?%!?!%%?%%%!%%%%%%%!%%!!!%!?%%%%!%%!?%%%%!%%%%%%%??!!?!%!?!!%%!%%!?!%!%!!!%%%?%%%!?%?%%%??!!!!!%%!!%!%%?%%!!%!!%!%%!%%%?%!!%?%%%%%?%%!??%%%%%%?!%%%%%!%!%%!?%!%???%%?%%%%!%!%!?%!!%%!!!%%?!!%%!??!%!!?%%!%%%?!%%%!%?%!%!%!??!%?%!??%!!!%%%!!%%!%!!?%%%!%%%%%%%?!%?%?%!%%!?%!!%%?%%%!%!%!%%??%!!%%??%%%%%?%%!%%%%%%?%%%!!!?!%!%!!%%?%!%%%%%!%%%%%%!!!?%%%!%%??%!??%%?!???%!%!%%?!%!?!!?%%%!%!%%%!%%%?%!%%?!%!!%!%?%%%?!%?%%%%%!!%!%!%!%!%?%%!!!!%%%%!%%%!!!?%%%%%!!%!!?%%!?%?!!!%%%??%%?%?%%??%!%%%!%?%%%%!%??%?!%?%!!%%!?%%!!!%!!%%?%??%!%%%!%%?%%%%!!%%!???!!%%%%%!%!?!??!%%?%%!!?%!!%%!!!!!%?%%!%!!!?%%%%%%!!%!!%?%!%!%%%%%!?!%?!%!?%!!!!%%%%!!?%%!!%%!%%!!?%?!!!%!!%%?%%%!%%%%!%!%!%!%?%!%!%%!?!!!%?!!!%!!%!!%!%%%%?!!!%%!!?%%%%!!%?%!!%%%?%!?%!!%?!%!!%%!!!%%%%!??!%%%!%%%%!%!%!!%!%!!%?%!?%!%?%?!!%?%%??%%%%!%%!?!!%!?%%?%%%%%!!%%!%%!?%?!!!?!!%?%??%!%?%%%!!%%%%!%%??%%%!!!%!%%%!%%??!!!%%?!%%%!!?%!?!%?!?!%!%!%%%!%!%??%!!%%?%!?%%!?!??%??!%%!??!!!%%%%%%!?!%%?!!%%!!!!!%?%!?%?!%?%%!%??%%?%!%!?%%%?!!?%%%!?!!%!%!!%%%?!%%%?!!%?!!????%%%%%%%%?!!!?%%?%%%%!%?%%%?%!!!%!?%%!!%??!?!%!%!???!%%?%%%!%%!%!%%%!%!!%!!%?!%!%?!%%!%!!%?%!?%%%%%%%%!?%%%%%%!%!%%%%?!%?%%%%%%%%%!%%%%!!%!%?%?%!!?%%%!!%!!%!%%!!%!?!%%%!%!?%%%%??!!%!%!!!?!%!%!%%%!%%%!!%!%%?%?%%???!!!!%%?%????%%%%!!%%%%%!?%%!!!!%!%!???%?%!!%%!?!!!%!%%!%!!%%!%!!%%!%!!!%%!%!!%%%!?!!!%?!!!!?%%%!?%?%%%%!!!%?!%%%%!%%%!%%!%!!%%!%?%%!%%%%%%?!!!?%!%!!!!!!!?%%!?%??!%!%?%?!%?%%?!%%!!!?%!%%%!!!!%%?%%!!%%?%%!!!%!%%%!!!!!%!!!%!%%%?!!?%!%!!!!%?!%%!%?%%%%?%%%%%!!?!%!%?%!%%%!%%?!!?%%%?%%%!%!%!!%%?!?%!%%%!%%%!!?%%%!!%%!!%!%%!?%!%%?%?%!%%?%%%%%!%%%%%?!%%%%!%%%%!!!%!!%?!%?%?!!!?%%?%%%%%%!%%!!%!%%!%%%%%%!?%!!%!?%!%%%%!%%%!!%?%%%%%!!!!!?%!!%%!%!%%!%?%!!%%%!!%%!%%??%%!%?!!%%?%%!?!%%%%!?!%%!!?!!!%%%%!?%!%!%!%!?!%!!!!!!%??%??!!%??!%%%!!!%!%!?%?%%%%%?!%%!!%%!%?!%%?!?%?%%%!%%??!%!?%%%%%%%%%%!%%??%?!%!%%!!!!?%%%%%%%!%!%%%%%%!?!%%%%!%?%?%??%!%%%?%%%!%?%%%%%!%!?%!%%?!?%%%?!?%%!?%%%%%!%!!%?%%!%?!!%!!%%%!?!%%?%%%%!?%!%%?!?%!%%!%!!%%?%?%%!%!??%?%!!?%!!!?%%%?!!%%%%!%%%%%!?!%!%%?%%!%??%%%?%?!!%%!%!%!?%%%!%!!%!?%?%!%%!%%!!!%%%%%!!%!%%!!%%!%?%%%!%%!?%%%!!%%!!%??%!%%%%%!%!!%%!!!!%?%?!%?!%?%%?%%!%%!!!%!?%%?!!!%!%?%%%%?%!!%!!%!%!?%!!%?!??%%%?%%%!%!!%%!??!%!%%%?!%%!%%%%!%!%!!%?!?%%!!!%%%!%%!%?%?%%!!!??!??!%%%%%!%!!%?!%!%??%%!%%%%?!!%%%%!%!!%%??%!!%%%%%!!%!!!%%%%??%%%!%%!%?%!!!%%%%!!%%???%!?!!!!!!!%%%%?%?!%!%%%%!?!%%!%%!!%!%?%%!%%%%!??%%%%!%%?%%%%%%!?!?!!%?!%%!%?!?%!%!%%?%%%%!%!%!?%!%!%%!!%%!%%!!%%?!%%%%%%?!!%?%!?!%%!!%%%!%%%%%%!%??%%!%!%%%%%!!!!%%!%%!?%%!%%!%!%%%!?%!??!%?%!%%%!%%%%%!!?%%%%%%%!%%%%!?!%%!%%!!%%!%%%!%!%!%%%%%!!%%!!?!!%!%!!!!!%%%?%%%!%!?%%%%!%%?%!%%!?%!%%?%%%%%!?%%!!%?%%%%%!!%%!!!?!%?%!%%!%?%%!?%%!%?!%%!%%!%%!!%?!%%!%!!%%%?!!%?!!!%%!!?%%%%%%%%%%%%!%?!!%%!?%!!%!!!?!%!?%?%!!?!!%%%?%%%%%%?!%!?!%?%?%!!!!%!%%%??%!?!!%%?%!?%!%%!??%??%??%!!%%!?%!?!?!%?%%!%?!%!%%!%!!%%??!%%!?%?%%%?!%%%%%!!!?!?!!%%!!%%!?!!!%%!%%??!?!??!?%!?!!%%!%?%%%%%!!%?!%!%?%%?%?!%!!!!%%!!%!!!%!%!%!%%??!!%%?%!%!!%%%%!!!%%!?%%%%??%?!!?%?%??!%%%%!%%!?%%!??!!?!%?!!!%!%%!!!!!!!!%!!?%%%?%!%!%!%!!%!!!!!%!%!%!%!!!?%%?%%%!!!%!%%??!%%%?%%%!%%?%%!%!%!%%%%?!!%!?%%!!%%!?!%?%%!%%!!%?%%!!%%!!%!%%!!%%???%?!%?%%!%?!?!!%%?%%!%?%%%%!%?!%%!%!!!!%%%%?!!?%!?!!%%%%!!%!?%%%%%%%?%%?%%%!%!%%%%!%?%?!?!%%??!%%%%?!!%%!!%?!?%%%%!?%!??!!!!!!?!?%???!%%%%!!!%%!%!%?%%!!!!!?%!%!%!%%!?%?%%!%%%?%?%%%%%?%!!%%%!!!?%!?!!%%!!%?%%%!%!?%?%!!%%%!%%?%%!%%!%!%!%!%!%!!!!%?%?!?%?!%?!?!%%??%%%??!!?!%!??%!%!?%?%%%?%%!%%%??%!%!!!!%??%?%%?!!%!%%?%%%!%!!%%?%?!%%!%%?%?%!%%%%?%%%%!%%!!!??%%!%%%%?%%%%!%!!%!%?%?!!%?%?!?%!%!%%!%%!%%%!%%!??!!!%???%%%%%%!!%%%%%%%%%?!?!?%%%%?!%%%%%%%??%!?%%?!!%%?!%%?%!!!%?!!?%!%%%!!%!%%%%%%???%%%?%%?!!!!!%!?%%%%%??%!!?!!%?!!!%!?%%??!%!%!%?%?!%%?!!%%!%%%?%%!%!%%?%%?%!!%%!!??%!?%?!%!%?%%?!%!%%%%%?%%%!?!%%%!!%%%?!?!%%!?%!%%!%%%!?!!?!%%?%%%!%!?%!%?%%?!?%%%%%?!%?%!?%%%%!?%%%%%%?%!?%%%%?!%?%!?!%!!?!%%!%%!???!!!%%!!%!!!!%?!%%!%!!!!%!?!%!%%??!!!!%!%%!%%%%?%%%%??!%%%!?!!%!%!%%!%!!%?!%!!!!%?!?!?!%%?%%!!!%%%%%%!%?!!!%%!?!?%?!%!%??!%%!!?!!!%!!%%%%%?!!%!%%%!%!%!%%%%%%!?%!!!!!!?%%%%!%?!!%?!%!?%?!%!%%%!%!!!%!?%?%!%?%!%%!%%?%!%%%!!?%!!%?!!?%%!?%%!%%%!!%%%%%??%%%!%!!?!!%!%%!!%%!%%%%%!!%!!!!%%?!?%!!!%%%!!%??!?%%%!!?!!%%?!%%%!!!%!?!?!%!?!!!%!?%!%%%%?%%%%???%!!!!%?!?%%!!!%%%!!%??%!?!%!%!%?%!?%%%!%!!%%!%%!%%!!%!!%!!%!!!%%!!%!?%!%!!!!%!%!%!?%!!%!??%!%!%???%?!%?!?!?%?!%%??%!?%!!%?%!%?!!?%%!%!%%!%!%%?%?%!%?!!%!!%?!!%%?%%?!!?%%%?%%!!%!!?%!!%%%%%?%?!!%?%%%%!%%?%%!!%%%%%!!%%%!??%%?!!%%!%!!%!%!!?%!?!%%!!%%!!%!%%?%%!!?%!%%%??!!!?%%!%!?!??!%%%%?%%!%!??%%%%%%%%?!%!?%%!%!%%%!!%%??%!%%!?!!!%?!!!!%%%%!%!!?%%?%%?!?%!%!??%!?!!!??!%!!%?!%!%%%!?!!?%%%%%%%%%!!%!%%%!%%!%%?%%%%!!!?%?!!!%%%%%%?%%%%!!%%??%%!%!%!??%%!!!!%%%!%%!%%!%?%%%!?!%!!?%!%!?!%%?%%??%%?%!%%!%%%?%%%%!%%!!%!?%%%!?%%%?%%!?%?%%!%%???!%!!%!!%?%%%!?%%!!?%?%?%%%%?!!%!!?!%?%%!%!?%%?%%!%%??%?%%%!!%!!?%%%%!%%%!%!!?%!%%%%!%?%%%%%!!%%%%%!!?%%%%?!%%%%%%!%!%%%%%?%%%%!??%%!!%%%!??%!!%?!%!!!??%!??!%!%%?%%?%!?!%?%!%!%%%?%!%%!%!%?%!!%?%??%%%!%%!%%%?%%%!%?%%%%%%%!!!%%!%%!%?%%!%!!!%%!%%%!!!!%!!?%%%!%!%!!%%??%%??!!%%%!%%!!%!%%?%!%%!%%!%!%%?%??%??!%?%%!%?!?%!!!??%%%%%%!!%!?!!%!%!%??%?%%%?%%!!?!%!!%?!%!?%%!?!%!%%%%%!!!%%%!?%%%!!%%!?%!!!!!!?%%%?%?!!!%!?!%!%!!%!%!%%%!?%%?!%!%%!%!!%!!!!%%%!!%%%%!?%%!!?%%!%!%??!?%!%!!%?%%?%%%??%%%!???!%%%%!%!?%%%%!%%!%%%%!%!?!??!!?%!?%!%?%?!%?!%!!?%!!!??%%!%%%!?%%%?%?%%!!??!!?%!???!?!!%%%!%%!?%%!%%!?%!%!!%%!%!%?!%%%!!%!%?%!%%%%!%??%!??%!%!!%%!%%!!%%!!?%%%%%%!!%!%%!%!?%%?%%!!%!!!!%%%!%??%?!%%%?%!%%?%%!!??!!!?%!!?!?%!!%%!!%%!!%!%!!!!%!%%%!%%%!%!%!%%%!%?!!%%%%%!%!!!%?%%!?%%%%!!?%!!%?!%%%%%%!!!?%%%!%!?%%%%%%%%!?!%%?%%%%!!!%%??!!%%%!?%?%!!?!%?%!%%%%??!?!%%%??!%%%%%%%%?%!!!%!%%%!%!%%?%?!??%%!%%!%%?%!!%!?%!%??%%!%%!%!!%%???%%!%%%!%??!%%?!!!%%%!%!!%%%??!%%?!%%%?!?%%!%%!?%%!?%!?%!!?%%%?!%?%%!%!!!????!?%!%!?%!%!%!%%?%?%!!??%%%?%%?%!?!%%!!%%!%?!!%%%%%%%%%!%!!!!%%?%%%!!%%%%%%%!?%!?%%?%%%%!%%!?!%%%!%%!%!!%%!?%?%!!!%?%%?!%%!!%?!!%%%?!%!!%%!%!!!!?%!%!?%%%!!%%%?%!%%!%%%%%%%%%%%%%!%?!%!?%?%!%%%!?%%%%%%!!?!%!%!?%%!%!%%!%?%%?%?%%?%?%%!%%!%???%!%?%%!!%?!%!%%!%?!%%%!!%%?%!%!%%?!%%%!!%%!%!?%%?%?!?%!%%%!%?%!?!?%?!!%%!?!%!%??%?%!!!%!?!%?%!%!%%%?%%%%?!%%%%%%%%%%?!??%!?%%!!%%%!%%!%%!%%!%%%%%%!%%!!!%%!!???%??!%%?!%%%?%%?!%%%%?!!???%%%!!%??%%%%???!!%!!%%!%%%!%%!%!%%!!%%?!!?!%%!%%!%!%%!!!%?!!?!%%%!%%%%%!?%!%??%%?!%%%%?%%?!?!%!%!!%%%?%%%%%%%?!?%!%!?%?%%?!%%%%?%%!?%??%%%%?!%%%!%%%!%!%!?%!!%!%!%%%%?%%!%%%%?!!!%?%!%%%!%!??%?!%%?%%?%%%?!??%%!%?!!%%%%%%!%?%?!%%%?%!??!%%%%%%!%%%%!!%?%%?%!!!!%!%%%%%%%!!?%!%%?%!%%%!!!??%!%%!%???%!?%%!!???!%!%%!??%%?%%%%!%%!?!%?%%%!!%?!!%!%%!%%%%%!?%!%!%!!?%?%%%!!%%?!%!?%!??!!%%?%%%!%%!!%%!%%%?!%!%!!!!%%!%%!!!?%??!!?%%!%?%!!%%?!?%!??%%%%!!!%%%??%%!%%?!!%!!%!%!?%%%!?%!%%%%%!!??%%%%%!!%%%!??%!!%%!%!%%%?%%!%%%%%%!%%%!%%%%???%!?!!!!%!!!%%%%%%%!?%!!!?!!!!%!%?%!!?!%%%?%%!!%??!%%%%!!%%?%?%%%%%!!?%%%??!%%!%%%?%!!%!%!!%%%?%%%%!!??%!%!%!!%%?%!!!!%!%%%%%?!%!%!!%???!%%!%%!%!??!!%!!%!!%%%!?!?%!!!%!!%%?%%!%%!?!%%%%?!%?%!!%%?%!%??%!!??%?%%%?%%%??!!?!%%!!%!!!?!?!%%%%!!!%%%!!!%!%!!??!?%%%!%!%!%%%%%%%?%!?%%%!%%%!!?!!%%?%!?%?%%!?%%!?%!%!%??%!%!%%%%%!%%!%%%%%%%!?%!%%!!!!%%?!%%!%?%???%%?!%!%!%%%%%!%%%?!%%%????!%%!%??%%!!%?%%%?!%!??!%%!%%!!??%%%!%!%!?%?!%!?%?%%!%!%%%%%%!!!%%%%?%!?%%%%%%!!!?!%!?!%%%?%%!!!??%?%?%%%%?!!!%%%%!%!%%%!!%%?%!%?!%%?%!!!%!%!%?!%%!%%%!!?!!?%%!!%!!!%%%%!%%%!!!??%!??!!!!%%!%!%?%%??!%%%!!%%!%%%%%%!%%%%%%!!!!??%%!!!%!?%%!%!!%%!%!!!?!?%%%?%!??%%%%?%%!!%%!%!!%?!%!?!%!%!%%?%%%!!!%%%%?%%?!%%!!%%!?%!!!!??%%%%?!%!!%!!%!%%%?%?%%%?!%%%!%!%%%!%%!?!%%%%%%?%???%%?!%%?!!!%%%!%%%%%%?!?%%!?%?%!%%%!!%?%%%!!?%!!?%!%%?%%%!%!!%%%%%%%%%!?%?!%!%%%%%?%!!!%%%?!!%%%%!!%?!%!!!%%?%?!%%!??%%!!!%%!??!%%%%%!?%?%%!!?!%?%%%!%%?%%%!?!!%%%?!%%!!%!%!%!%%%!%%!!%!%%!%%%!!!!%%!!?!%!!%!%%%!%!%!!%%%%?%!%!%%!?!%?%%%!%?%?!!!?%%!%%!!!%!?%?!!!!!?%%%?%%%!%!%%%%!!?%?!%%?!!%%%%?!%!!?%!!%!!?!%?%!%!%%%!?%!?%%%%!%!%%%?!%%%!%!%%%?!%%%%%!%?!!%?%%!?%!?%%%%!!?%%!%?%%!?!%%%%!%!%%%%%%?!%%%!%!%%%!%?%!!%%%%!%!!??%%?%!!%!%?%?%?!!!%!%%%!!!%%%!???%?%?!%%%!%%%!%%%!%!%%?%%%%!%%!%%!%%%%%!%%%%!%%?!%%!!%%%%%!?%%%%%!%!%!?!%%!!%%!!??!%!!%!%%!%?%?!%!!%?!??%??%%%%!%!%%%!%%%%?%!!?!%%%%%%%%%!!%%!!%?%%%%?%!?%%?!%??!!!!!%%!%!!%?!%%!%%!?%%%!?%%%%!?!?%!!!!%!????%%!%?%%%%%!%%?%!%%%%!%%?%?%%?%!!!??%%??!!??!!?%%!!!%!!!%!%!%?%????%!%%?!!!%?%?%!?%%!%%?????%!!?!?%?%%%%%%!?%%%%?%!%%!%%!?!%%?%%!%%%!!%!%??%?!!%!%?%!%?!%%!!%!!!%?%?!%!%%!?%!%!%!%!%?!?%%?%!?%??!%%???%%%?!%%!%%?%!%%%!%!!??%!!!%%??!!!!%%%%!!?!%!?%%%?!%!!!%!!?!!?%%%%%%%%!!?%%?%%?%%!?!%%?%!%%?%%%%%!!%%?!%%%!?%!!%!%?%%!%%%!%%%%%%!?%%%%!!?!%??%%?%%!!???%%!%!?!%!%%!?!%!?!%!!!%!!?%?%!!!?%%?!!?%%%!%%%%!?%%??%%%!!!%?%!%%!%%?!?!%?%!?%%?%!%!%%%%?%%!!!!%?%%%!%!%?!%!?%??%!%%%!%%!!%%%%%!?%??!??%%%%%?%!%%?!%%%%?%!!?!%%%%%%!!!%%%%%!%%!%!!%?!%!!%?%%!%%%!!%??!%%!%%?%%%??!%!?%%%%%?!%!%!???!!%%%%%%?%!%%%%%?!%%%?%?%!%!??%%%?%%?%%?%!%%?!%!!?%!!%!??%!?!!?!!!%%!%%%!?!!?!%!!%?%%%%%!?%!?%%!%!!%%!?%?!%!%?!%%%!%!%%%%?%%%?%!!%%%%!%?!?!?%!!%?%!!?%?!?!%!%%!!%%!!%%%!?!!?!??%%??%!%!%%%%%%%%%%%%%%%?%%!%!!!%?!!!%%%%?%%!%%%?!?!?%??%%?!!?!?%%%%%%%%!%%?!%?%!!%%!%%!%!%!%!!!%%%?%%!!%!%?!%%%????!!?!%%?!%!%%%?!%?!!??%?!?!??%!%%%?!%%!!%%!?%%?%?%?%%!%%??%!!!%%!??!?!?%?%%%%%%%%%%%!%%%%!%!%!!%!%!%%%%%%%!%?!!!?%!%!%!%!%%%!%%!!%!!%%%%%?%%?%%!?%%!?%!%%%%?%!%!%?%!%!!?%%%%!?!%%%%!!!!!!!%!?%%%!!!%!%%%%?%%%!!%%%!!!!%%!!%?%%%!!?!!!?!!!%!%!%?%?%!!%!%?%%%%%%!%?%!%%!%%%?%%?%%?!%!%!?%%%%%%%%??%%!?%%%%!%%!?%?%!!%%?!%!!!%!!%%!%%%%%?!!??%!%?!!!%%!?%%?!!%!!%%!?%?%???!?!!%%%!%%%%%%%!!%%!?!%!%%%!!!!!??!!%!%%??%?!%%%%%!%%%!!!%!%%%%%%%%%%%!%?%!!%%%%?%%%?!!!!%!%?%?!%!!!!?!!!!%?%%???!?!?!%%!!!%!%!?%??%%%?%!%%%?%%?!%%!!%?%!!%!%%?%%!!%%%%%?%%!%%%?%!?%!!?%!?!%!%!%?%!%%%%%%?%%%%%?%%?!!%!%%!?!%!!%%%%?!!?!!%!%%%%!!?%%%!%%%%?%%?!!!?%??!??%%%!%!%%?%!%?%!!!!%?%%%%%%%%%%!?%!%%!!?!!!%!%?%%%%!%%!%%%!%%%%%?!!%?%%?%%%!!%!!%%%%%%!!!?%!%!!?!?!!!!%%!!%%!%%??%!?%!!%%%%%%!!?%!%%!!%!??!!!%!!%%%%%%%!?!%%!%!!%%!!!%!!%%%%?!?%%??%!%!%?%??%%!%%!!%!!%?%!!?%?!%!?!?%!%?%?%%%%%!%%%%!!?%%%!?%%!?%%!!!%%!?%%?%%?%!%?%%%!%%%!!%%%?%?%!?%?%%%%!?%!%%!%?!%?!!!%%?!%?%%%%%!%!%%%%!%!?!%!%%%%?!%%%!?%%%?!!!%%?!!%%?%%%!!?%!%!!%!?%%%!%%?!%!?%%!!%%!%!!%%??%%%%!%!%!!%%%%?%%!%!%%!!%!%%!?%%%%?%%%?!%!%%%%%%!???!!%%!%!!%!%%??%%!%%!%%%%%%!!?!%?%?%!%%%%!!!?!!!?!%%%!%!!!%%%?!%!%%%%%?!?%%?%?!!%%%%%!%%!!?!%%!%%?!!!%%%%%!%!%!!%!%!%!%%!%!!%%%!!%%?%!%!??%%?%%%!?!%%%%%%%!!!%!!!!%%?!!?%%%?!%%!%?%!!?!%?%!!%??%!%%%?%!%%!!!%%%?%%%%%?%%%%%!%%%%%?!!%?%?%!!%%?!!%!!!!!%%!%%%!!??!?%%%%!?!!%!%!%?%!%%!%%%!?!%%%%%%?!!?%?!%!%!?%!!%%%%!%!%%%%%!?!?%!!%!?%%%!!%!!!%!?%%!??!?%?!%?!%!%!?%%%!?%?%%%?!%??%!%?%!?%%%%!%%!!%%%!!!?%%%!?!!%%%!!%%!??%%!%%%%!!!!%!??%%!%!!%!!%%%%!!%%!!%!!%!?%?%?!%!?!%%%%%%!%%%%?%%%%%%%%!%!%%%!!!%%?!!!%!%!%!%!%%!!!!!%??!?!?!!!!%%!!%%%!%%%?%%?!%%%%%%%!?%%%!%%%!!%!%%%%%?%??%?%%%!%%%!%%!!!!%%%?!%%?%%%?!!?%?!?%%!%!?%?%!%%%!%%!%!%?!?%!%%?!??!!!%?%!!%%%%?!!!?%?%!%?!??%!%%?%?%!%%!!%%%%%!?%%!%%!%!!!!!%%?%!%%%%%%!%%??%!%!%%%?!%!%?%!!%!%!%%?%%!!%!%!?!%%!!%%%?%?%%??!%%%%%!!%%?%%!%!?%!!!%?%%!?!!%%???%%!!%%%%!%?!%!!%!%!!%?%?!!!?%%%%!?%%??!!%%%??!%!%!%!!!%%%?%!%?%!%!%????%%?%!!!!!!%?%%%%%%%?!%%!%%?!??????%%%%%%%?%%%%%?%?!%?!!%%%%!%!%%%%%%%?!%%%?%!!!%%%?!%!!%!%%%%%%%%%?!???%?%%%!%!%!%%!?!%!!%%%%!%?%!%??%%%%?!%!%%!%!%%?!%%!%!%%%!!%?%%%%!!%%%!%%%?%%%%%?%%%%%%?%%!!%%!?%!%!%?%%%%!?%%%%!!%%!%%!%??????%!%???!%%%?%%%!!%!%%?%!!%!%%!%!%%?%!%?%!%!!%?%%!%!!%%%!?!?!?!!%!!?%!%!%!%!%%%?%?!!%!%%!%%%%%%%!%!!!%%?!!?%!%%!%!%!%??%%%%!%?%%!%!???!?%%?%?%?!%%%%!!?%%!%%%%!!%%!%%%?!?!!%%%??%%??%!?%%?%!?%%!%!%?%%!%!%?!%%%%%!!?%!!!?%!!%!!%%%%%!!!%!%%?!%!%!!!!!%%!!!!%?%!%%?%%%!%%%!%!?%!!?%%!?!%%!%!!!?%%%!%!%%%!%%?!%!!%?!!!%!?!?%!%!%%!?%%!%!%!?%%?%%!!%?!!%%!?%%?%%%?!!%%!!!%!!%!%%%!%?%%%%!!?%%%%%?%%%%!!?!%!%!??%%!%?%!!!?%%%%!%!!!!?!?%!%%!?%!%%%%%%%!%%?%?%??%!%%!!!%%!!%!!%%!!?%!%!?%%???!%!%!%?!?%!%?%%%%?!%%%??%%!?%!%!%??%%?!!%%%?%!!%%!?!!!??%%!?!!!%!?%!%%!%%%!%%%%?!%%%%?%%%%%%?%?!!!%%!%%!!%%?%?%%%%!%!%!!%%%%!!%!%!??!??!????%!!%%!%?!?%!%%%%%%%%!!%%!%?%%?%!?!%%!?%?%%%?!%%!!%%!%!%%!!!%!!%%%?!!!%%!%!%%%%%%%!!?%!!%%%%%!?!%%%!!!%!%!!!%!?!?!%%!%!%?%%%%%%%!?%%!%%???%%!!%%?!%%%!?%%%%%!%%?%%%%%!!%??!!!%?%!?%?%!%%%%!%!!?%???!!%!%!%!%%?%!!?!%%!?!?!!!%%??%%%!%%%%!!%!%?!?!?!!!!!%!%!!%!%!%!%!??%!!!%%!!!%%?!%%%%%!%%!%%%?%!%%%%!!%%%!!?!!?%!%?%?!!!!%%%!!!?%?%!!!!%%%?!!%%%%%%!%!???%%%%!?%?!%%%?!%!%%?%%%%!%!?%%%!!!!!?%!!?%??%%%%%?!!%?!?%!%%!!%%!%!!?%%%!%!!%?!%%%%%%%??%%%%!%%!!?%%?%%?%%!%%%!?%???!!?%!?%%!!%!!%?%%%?!%!!%%%%%%?%%?%%%?%%?%%!?%!%!%!!%!!%%%%%%!!?!%!!!!%?%!?%%%%%?!%?!%%!?%%!%?%%%%?!!%%%!!!%??!%%!%?!!?%?!%%%%!%%!%!%!!%!%%!%%!??!!%!??%!!?%!!!%%!!%%!%!%!!!%?!%?%%!?!?!?%%%?%%%%!%%!%%%!%!!?!!!!!!!?%%%?!!?%!%?!%%!%%!!!??%%%!?%?%%!%%!!%!%!%??!!!%!%!??!%%%??%!!%%!?!?!?!!!?!%!%!%%??!!%!?!!%?%%%?%%%%!%%%?%!??%!%%!!?%%%??!%??!?!%!%%%!!%%%!!%!!!%!?%!!?!%%%?!?%%%!%%?!%%!?%!%?!!!%!!%%?!%!!??%!%!%?%%!%%!!%?!%%?%?!%%%!%??!%!?%%%?%%%!?%%%!%?%%?!%%%%?!????!%%%?!%!%!%!%!%%%%?%!!%!!?%%!%%%%!!%!?%%%%%%?%!!%%%?%?!%%!%%!?!!%!%%%?%!%%%!%!!!?%????!!%%%!%%%%%!%%%!!%?%?!?%%!%%%%%%!%%%%%!!!!%%%!%%%!!?!!!!?!??!%!%!%%!%%!!%%!%!!?!%!!%%?%%!!%%%%!%%%%?!!!%!!%%!%??!%%!!!%%!!%!%%!%!%?%%%!?%%%?!%%%?!!?%%?%!%!!%%%%!!%%!!!?%!%%%%%?!!%?!%%!!%%?%%%%%%%%!%%!!%%%%%?%!%%?!%!!!%%!%!%?%%?%%?%%%!%?!%!%%?%%?!%%?%!!%!?%!!?%!!%!?%%%%?%!!%%!?%!!%!!%!!%%!!?%!!??!%%!!!!%!?%??!%%%%!!!!%%%!%%%%!!%%?%%!!%?!%!%??%!%%%%!%!%%%%???%%%%!!%!?%%%%!!?!!!%%!%%%%%%!!%!?%%%%!%%!!!!!!!!!!%%%!%?%!%!%!!%!%??!?%%!!%%%%!%!%!??!?!%%%%%!!?!%%%%%!!%%!%!%!!%!?%!?%%?!!%??!!?%%%!???%%%!?!?%%%%!%%%!!!%%%%?%?%%%!%%!!%!!??%%%?%?!!%!?!!??!%%!!%!!%%!!??%?%%%%%!%!??%%%%%!?!!%%!??!?%!%!!%?!%??!!!!%%!%!!!%!%%!!%%%!%%!%%%!%?!?!%%%%?!??!!%%%!%!%%??!!?!?!%!%%?%!%%%!!?!%%!!%?!?%!!%!%!%!!!%?!%??%!?%!!%!%!!!%??%%??%!%%!%%??!!?!%%?%!!%!!!%%!??%!?%%%!%!!!%!?%!%!%?%!!%!!!%!!%!?%%!%!!%!%!!!%!?!%?!%!%%?%!!%%%!!?%??%%?%%!!!%!??%?%%%!?!!%%!!%?%%!%%!!%!!%%%%!?%%!!?%!%!!?%!?!?!%!!?%!!!?%%??%!%!!%%!!!?!%%!%!?%%%?%!!??%?%%?%!!??!%!%?%%%%!%?!%!%%?!!%!!!%%%?%!%!%!%!%?%?!?%?%%??!!!!!%%%!%?%%!%!!%?%!%%%%%%!!%%!%!%%%%??!?%!%%%??%%?!!%!%%!%!%%?%%?!%%%%!!!%!%?!%%%!!%?%%!%%!!%!%%?!??%!!%%!?!!!%%%%%%%%!!%!!!%!!!?!!?%?%%%%!!?!%?%!!??!%!%!!?%%!!%!%!!!!%!!?!%?%%!!%!??%!!%%%!!%?%!!%%%!!!%!%%%%!!!?%%%%!!!????!%%%%!!%??!%!!%%!%?%?%!!%!!?%%!%!%?%%!%%%%?%%!!%?%%%%??%?%%!!!??!!%!?!%%!!?%%%%%!%%%%%%!%??%%%?%?!?!?!%%%!!%?%%%%%!%!%?%!%%%???%%%!!?%%%!%%!?%!%!%%?%!%!!%!%%%!!%%!??%%%!!%%%%!%%%%%!!%%%?!%!!?%?!!!?!%%%?!!?%!!%??!!!%?!%?%?%%!?%%%!!!!%%!%%!%!%%!!!%!%!%%!!?%%!!%%%?%%!?!!%%%%%!%%%%!?!%!!???%%?!!!%!%?!%%!%!?%%%!%!!%!%%!%%?!!!!%%?%!%%%!%!?!%?%%%!%??!%%!%%!%%%!%??!?!?!??%!%!!%?%!!!%%!%%%!%!?!%!!!%!%%%%%%%!%%!?!%%!%!%%?%%!?%%!!!!!%%%%!?!!%%%!%!!%!!%%%%%%%?!!!!!!!%!!%!!%%!!?!?!%?%%?%!?%%%%%!%%!?%!!%%%%%%!%%%%!!%%!%%?%%!!%!%?%%?!%!?%!%%!%?!%?!%%?!%%!%!%%%!??!%?!!%%???!%!!%!%%?%!%%%%!%!%%%%!%!!!!?%%%!!?%%!!?%%?!!!%!%!!?%!%%%%%%!!%%!%!%%?!?!!?%!?!!%%%!%!%!!%%?!%!!%%%?%!%%%%!!%%?!?!%!!%%%!%%%%%%!%%!%!!?%%!?!!%%?!???!%%!?!%!!%!%!!%%!?!%!%??%!??%%!!%!%!??%%%%%%!%??!%%!?%!!?!!%%?%%%%%%!??!%%!%!!%%?!%%?%!?%%!?%??!%%!%%%!??%%%!!%%%??%%!%???%!!%?!%%!??!%!%%?%%%%%!%?!?%?%!!!?%!%%!?%%%?%?!%%?!!!?%??%!?!?!!%!%%%!%%?%%!%!%?!%%%%?!%%%%!%!%??%!%??%%?%?!%!!!%!%%!!!%%!%%%!%%%%%!!%%%!?!!!%!!?!!!%%%?!??!!!!!%%%!%%!!!!!%?%%%!!%!!!!%!%%?%%%!%%%??!%!%%!!%!%!!%!!%?%!!?%%%?%%%!%%?!?!%%?!!!!?%?%!!?!!?%%%!%%%?!!!?%%!!!!%?%?%%%%?%%%%???%%!!%!?%%??%%!!?%%?!%%%!!%%!?!!%?!%%%!%%%%%%!%%!%!%%%!!%!!%!?!?!%%%!%!%%%!?%!!%?!!!?%%%!?%%??%!!!?%?!!%%!?%!%%%%%?%!%%%%!!!!%!!%%%?!??%!%!??%!%!!!?!!!!!!?!%!!!!!!%%%??%%%%!%?%%%!%%%?%%!%!?%?!!%!!!!!%!!%?%%!%%!!%%!%%!!%%%??%!!%!%%%%%!%?%%%%?%!!%!%!!!!!!%%!!%!!%!%!%%!%%!%!%?%!!!%%%%%%%%!??%!%%!%!%%%%%!%%%??%!%%%!%?%?%%%?!!?%?%%!!!????!%??!%%!!%%!%!?!%%!%%%?%%%%?%!%%%%??%%!?%%%!?%%!%%?%?%%!?!!????%!%!?!!!%%%%??!?!?%%%%!%!%%?!%%!%%%%%%!!!!!%!%%%!!%!%!!?%%%!%?%%%%??%?!!%%!%%??%?%!?!?!!!!%%!%!%%!%%%%!!!!%!!%%!%?%%??%?!%!!%%?!%!!?%%??%?%!%%?!%!%?!%%%%!%!!?!!%%%%%%!!%!%%?!?%!!!%!!!%%%%??!!?%%%!%%!?%%!%???!%%!%!!!%??%%%%!%%%?%%!%!!%!!!%%%%%!!!?!!!%!!%%%!!?%!%%!%%!!?%%%%%%?%!%?!?!%%%?%!!%%%%?%??%%%%!?%!!??!!%%!!!?!?%??!?!%??%!%%?%!%%?%%%!!%!%%%!!%?%%%%!?%%%%?%%!%!%%!!!!?!%%%%!?!?!!!%!!%??!!!!!%?%%%?%!%%!!?%?%%%??%!%%%!%%!?%%%%%%?%%%!%!!?%!%%%%%!?%?%%!!%?%!!%!!%%?!?!!%%%%%%%?%%!%%!!%!!!%%%?!%??%%!%%%%!!%!%%%%%%%?%%!!%%?!%%%??%!%%!?%%?%%!!!%%??%%!!%%!?%!%!?%!%!%%!%%%%%!?!!!?!!?%?!??!%%%%%!?!!!%%!%?%%%%%!%%%%?!%?%!!%%%%%!%!!%%!%!!!!!?%%%%%%!%%%!?%!?!%%%!?!?%!%%!?!?!!%!%!%!%!?!?%%!!%??%%!%?%%?!!%%!%!!!!!%!%?%%%%%%?!%%?!!!!!??!%%%%%!%%!!%?!%?%!?!%?%%%%%%?%??%%!%%%%!!?%%%%!%%??%%!?!%%!!!%%%%!!!!!%%!%%%!%%%!!%%!?%??!%%%!%!%%!%!?%!!%%%!%?%!?%%!?%%%???%!!!%!!!?!?!?%!%!%!%?!!!?%%%!%!!%%!!%!%!!!%%?%!!!!?%?%?%!?%%!%%%!?!!%%!%%%%%?!%%?!%%!%!!%!?!%!!!%%%%%?!%!%%%!%!?!%%%?%?!%%%%!%%!%%!?!%??%!%??!%?%%%%!%????!??%?%!%??!!%%!%!%%%!%%!!!%%%!%!!%!!?%?%%?%%!!%?!?%%%?%!%?%%%!%%!%%?%?%%%%%%%!%?%%??!!?%!%!%%%??%?%%!!?%!!%%!!%!%?%!!%?%!%%%%%%%%%%%!%!%!%%%%?%!!%%?!%?!!!%!%%?!%?%%%%%%%!?%!!%%!!%!%!!!%%%%%%%%!!%%%!??%!!%%%%!?%%%%?%!!!%%%?!!%!??%%%!%%?%!%%%?!?%%!!!!%!!%%!%!!!%%?!!%%!%????%%%%!!%!%%!%%!%%%!%%!%?!!%%!!%!!%!%%!%%%%%!%%%?%!%%%??%?!?%?%!%%?!%!%%%%?%!%!%!%%?%!!?%%%%%%?!%?%!%!!?!!%!%%!%%!%!%?%!%%!!%!%?%!?%%!%?%!!!!%!??!%%%?%%!%%??!%!%?%%%!!!!!%%%%!!?!%%!%!%!?!!!!%!?%!%%!%%?%!%!%%!?!%!!!!!!!%?%?%!?!!%?!!%!!!!!?%!!%%%!%%%%!??!!!%%!!!%%??!!%!!?!%%%%?%!%!%?%%!%%%?%%?%%%%%%%?!?%%!%%%%??!!??%%%?!%!%%?%%%?!%%%%!%%%%!!%%!!?!%?!%!!%!%%!?!!!!!!?!%%%%!!!!%%%!!!!?!%!%?!%%%%%!%??%%!%%%!%??%?!!!%!%%%!?!!?%!!!!%%%%%?%!!!??%%??%!!%%?%%%!%!%%!!%%!?!?!%?!%!!%%%!!!%%??!%?%!%%!%%!%%%%!!%!%%%!!%%!???!?!%%%%%!!!!???%%%%!%?!%?%%?%!%?!%!!%?%!%!%%!%%%!!%!!!!%?!!!!!!!!%!%!?!?%%%?!%!%%!!%!??!!!%%!?!%%?!%%%!%%?%%!!%!!!%%!??%!??%%%%%?!!?!!!!%!%%%%%?!%!?%!!%%!!%%!?!?!?!?%?%!??!%!%%!?%%!!%%%%%%??%!%?!%!%???%!%%%%!%%%%%%!?%!!%!!!%%%!%%%!?%%?!%!%%%%!%%%%??%!??!%%%%!%!%!?%%%%%!%%!%%%%?%?!?!%?%%?%%%%!!%!%?!%%%!%%%?!?%!!!%!%%%?!%!%!%!%!!!%!%!%!%?%?%%?%!%!!!%%!%!%%!!%%%!!!%%?%%!%%!!!%%%!%!%%!?%%!!%!%?!%%%!%%%%%!%??%%!%%!%%%!?%?%%%%?%%%%??!!%%%!%%%!%!?%!%!%!?!%%%!%%!%?!!!!%?%%!!%%!!!!?!%!!!%%!?%!?!%?%!%%!%%!??%%!!%!%%%??%!%!!?!!??%%?!!!!?%?%?%%?%!%!?!%?%!%!%%!%%%!%!%%?!?%%%?%?!?!%??%%?!?!%%%%%%%?%!%%%!!!?!%%%%!!%%%%%?%%??%!%%?%!%!%!%%%!%!%%%%%%%!%%%%!%!%%!!!!??%%%%%!%%!%!%%!?%%%?%%!!!%%%%!??%%%%%!?%%%!%?%!!!%%%?%!%?!!%%!?!%%%!%!!!!!%!!%%!!%!%%%!%%???%!%%%!!?!%%%%%!!!!%!?%%%?!%%%%!??!!%??!!%%!?%?!%!%%%%%!?%!%?%%%!!!!?%%!%%%?%!%!%%%%%!!!!!%!%!?%!%??!?!%%!%!%%!?%??!%!%!!?!!!%?!!%!%!!!!!%%?%!!!%!?%!%!%?!%?%!%%%%?%!%!%%%?!%%!?!!%?%!%!%!%%!%%%!!%!%!%%%!??!%%%!%%!?!%%%%%!%%!%%%%%%?%%???%!?!!!!%!?!%%!%!%%%%%%%!%!!!!%!%!?%?%!!%%!%!!%!!%%?%%!!!!%!%!!%%%!?%%!!?%?%!%%!%%%%%%?%%!!?!!!!!%?%%!%%%%%!??%?!%!!!%!%!!%?!%%%%!!!%%!!%!%%?%!%%??%%?%!!!!%?!?%%?%%?%%%%%!!!%%%?!?%%%%%!!?%?%!?%%!%!%!%%%!!?%!!%!?%%?%?!%!%?%%%?!%%%%!%!!?!%!%%?!%!%%!!!%!!!%!%%%%%%%!!%%%%?%%%?%!!%??%%%?%%!%!%?%%?!!?!?%%%%!%!?!?!%?!?%?!!?!!%%%%!%!%%?!%!%%!?!!%!%%%%%!!?%%?%%%?%!!%%!!%%%!!?%%?%%!%%??%%!%???!%%??!?%%%!?!%!%%!%!%%%!%%%?%??%!%%?%%!%!%!%!%%%%%%%!?%!!%%%!!%%?!%!?!!!!%%%!!!%!!!!??!%%%?!%%!!??%!!%%%!!!%?!??%%!%%!!???!%%%?!!%%!%%%%!?%%%%!!%%%%!%!!?%%%!%%%!%!%%%!!!%!%%!!?!%%%%%%!???!%?!%%%?!!!!%!%%!%!%%%!!!%??%%%%??%%!!%?!%?!%%!?%!!?%!%%%%!??%!?%!!?%%%%%??!%%?!%?!%%?%?%%%!!%!%%!%%%?!!!!%%%%!%%%!%%!!?!!%%!%%?!%!%%%%%!%%%!%%%%%%!!!%!!%%!?%!!%!%%%%!?!%%!??!%!?%?!!%%%!%!??!%?!??!%%!!%????%!%??%%!%!%?%!%?!!?%!??!!?!!%!??!!%!!%!%!%%!%?!!%%%%%!!%!?%!%????%!%%%%%%!!%%!%%?%?%%?%!?!!%!%!!%%%!?%??!%?%!%!%!??!%%%%%%%%?%%%!%%%!%!%%!%%?%%!?%!!?%%!%!%!!%%%%%!!%%%%??%!!%!%%?%!%%%!%!%%!!%%%?%%%%%!%%!%%%%%?!!!%???%%%%%?!%%%%%!!!%%%%!!%%!%%%!?%%!!%!%%%%%?!!%%%!%%!!%!%?%??%!?!!!%%%%%%!%?!??%!!!%?!???!!%%%!%?%%?%!%??!%!!%%!%!%%%!%?!%!%?%!!%%!%%!?%!%%%?%%!%%!!%%%!%%?%%%?%%!%%!!%%%%%!!%%!%!%!!!!%!%!%!!!%%!!?!%%%!!%%%%!!%%!%%!!%!!%?!%?%???%%?%%!?!%%%!%!%!%%%!!?%%%!%%!!%!%!!%%!!%%%%%!%%%%?!?!%%!%?!!?%!!%%%%!!%!%!%%%%%%%%!%!!%%%%%%%?!%%%%?%%?%%!%?%!%!%?!!%!%!%!!!!!%!!%?%%%!%%%?!??!%!%?!!!%%%!%%!?%%!%?!%!%!%?!!!%%!?%!%!!??!%!%!!!%%!!?!%!%?%%%!%!!?%%%%%!%!%%?%%%!%!?%?!?!?%!%%??%!?!%!%%%%!!!%?!?!%?%%!%%%%%?%%%%%%?!?%?%!!%%?!?%%?%%%!%?!?!!!!%!??%!%?%%!!!%!%%%%%?%!%%%!%%%%%!!!?!?%?%%%%%%%%!!?%???%%!!%%%!?%%%%!!!%%%!%?!%%%%!!?%!??%?!%%??%?%?%%!%!%%%!?!%%%%%!??%!!%!%%%%!!%!?%%%!%%?%%%!%!!?%%%?!%!!%%%??%%??!!%!%!?%!!!%%%%!%%%?!?!%%%%!!%!!!%%!%%%%?%%%!!%?%!!!!%%!!%!?!%!%%!%??!?%!%%%%%?%%!!?%%??!%%%%!%?%%%?%%!%!%%%!!!%%!%%%%!!?!%!?!%%!!!?%%!!!%?!%!!!?%!%?%?%!?!%?%%%%%%?!%%%?%%%%%!?!!%%%%%%!%%%%%%%%%%%!%%%?!%!%!!!%?%%%!?%%%%%%%%%%%!!!!%!%!!%!!%%%%!!%%??%!?%!!!%%%!!%!%?%%%%??%?%!%?%!!%??!!?%!?!!?%?%%%?!%%??%!!??%?!%%?%%%!%!%!%%%!??%%%!?%!%%%%!%!?!?!!!!%!%!%!!%%?!?!%%%!?%!%!?%%?%!%%%!%!%%??!%%?!?%%!?!!!?!!!%%%!%!!!%!%?%!??%%?!%%!?!!%%?%?%%?%!%!!?%?!%!!?!!%%!!%%?!!!%!%?%%!%%!%%?%!!%%%%?%%%%%%!!!%%%%?%%!%%!!??%%!%%%??!%%!?!!!!!%!%%%%!!%?!%?!!%%?%%?%%%!?%%!%%%!%%!%!%%!%%%!%%%!%%%!!%%!%!%!?!!%??!%?%!?!%%%!%%%!!%%!%%?%!%%!%!!?%%%%%%%%!!%%%!!!?!%%%!?%!%%%%?%!%%?!?!%!%?!%?!%!?%?%!??%!!???!!!%%%%%!!%%%%!%?!!%!%%!?!%%?!!%!!%%!!%!?%%!?!%%?%%%!%%%????%%%?%%!!?!%!%!!%%?%%%%%%%?!%?!!?!%!!!%%%%%%%%?!?%!%%%!!%!!!%%%%?!%!?%?%?%%%!%?%%!!!%%%%!!!%!%%!?!?%%!?%%!!%?%?%?%%%!!%%%!%?%!%!%%!%!??%%?%%%%?%%%?%!%%%?%%%%%%%?%!%%%%!%?%%!!!%!!%!%??!%?%!%?%?%?%%%?!??%?!%%!%!%!%%%%?%%%%%!!!!!%?!?%%%!%!%!%%%?%?!%!!?%!%?%%%%%?%%%!%?!%%%%!?%?!%%%%!%!!%!%?%?!%!%%%?!??%%!%!!%!!?!%??!!%!%!!%!%!!%%%!%%%!!%!%%!%%%%!%%!%%?!?%!%!!?%!%%!!?%%%!%%%?%%%!%%%!%!!!!%%%%%?%%%!!!%%%?%%%!%%%%%!??!?!!%!%!!!%!%!!?%%!!?!!?!!%%!!!%?!%!%%!?%!!%%!?%?%!%??%%%%%?!!%%%?%%?!%%%%%%%!%%?!!%%!!%%????!!??%!%?%?!!!!!%?!%%%?!?%%%%%%%%!%%??!!%%?!%!%!%!!!??%%%%?!%!%!%%!?%?%%!%?!!%%%%%%%%%%?%?!!!%%%%!%!%%%%%%%!!%?!!?!%%%%%%?!?%%!%?%!%!%%%%!%!%?%!!%!!%!!!!%%!?%!!!%!!%!%%%?!%%?%!%!!%?%!?%!!!%%?%!%?!?!!%!!%!??%!%%%!%??%%!%!?!%!%%!%??!?%%%%%!%%%!!!%?%!%!?%%!%%!%%!%%!!%%?%?!!%%!%%?!%?%!!!!%%!?%%!%!%!%!!?%!!!%??!?!!!%%!%%%%%%%%!!!%%!%%%%%%!%!%%%!!%!%!%%%?%%!!%%%%!?!?!!%%%!???%%!!!%%%!!!%%%%!?!%!%%?!%!?%?!%?%%%??!%!?%%%%!?%%%!%?!%%%!?%!!%!%?%!%?%%!%%?%?!!!%!%%%%%%%%%%!%%?!%%!%%!!%?!%%!%%!!?%!?%%?!%!!!%?%%%%?%%%!%%%%%%!%!?%%?%???%?!%!!?!%%!??%!%%?%%??!??%%!!!!%!!%%%%!%!!%%%%??!%!%?%?%!!!!!%!%!%%?!%%!?!%!%!%%%!%?%!%!%!%%?%!%%%%%%!!?%!%!!%?!!%%!?%%%!?!%%!%%%?!!!!%??!%!!!?%!?!!%%!!%%!%?!?%?%%%%%?%??!%!%%%%%!%%%%%%!!%%!!!%%!!!!!!%?%!%%%%!%%%%%%%!%!%%!%%?%?%!%!!%%%!%?!%%%!?!!?!%%?%%%%%%%!!!%%%%?!%%?!%!%!!?%!%!%!!!!%%%!%%??%%!%!!%??%!!!?!?!%%!!%!!!?!??%%%%!!?%!?%%!%%!!%!%%%?%%%%!%%!?%%?!!?!%??!?!?%?!%!?%!%%!?%!%%%!%?%%%%!%%%%%%!%%%%%%?%!?%%%%!%!?!?%%%!%!%%??%%%%?!%%%%!?!%%!%%%%%!%!%%?%!!?%%%%!!%%%!%!%!%!?!%%%!%!%?!%!%!?!%!!%!%%!!%??!%%%%%!??%????%%!!%?!!%%%?%?!%%!!!%!?%?%!%%!?%%!%%%!%!%!%?!%%!!!!!%?!%%?!!!?%%!%%?%%!%!!%%%%%!!!%??%!??!?!%%!!!%!%%?!?%!%!%%%?!!%%%%%%%!%?!%!%?!%%!%%%%%!%!!!%!??%!%%%%?!%%?%?%!%!%%!%%?%??!%?%%%%!!%%%%?!%!!!%!%!?!%%?!!?%!%%%%%%!%!!!!%!%%%%!!?%%!%%?%!!%%%%%?%%%%!?!%%%?%!%!%!??!%%%%?!?%!%?!??%%%%%%!%%?%%%%%%??%!?%%!???!%??%%!%%?%%%%%%!%!!!%%?!%!!%%!!?%%!?!%!!?%!%!!?%!%%!%%!%?%%%%%%%%%!%!!%?%%%!%%!%%%!%%%%??%%%!!!%%?%%?!%!!%!%!!%!%%%%%%?!!%%??%!%??%%%!%!!!?%!!%!%!!?%?!!%%%%?!%!%%!!%!!%!!%?%??!!!%!!%%!%%%!?%%!!!%?!%%%!!%%!%%%!%%!??!!?!%%?%!%%!?%??%%!!%%%%?%%?!!!!%!%!??%!!%%!!%%%!?!!%!%%%!!%!!%!%?%%%%!!?%?!!%%%!%?!!%%!!%%!!%!%%%!%!!!!?!%%?%%?%?!%%%%!!%!!!%%%%%!%!%!!!!%%%?!?%%%?!?!?%%?!%%!%!%?%?%!!?%!?!!%%?%!%!%!%%%%%%!%%%%%%?!%!%%?!%!%!%?%%!%!!%%%!%%?%!%%%??%!%!%?!%!%%??%%%%!?!!%%!?!%%%%%!!%%%??!%%!%?%!!%%%%%!?%%%!!%!%%%!%?!?!!??%%?%?!!!!!%!!%!%?!%%!?!%!!!!!!%%%%%??%%%%!!%!%??%??%?!!%%%%!!%!%%%%!%!%?%?!!!?!%%?!!!??!?%%%%!?!%%%%?!%!!%%%%%%%!?!!%%??%!!!%%%%!%%!!%%%%%%!%%%?%%!!%!!!%!%%?%%%%%?%!!%!?!!!?%!?%%%%%%!%!!!!%%%%??%!%%%%%%!%%%%!%%?!!%!!?!!?%?!%%!%%?%%!%%!%%%!!!%?%%%?!%%!!!?%?!%!!!??!!%%%%%%%!!?%%!?%??!%?%%%!%%?%!%?%?!!%%!!?%%!%!!!?%!%%%??%%%!!%%%!%?%%%?%!%%%!?%%!%%??%?!!?%!%%%!???!!%!%!%!%%!!!%!%?!%!!!%%!%!!%%!!!%!?!!%!%%!%?!!!%!%%!%%%?!%%!%?%%%!%%!!?!?%%%!%%!%%!%%%!%%%?%%%!%?%!%!?!%%%!?%%%!!%%!!%%!%%!%%?%%!%!!?%?!!!%!%%!%!!%%%!%??!!?!%%%!!%!%?!?%%%%%%!%!!%%!?!?%!%%%!!%%%!%%%!!%%?%!!?%%?%%!!!!%%%!%%!%%%?%!%%!%%!%%%%?%%%%!?%?!!%?!!?%!!!!%%%!%%!%???!?%%%!%!%!!!%%%???%%%%!!!%!!!%!!!%!!%!%%%!%%!!!%!!?!%%!%%!!!!???!?%?!!!!%!?%?!%%%??!%%!?!%%%?!%?!%!!!!!!%%%!%!%%?%%??!!%%?!%!%!%%!%!?%!?!%!%?%%!??%!%%%?%!%%!%%?%!!%?%%%%%%?%%%%%%!%!%%%%?!%!!?%%!%%!?!%%%???%%%?%%%!?%%%%%!??!!%%?%%!%!%%%%%%%%!%!%%%?!%%?%!%!%!?!%%%%?!!!%%!!%%!!!!%%%%?!!?!%!%!%%%%?!%?%!?!!!%!%%%??%?%!%%%%!%?%!%%!%%?!?%%!%!!!!%!%%%?!!%??!%!?%%!%??%?%%?!%%!%!%!!?!!%!%!!%%?%!%%%!%%%??%!%%!%!?%%%?%%?!%%!?%!%%%%%%?%%%!!%!%%?!%!%!%%?%%%%!?!%%!!!%%%?%?!?!%%?%!%!%%%!!%%!!?!??%!!%%%%%!!!%%%?%%%%!%!%!??%%!%!!%?%%%!?!!%%%%!?!%!%!!%?%%!!%%%%?%%%%!%!??%!?%%?%%!!%%%%%%%%!!!%%!%?!!%!%!!%%%?%??%?%?!%%!%%!!?%%!!!%%%?%%!%%!!%%%??%%%%%?%%?%%%%%%%?!%?%!%!?!%%!!%!%?!!!%%%%%!!%%!!!?%?%!%!!!%%!%!%!!%%%%!!%!!!?%%%%!%!%!?%%!%!??%?%%%!!!!!%%%%!%%!?!%!%?!%%%%%!%%%%%!!%!?%%%%!%%!%!%?%%!%?!?%%%?!!%!!!!?!?%%!%%%!!%!%%%!?!%%%?!!!?%%?%%%%%!!!??!?%%!!%%!!!%!!!%!%%??!!!?%????%%!%%!%%!!!?%?%!?%%%%%!%%%!%%%%!%!%%!%%%%!?!%%%!%?!?!!%!??%!!!%?!%%!?%!!!%!!?%%%%!%!%%!%?!%!%!%?%??%!?!!%!??!!!???%%!%%%%%%%%%%%???%!?%!!!?%!%%!%%%!%!!??!!%%%!???%%!%%%%!%!%!?%!%%%!%%%!%?%!%%%!!!%%!%%%!?%!%%!?!!!%?!?%?!%%%?%%!%!%%!!%!!%%%%!!%?%!?!!%%!!?%%%!%?!!!!!%!%?%%%!%??%%%!!!?!%!%%!!!!?%%!!!!!!??!%%!%?!%!%!%?!!!??!?%!%%!?%%!!%!%!!!%%%%%%%%?%!%%%?%!%?%%%%%%!%%%?%%?%!!!%!%!?%%%?!%!!%?%%!%%%!!!%%%!!?!??!!!!%%%!!!!%!%!!!%!!?!%%%!%!%!%%%%%%?!%?!?!!!%!%%%??!?%!%!?!?%!!%!!?%%?!%!%%?!!!!?%%%!%!?!?!!?%%?!!%%%%?%%!?%%%%!%%!!!%%%%!%?%%?!%%?%%%!!?%%%?!%%?%!%!!%%?%!?!%%%%!%!%?%%%%%%%?!!!%?!%%%%!!%?%!%%!!?%%%!!!!%?!%%%!%!%%?!?%%%?%!%%!%%?!%%%%%!!??!?!?%%!%!!??!%?!%%%!!%%%%?%%!%%!%?!?!%!%%%%!%?!%??%?%?%!%!?!%?!%?!%?%%!%?%%!?!!%%???%?!%!?!?%%%!!?%!%!?!%%%!%??%%!!%!!%!!%!%%%%?%!?%?!%%!!!!%!%%!!!%%!?%%%%!!!!??%%?%%!?%!!!!??%!%%%?%%!?%%?%%!%%?%??%%!%?%?!?%?!%?!!%%%!%%??%%%??%?!%%%%%%%!%%%%%%%%!%!%!!!!%?!%%!?!!%%!!%!%%%!%!!!%!%?!%%%%!?%%%?%%%%?%?%??%%?%!%!?!%!!?!%%?%?%!!%?!!!!?%%?%%!?!???%%%%%?%!!?!%%?%%?!%!%?%?%%%!!%!%%%!?%%%!%!!%%!!!%!%!%%%%%%??%%%%%?%%!?%%%%%%?!!!%%!!!%?!?!%%%!!%???%%%%%%%!!%%!?!!%%??!%%%!%%%!%?%!?!%%!??%%!%!%?%??%%%%?%!!!!!%%%!%%!%!??!%!!%%?!%!%?!?%?%%%%!%?!%!?%%%?!!%!!!%?%%%%?!!!%?!%%%%?%??%?!!%%!!%?!%?!!!%%%%!?!%%!%!!!%%?%!!%%?!?!!!!!??%%%?!!??!%%%%?!%%%!?%!?%!!%!?!%!!%%%!%%?!%%?%%!!!!%!!!%%!%!!%%%!%?%%???!?!?%!%!%?!%%?%%!!!%%?%??%%!!%%?!%!!%!%%!%%%!!%%%%%%%%%%!?%??!!%!?%%!%?!!%%%%!%?%!!?%%?%%%!%%!!!?%!%!!!!!%%%?!?!?%%!!?%%%%!!!?%!?%!?!!%?%?%!!!!??!?%%%%%%?!?!?%?%!%?!?%%%!!%?!!!!%?%?%!%!%!?%%!%?!%%%!?%%%!%!!!%%%?%!?%%!%%!!!%%%%%%!%?!%%%!?%!%!%%%!!!?!!!!%!!!!!%!!%%%!!?%%%?%%!?%?%%%%?!%?!%!%%%!%%%!%!!!!%!%!%!%!%!%!!!%?%!!%?!!%??%%%!!!%%!%%%%%%!!%?!%%?%%%%%%!!??!%!%%!%%%?%!%!!%%%%!%?%%%%%?%?!!%%%%?%?!%?!%%!%!?%!??!?!?%%%!%%%?%?!!%%%!!%!!%%%%%!?%?!%!%!%%%!!%?!?%?!%%?!?!!??%%%?%!??%%%%!%%!%%%%%!?%?!!!?%%?!%!!?%%?%??%?%%!%%?%%%!!!!?!!%!%%%%!%!?%!%?%!%%%%!!!?!%%!!?!%?!%!!%%?!%?!!?%%?%?%?%%!!!%%%%%%!!?%%?!%%%!!??!?%%%!!%%%?!%?!!%!!%!!%%%!?%?%!%?%?%!%%!%%%?%%?%%!%%%%%%!?!%!%%??!?!%?!%?!%%!%!%!?%%!%?!%%%%!!!??%%%?!%%%%%?%!%%%%%%!%!!?%!%%?%!%!!!%?%%%%!!%%!?!%%%!%%%!%!%!%%%%%!!!!%%%%%%?!%%%!%%!%?%?%%%%%?%!%!!!!%?%!%?%%%%!!?%%%?!!!%??%%!%%%%!?%%%!!!!!%!%%!%?%%?%%!??!%%%%?%?!%!%!%%%!%!!%%%%!%%%%%!%!%%!!%!%?%%!??%!%%%!!!!%%%%%!%%%%!?%%!%!?%!??%?!%!!!%%??!%%?%!!!%%%?%!%?!!%%!%%!%?%!!!?!%!!%%%!%!%%!%%!%?!?%%!%!!???%?!%!!%?%??%!%!%!%!!?%%%!!!!?%?!%%!%%%!!%?!%!?!%???%%%!!!!!%??%%%%!?%%%%?%%!!!!%!%%%%%!?%%%?!!!?!?%%?%%%%%!%!%%%%?%!%!?!!!?!%%%%%%%!%??!!??%%%!%%%%%%!%!%%%!%%!%?%!!!!!%%?!%?%%%!!%%!%%%%!!?!!!!%!!?%%%?!!!%!!%%%%%!%!!?%!!?%!!!!%%!%!%!%!?!%!!!%%%%??%??%%!%?!%!!%!%!!!?%??%%!?%?!?!?!%%??%%%%%?%??!%?%%!!%%!!%?%%%%%!%!%%%??!?%?%!%!%%!!%%!%?%!!!!%!?!%?%!!%?!!%!!!%!%%?%!%!!?%!!?%%%%?%!%!%%%%!%!%%%?!!%%%!%!!%%%!%%%%%%!??!%%%%!%%?!%%?%%%%%%%??%!!%%?!%%%%??%!?!%!?%%!!%!!%!!%%!?!%%%!%?!?!%?%%%!%?%%%%%%%!?%?%%!%%!%!!%?%%%%?%?%%!%%%!%%%!%!%?!%%?%%!!!??%?%!?%!!?!??%%!!!%%%%!!%?!?!%!%%?!!%%%?%%?!?%!%%%!?!?%!%!%%%!!%!%??%%%%!!%%?!%%%%!%???%!%!!%!!!!%!!%!%?!?%!?!!?!%!!!?%?!?%%?%%%%!%%?%%?%%%%!!!!%?%%%%!%%??%!%!!!%!%!!%%%!%!!%?!!%%%??!%!?%?!%!?%%!%%%?%%!?%%!%%!%%!%%??%%!?%!??%%?!%?!!%!!?%%%!%!%%%%!!!%!!%%?%%%%%%%?%%?!?!%?!!?!%%%!%!%?%!%%??%?%??!%%?%?%%?%%%?%!%%%%%%!%%%?!?%%%???%%!%%%!!??%%%%%%!!%??!!%!!%%%%!!!!?%!%%!%!!!?%%!%%%%!%%!%%%%%%%%%??!!%??%??!!%%!?%%%!%%!?%!%!!!??%?!!%!%!%%?%%%!!%!?%%!%%%!%%?!%%??!%%!%%%!%%!?!%%%!%?%%%%%%%?!!?!!!%!%%?%%%!?%?%%%%!?!!%?%%???!%%?!!!!%%%%%%%!%%%%???!?!!?!!!!%!%!?%%!%%?!?%%!%%%%%??%%%!!%!%?!%!%!?%!%?%%%!?!!%?%??!%?%%!%%%%!%?%!%%%%%%!!%!%!?%%!??%%%!%?%%%%!%%!!%%!%?%%%%%%!?%!!%%%!%?!%!%%%!%%??%%%!%!%%?%%!%!!!!!%%%!%!!%%!%%%?!!%!%%!?!%%%%!%%!!%%!%?%%%%%%!!!%%?%?!%???%%!%%%%?%!!%%?%%%%?%%%!%!??%?!!%?%%!%!%!!%!!!%!%%%%!??!??%!%%%?%%!?%?!!%%!%%%%!!%?!%%%!?!%%%%%!%!%%?%%%?%!!!!%!%?%!%%?!?%!%%%%%%%%%!?%%!%!?%??%!!%!%?%!%?!!%!!!!!!%??!%%?!!!?!%%!?%???!%%!!%%%?!%?%??%!%%!%%!%%?!!%!%%%!%!%%!!%%?!??!%%!!%%%%?%%%%%!%?%%!%%!%%!!!!%%%?!%!%!!%%?%%!%!!%%%!%%%%%?!%!%%%!%!%!%%%%!%!%?!%%%%%%%%%%%!!%%?%?%%?%!%?%?%%!?!%?%%!?%!?%???%!%?%%!%%?%?%%%%%%!?%%!?%!%?!%%!%!%!?%%!!!!%?!%%%!!!?%!!%!!?!%%!%!%%?!?!%!!%?%?!?%?!%%%%!??%%%!!%%!!??!%?!%%?%!%!!%%??!%%%!?!%!%!%!!%??!!!!%!?!!%%%?!?%?%!%!%?%!%!%%%%!??%%%%!%!?%%%!?!!%%!!!!%%!!%%%%?!!%%!?%%%%%!!!%!%%%%%%%!?%!!!!%%%%?%?!!?%!?%%%?%!%!%%%%!%%!%!!??!!?%%%%!%!%?%%%%%%?%%!!!?!%%%!%%!%??!%?%?%%%%!%?%!%%%%%??!%%????%!%%!!!?%!!%!%%!%%?%??%!%?%?%%?!!!%%!!%%%!%%?%!!%%??%?!%%!!%%%?%!%%%!!%!%%!?%!%%!!%!%%%%!!!!?!%!??!%!?%?%%%%%!%%%%!%???%!!!!!!!!!%%%%!%%%%%%%?%%?%%%?!?!%%?%%?!%?%!!%%%%%!%%%!!?%%%!%%%%%%!!!!%?%?%!!!!%%!%?%?!!!!%%??%!?!%!????!%?%%!%!?!!!!?!%!?%!!%%%%%!?!%%%%!%?%!?%?!?!%%!%!??!!%!%%%?!!%%?!?!%!!!!%!?%%?!%!%!%%%%%!?!%!%!!%%!%!%%%%%?!%%%%?%!?%!??%!!%?!%%!!%!!%%%!%%!?!!!%?%??%%!%?!%%%%!!?!?%!%?%%%%%?%%%?%%%!!%%%?%%%%?!%!?%!%%!%!%!%%!%!!?%!?%%%%%!!%!?!!%%!!???!%!!??%!!%!%%%!%%%%%!%!?!%!!?%%?%!?!%!!%%!%%!?%%%!?!%%%%!!%%!%%%%%%?!!!!%?%?!!!?%%%!%%!%?%%%!!?%!!%?%!%%%?%!?!!%%%?%%%%?%!!??%%%%%%?!%%%%!%%?%!!%%%?!%%!%!?%!%%!!!!!%?!!%!!%!!?!%%%%%%?%%!!%%!%%%%%%%!%%!!!%%!!!!%%?!%!!?%%!!%?%%?%?%!???%!%!?%?!?%%!!%!!%%?!!%!!?%%!!?%!!???%%!!%%?%%%%?!%%%!%!?!?%%%!?%%%?!!%%%?!!!%%%!%!%%?!%%!!?%%?%%%??!%%%?%%!%%?%%%!%%%%%!%!!%?!%%%!%!!%?%%?%%%!!%%?!!!%!?%!!%!%?%%%?%%%%%%%!%!%%!%%!%%%%%%?%?%%%!%%?!!!%%!!!%%%?!!??%!?!%%%%?!%%!%%%%%!?%!%%!%%%%!?%%!%%!%!%!?%%?!%%%!%!?%?%%?%?%%%%%!!!%%?!!?%?%?%!?%%???%%!%%%%%%%?!!%!%!%%%?%%%%%%!%%!!%%!!%!%%%!%!%?!?%%%!%!%%%!?%?%!!!%%%%??%%%%?%??%!%%%%%!??!!??%!!%%!%%%%%%%??%?!%%?%%%%%%%!!%!!%!!??%!?!%!!!%?%%!!%%%?!%!%?%?%?%%??%%!!%!!%%%?%%%?%?%?!?%%!%%????%%%?%?%%?!!?%%%!%??%%%%??!%%!%!%!!%!%%!%?%!%!?%?%?!?!?%%!%?!!!%?%!%!%%!?%%!%!???%!%%%!?%!%%!??!%!%%!!!%??%%!%!%%!%!!!!%%%%%!%%?%%%%%%?!%!%!%%%%%%?!!!%?!!!%??!!!!%%%?%%!?%%%%?!!?!%!?%!%?%!%?%%?%!?%!%??%%!%!!!!%???%%%!!%%%!!!%%?%?%?%!!!!%?!!%!?!!!%%%%%?%!!?!%!%!!!?%%!!%%%!!%%??!!%%%!!%%?%!!!%%%!%%!%%%%%%%%%%%!!!%!!%%%%!!!%!%%?%%!%!!!%%%!%%?%%%%%%%!!%?!?%!!!?!%?%%%%!?!?!%!%%!%?%%%!!?%!!!!%%?%%?!%?%!%%!%%%%?!!%%!%?%%!%?!%%%?!!!!%!%!%%%%%%%%!?%%%%%%!?%!!?!%!%%%!?%?!%?%%%%?%!%%%??%!!!!!!!!??!!%%!%!%!!!%%!%%%!%%?%%!%!%!%%%!!!%!!!!?!!%!%%!?!?!%!%!!!!!%%!!%%%!!!!%%!!%?!%%%%%?%!%%!?%!%%%!%%%!!!%%%!%%%!%!?%!%%!!%??%%!%?%%%!%!%!%?%!%?!!%?%%%%??%%%%%!%!%!%?%%%!%%!?%!%!%%%%%!%%?%%%?!!%%%%!%?!%!!!!!?!??%%!%!%%%%!!!!%%%!?%!?%!!%%%%%%?!!!?!!%!!%?!?!%!%??!%?%!%%?%!?%%%%?%%!%%!%!?!!!!%%%!!%!%%!%?%!!!%!%%!%!%%??!!?%%!%%%%%%!%%%!!%%%%?!?!%!%?%%!%%%%?%%%?%!!!%?%%%%%%!!??!??%!%%!%%!%%!!%??!??%%%!%!!!!%%%!%!??%!!?%%!!?%%!!%%%%!?!!!?%!%!%%?!!%%%?%%%%!!!!!%?%!%%!%%!!%%?%!%!!%%!!!%%??%%%?!!%%%%!?%?%%!?%!?%%%%?!%%!%?%%%%?!!!!!!!?!!?%!!?%%?!!?%?!!?%%%%%%%?!?!%%?!!!!%?!!??%!%?!?!%!!!%%!%??%!!%!%%%!!%!%?%!%%?%?!%%!%!!%??%%%?%!%!?!!?!?!?!%%!%%?!%%%?%%%!?%%%%%%%!?%%!!%%%!!!%%%%%%!%!%?%%%?!!%%!!!%%?%%!%%%?%%%?%!?%!?!%%%%%%%?%%%??!%!!%!%!%%!!?!!%%%!%?%%%%%!%!?!%!%%!%!%%!?%%%%!%!?!%%%%%!!!%?%?%!!!%%%?!!?!%%!!!%!!%!%%!!%%?%!%?%%%%??%%%?%?%!!!%!%!%%%%!%!!%%%%?%?!!!??!%%%!%%!%?!%?!%%!?%%?%%%!!%!!%%!%%%%%%%%?%!%!%!!%%%%?%%%%!?%%!%%!%!%%%%%!!!?!%!!!?%%!%%!%!!?!!%!!%?%!?%%!!??%?!%%!?!%%!?!%%%%?!%%??%?%!%%%%!%%!??%!!!!%%?!%!%%%!%!!%%!%%%!!%%?%!%?!%%%%?%%!!?%!%%%!!%!!%%!%!!?%%%!!!%!%%%%!%%!%?!?!%%?%?!%%%%!?!%%%?%??%??!!!!!?%%%??!%%?%!%!!!%%?!?%?!%?%!!%%%%?%%%%%%%%?%%?%?!!!?!!%%%%!%%%!%%%!!%!?%?%?%?!%!%%!!!?%!?%%!%!?%%%%%%%?!%!%%%%%%!?!!!%!%!%%%?%?%!!!!!?%%!?%?!%?!%%?%!!!!?%!%!%%?!%%%!%!!%%!!%%%!%!??%%%%%%!!%?%!%%%!!%%?%%%!%%%%!!%!%!!%!!!?!!!!%%%%%%?%!!!?%!%%%?%%?!%%%!!%%!!!!%%%%?%!%%?!%?%!%%%!%%%%!!!!%!%!?!%!%!?%%%!!%!?!%?!!?!?%!%!!!%!%%%?!!%!%!%%?%%%%%%!%!!!?%%%%%%%!%%!!%%!%%!!%!???!!%%%%!!?!!%%%?%??!?!%%%?%%!%%!!!!%?!?%%!!%??%?%%%%%??%!!!%%%??!!%%%?%%%!%%!%!!%%?!%%%!%!!?%%%??%%?!%%?!%%%%%%?!%!%%%!%!%!%!%!?%%!%?!%!%%!%%%!!%!!?%!?%%%!!%?%??%%!!%%?%!?!%!%%!!%?%%%%?%%?!!!!!%!%%?%!!%%??%%?%?%%%%!???%?!%!!%%%!?%%%%??!???!!%%!!%!!?!!!%%!!!%??%%?!%%%%%%%!?!!%!%%%!!%?%!?%!%?!?!?!!!%%%%%%!%%?!?%!!!%%!!?!!!!!%%!!!!%%!%%%%%!%%%%%%!?!%?!???%?%%%???%%!%!%!%!!%%%%%%?!%!!%!%%%!%%%%!%!%!%%!!!%%?%!%%!%!!!!%%%!?%?!%?%!%?!%%?!?%!%%%!!?%%!!%%%!!?%%%%%%!%!%%?%%?%!!?%!!%%%%%!!%%?%?!%%%??%%%!!%?!%%%?%%%!%%!%!!!?%%?%?%!%%!%!%%!!%!%%!%?%!%%!!%?%!%%?%%?%%!%%?!?!%?%%!?%!%%%%!!%%?%?%!!!%%%!!%!%%%%%%!?%!!!!?%?!%%%%?!%%?%!!%%%%!%!!%%%%%!%%!%%%!%?%%!!%%%!%?%!%%%!!%!?!%%?%!!%?%%%!!%!%!%!?%?%!?%?!%!%?!!%%%!??%%%%!%?%%%%%%?%!!%!!%%%%!%!!%%%!%%!%!%!!%!!%%!%%%%?%%?!%%?%!!!%%!%!%%!!%??!!%%?%!??!%!%%?!%%?!%%%%%%??%%!!%!!%!!%%%%%%%!??%?%!%!%???!!%%!!!!%%%!!?%?!!%!?!%!%!!%!%!?!!%%%%!%%!!%!%!!%?!%%%!%?%%!%%!%%!!%%%%%!!%!!!!?!??%!%%!!%??%!?%!!%%?!!%%%!!%!!%%%?%!!!?%!!?!!%%%!!?!%!%?%%!!!?!%%?!%!!%?!!%?%%%!%%%%!%!%%%!?%%%!%%%%!!!%%%%%%?%!%!!!%??%%!%!%!?%%%!!%!%!!!?%%%%%%!%%?%%%?%!%!%%!%%?!%!%%%%?%!%!%%%!%!%??%!%%%!!%%%%%!%!?%!!%?!%%%%?%???%?!??!%!!%?%!?%%%?%!%!!%!!%%%%%!%%%%%!%%%%!%%%%%??%%!%%!%?!!%%!!!%?!%%%!!!%!%!!%%%?%%%!?!?%%%%%%%!%%%!!%?%%%!!%!%%?%%%%!!?!!%!??!!%%%%%??!?!%??%%!?%%!%!%%%!!%%!?%!%%?!?%%%%%%%!%?!%%!!%%%%!?%?%%!??%%%!%%!%!!%?%!!!!!!!%!%%!%%!%!%%%?!%!?%%%?!!%%%%%?%?%%!%%%!%%!%%%%!!%%?!%!??%%!%%??%%%%!%!%!!?!%%%?%%?%!%%!!%?%!%!%!%!%%!?!!!%?%!?%%%%%%%%%??%%!%?%%%!!%!%%!%%%!?%?%??%!%!!%!%%!%%???%!!%?!%?%%?!%%%%%!%%%!%?!!!!!!?%%?%!%?%%%!!%!%??%!!%!!?%%?!%%?%!%%%!!%!!??!!!?%!!%??%???!%!?%%%%%%!!!%!!!!!%!!?!??%%?%%!??!%%%?!%%%%!!%%!%!%%??!?%!%%%?!!%%?!!!?!%?!%!%?!%?%%!%%?!%%!!%%?%!!%?%%%!%?%%!?%%%!!?!?%%!!?%!%%!%??%?%%??%?%%%!%!!%!%%%!!?%%%%?%?%!%%?%!%!%%?%%!!%%%?!?%%!!?%!%%!%%!%!%?%%%%%%%%%?!%%%?%%%??!%?%%?!%%%%%?!%%%!!%?!?!!%!?%!%!?%?!?%!%%%%%%%!%%%?!!%!%!%!%!%!%!%%!%?!!!%%?%!?!!!!!%!!!%%!%%?!?!!%%%%!%!!?%%%%!%!%%!%!%%!!%???!%%!%!?!!?%!%!%?%?%%%%!%!%!?%%%%%%?!!?%%%%%?!%%?%!%%%?!%%%%%!%??!!%!%%!%?!!%%%!%!%%!?!%?!?%!%%!?!%?%!%?%%!!!!%%%%!%%?%?%%%%!?!%%!?!%?!!%%!%%%!%%%??!%%%%!%%%%!?%%!?%%%!%!%!%%!%!%!?%!%%%!%!%!%%!!%?%%%!!%!%!%%%%?%%?%%%?%%!%%%!%!%!!%%%!!?!%!!!?%!%?%!%%??!%!?%%!!%%?%?!%%%!!???!!?%%!%!%!!%?%!?%?%%!%%!!!%!%!%%!!!!?%%%%!?%!!?%%!?!%?!?!%%%%%!%!!%??!%?%%?%!%%%%?!%!!!?!%??%!?!%%%??!?!%%%!%%%?%!!%%%!?%?!%%!?%%!?%!%?%%!%%%%%!%!?%%!%?!?!%?%??%%?%!%%?%?!!%%%%?!%%%%!?!%%!%%!%%%%%!%!!!%%?%%!!!!%%%%?!?%?%%!!%!%!%%!?!%%???!%%%%%%!%%!%%%%?!!%?%%?!%!%?%%%%%!!%?%%%%%?%!%%%!!%%%%!%!%?%%%%?%%%!?!!!%%!%%!?%%!?!!%!!%%%!!%%?%?%%?!%!%%!%%!%?!!!%!%?!!%%%!!?%!%?%%!!!%!%%%?%!!%%??%%%!%!%%%?%%%%%!%!%%%%%!?%%??!%%%%%?!%?!%!?!%!%%!%?%%?!%%?!!%%%?!?!!?!%%%%%!%%!%%%!%!!%%%!!?%%%!!!%%!%!%!!?!%???!%%!%!%%!%%%%%!!?%!!%%!??!%%?%?!!%?%!!%%%?%!%%%%%?!?%?!!!%%%%!%!!%%%?%!!%!!!%%!%??%??%!?!!%!?%!%?!%%!!!?%?%!!%%%!!?%%!%?!!?%!%!%%!!%!!?!!!%%%%!%!!?!!!!???!!!?%?!%?%%!?%%%!%!?%%%%??!!%%!!?!%%%%%%%!!%?%?%%%%%%!%!%!%%!?!!%%%%%%!%??%%!?!%%%%!!%???%?!%?!%!!!!!%%!!%?%!?%??!!!!!?!%?!!%?%%%%%%%%%!!%%%%%!%%!!!%%%!%!!?%%?%?%%%?%%!%??%?%%%%%!!%%!%%%!%%%%!%%%%%!?!%%%%!?!?!!%?!%%%%%%!?%%!!%!!%??%!%%?%%!%%!%%!%%!?%?%%!!!!??%%%??%%%%%%%%!%%%%!!?!%?!%??%%%%%!!!%!%!%%%!%!%?!%!!%%%?%%!!%!%!%%?%!%!%%%!!!?!%%!!%%!%!!%!!%%?!??!?!%%!!!!%%%%!%%?%?!?%!!%%?%??!?!?%!!%?%!!?!!%%%%%%?%%!!%?%%%!%%%%!%%%%%%%%%??!!?%%%%!??!??%%!!!%!?!%%%!!%%!%!%%%%?%%%%%%%!%%!%?%!!%%%%?!??%%%?!!!%?%!?%%%%%!!%!%%%!%!%!?%!%%??%%%%%%!!%%%%%%%!%%?%?%!%%%%!%%%!??%?%!!!%!!??%!%%!%!!!?%%%%!%%!!?%!%%?!!!%%!%!%%%%%?!%!%%!!%?%!?%%%%!!%%?%!!!!?%%%!!!%%%!!!%%%%?!!!%%!%?!!%%%%%?!%!%!%%%!%?%?!??%!!%!%%%%!%%?%!!?%%?!?!%!!!%%!%%%!%%??!%%!?!%%%%?%!%%%%?%%%!%%%!!%?!%??%%%%%!!?%!?%!!!%%!!%!!%?!%!!?%%!%!%?!%%%%!??%!%!%%!!%!%!!?%%%!!!%%?!!!%?!!?%%?%?%%!%%%!%%?%!%!!??%!%%%%!?!%%%%!%%!?%%?%%!?%!%!%?!%%%%%%???%!%?!%%%%?%!%!%!%!%!!%%!!?%%?%%%%!!%??%%%%!%!%%!!%%!!?%??%!%%!%?!!%%!%!!%?!%%!%%!%!!!!%!?%%%!!!%!!%!%%!!!%!%%?%%%?%%%%!%%?!%%!%%!!??!!%??%!%%%!%!!!%%%%%%%%%!%??%%%!%%!%!%%%!%%%%%?%??!%!%%!%%%!%%%!!!?%!??%%?%%%%?!%%%%%!%%!!!%%???!!?%%%!!%!!%?%%%?!!%%%!?!?%!?%!%?!?%%%%%%%!!%!?!!?%!!!%%%!%%%%!%?%!!%%%%%!%?!!%!%!!!!%%%%%%?!!?%!?!?%?%?%??%!?%%%%%%!%!!%?!%%!%%!!%??%%!%?%!%!?%!%!!!?%!?%%!??%%%!%%!?%%%%!?!%!%!!%%!!?!%!%%?%!%%%%!!%%!%!?%!%%%%?!%?!%%%%%?%?%?!%?%?%%!!!%!%?!%%?%%%%!?!!%%%??%!!%?%%!?!%?!%%!?%?%%!%!?!%!?!%??!?%!%?!%%%!?!%!!%!!!%!%%?!%?%%%%??%%?%?%%%%%%%!!!%!!%%!%%%!%%%%%!%%!!!!?!!%!%!%!?!!?%!%!%%!!?!%?!%%%%%%!?!%%%%??!!?!!!%!%%?%?%%%%!!?%%%?%!?!?%%%!!%!!???!%%%!%%!%%%!%?!!?%%?!?!!!%?!!%!%%!!%%%??!?!%!%%?%%%%?!%?%%%!!!!%!%%!%?!!%%%%!!%!!%!%%?%%%?%%?!!!!%!!!!%%?%!%%?%?%%??%%%%%%%%%%%!%!?!!%%!!?%!%!%%%?%%%!?!%%%%%%!!!!!%!?!%!!?%%?%??%?!!%%%%!%?!%!%%%%%!%!?!?%%%!%!%?%!%%%!?!!%%!%%!?!!!%!%%!!%?!?%?%%?!%?!??!%!%?!%?!%!%!?%?%??%%??%%%?%?%!%%!%%!?%!!%%!%%%%%!%!!?!!!!!!%!%!%?%!%!%%!%%%?%%%%?!%?%?%!%%%!%%%!%%%%%%??%%%?!?%%!??!!%??!%?!%!!%?%!%%!!%!%%%%%%%!!%%?%!!?!%%%!%!!!!!%?!%?%!?!%%%%%%%!%%!%%!?%%!%??!!%%%%%%%%?!%!%%?!??%%%%?%!%!!%?%%%%?!!%??%%%!?!%%!%!%!!%%%!!%%%?%%?%%%!%?!%%%%?%%%!%?!?%?!%%%!?%%!!%%%%!?!?%!%!%%!?%%%!%!?!%%??%!%%%?%!!!%!!!%!%%%!?%%!%??%!%!%!!!!?%!??!??!!%%!%%!?!%!!%!%%%%?!%%!!!%%%!!!%%?%%!%!%?%%!??!%??!!%%%?!!%%!?%!?%!%%!!%?????!!!?%?%%!%%%%?%%!!?%%%!!!!%?!%!%%%%!?%!?%%???!?%%%%%%%%!%%%%%??%%%!!%!!%!!?%%%%!%!!!?!!%!?!%?%%!%%%!!??!%!!!%!!!?!%???%%!%?!!!?%%!!%%!%%%?!%!?!!%%!%%?!?!%%%?%!!%%%!?%%!%%!!%!?!%%%%!%%%%%!%?%%%!%%!%!?!!%%%%%%%!!!?%%?!?!!?!!!%%!%%%%!%!%%%%%%%%%!%%?!%?%!%?%%?!?%%!%%!%!%%%%!?%%!%%!%!%%%%!%!!%!!!%?!%%?%%%!%%!%%%%??%!%%%%?%!%%%!?!%?%%%%%!%%!!%?!%%%%!?%!%?%!!%%!!!%!!!!?!%!!%?%%?!!%%?%%?!?!%!%?!%%??!!!%%%%!??!%!%%%%%!!!%!%%?%%%!%!%%!%!!%!%!%!%%%%??%%?!!!!%!!%?%!%%%%%%%%%?!%%%!?%?%%%??%%?%!%?!!%%?%?%%%!%?!%%?%%!%!!%%%%!!!%%!?%!%?%!!?!!!%!!%%%!?%%%%%%%!!!?!!%?!!%%?!!!!%%%??%!!%%!!%%%%!!%%???%!?!!!?%!%%%!%%!?%%!!%!%%!!!%%%%!!%%%%%!%%%!%%!%!!%!%%!?!%???!%??!??%!?!!?!!%!%%!!!!!!??!%!!%%!!?%???!%?!%!%!%!???!%!%%%%!%?%%?%!!%!%!?%!?%%!%%%?!%!!%?!!%%%!%%!?!%!!%%!%!%!%!?%!%%!%!%%?%%%!!%!%%%?!!!?%%!%!!!%%%??%!!?!%%%%?!?%%%%%%%!?%??%!%%%%?%%!?!?%%%!?!%%!!?%!!!%?!!%%!%%!%!!!!%%!!!%%%%!%!%!!%!%?!%%!%!%!!!!!%%%!%%%%!!%%%%?!%%%?!%%!!%!?!??%%!%%%?%!%!!!!!%%%%%!!%?%?%?%%?!?%!!?!%%%%!!!!!%%!!%%!!!%%%!!!%?!%!!%!!!!!%!!%%!!?!%?!?%%%%??%!%!?%!!!%!!?%%%%%%!?%!!%%%%%!?%%?!!!%?%!%%%%%!%%%!?%!%!%?%!!!!%%%!?!!%!!??!?!%!%%%!%!%!??!%%?%!%?%%%%%?%??%?!%!?!!%!!!!%%?%%%!%!%?%%!%%%!%?%!!!%%!!!%!!!!%%%!%%!!!%!??!!%%!?%!%%?!!%!!!%%%%%%%?%?%%%%!%!%%?!%!%!!?%%?%%!!!!%%%!%%!%?%%!%%?%!!%%%%!!%!%%%?%%%!!%%?%%!%?%?%%%%%?%%!?%!%%%%%!!%%!%!!!%?%%!?!%!??!!?%%?%!???%%%!%!!!%%?%!?!%?%%%!!%?!%%%!!%%%%%%!?%?!%!%!!%!?!?%!!?%%?%%%!?%%??%!%?%%!!?%%!?%%?%!?!!%!%?%%%!%%%%%%%%!!?%%!%%!!%%%!%%%%%!%?%!??!?!%!?!!!?%!!!%!!%%%%%!%?%!!%%%!??%%!!?!?%%?%%?%%%%!%!?%%!%%!%?!!!?%%%%%%%!%!%??%%!%%?%!!?%%?%!?%!%!%!!?%!!!%%%!?!!!%?!??!!%%!??!!!!%!!?!%!%??!%%%?%?%?!?!%!!?%?!??%!%?%!%!!%%!%%%%%!%%?%?%%!%!??%!%!!%%%?!%%%?%%%%!%!!%?%%!!!%!?%!%%%%%%%%%%%%%!!?%!!!%%%?!!?%%%?%%%!!?!!%?!!%%%!%!???!%!!%%?%%%??%%%%!!?!%%?!%%!%%!%%!?!!%%%!%%!%?%%!!%?%%%!%%%!!%%?%%?!!%%%!%!!?%!??%%!%%%%!%%!%%%%%?!%%%%%%%%!%!%%?!!%%!%!%%%?!!!%????!!!%?%%????%%%%!!%%%?!?%?!%?%!?!%%%!%?%!%!%!%!!%%!%%%%!!%%%%%%!?!%!!!%%%%%%??%!%%%%!!!%%%%%%?!%%%%!?%%!!%!%?!!%!%!!!??%%?%%%%%%%!!%!?!?%!%%!!%%?%%!!!%!%%%?%!!?%!%%!?%%%%!%!?!!%!?%!%%%!%%%%!!?%%?%!%!!%!!!%!!%%?!?!%%!!%!%%!%!%%!%?%%%??%%!?%%%%!%!%!!%??%?%%?%%%%?%%%!%%%%!%!%!%%%?%?!?%%!!%!%?!?!%%%%!%%%%?%%%%?!!%%%%%%?%%%?!%%???!!%??%%%%%%%!%!!%!%!!!!!!%?%!!%?%%%!!!%!!!%%%??%%%!%?%%??!?!%%%%%?%%!%%%%?%%%!!%%%!%%%?%%!%%!%!!%%%!%%!%%!!!%%%%%?!!!?!%?!!?%!!!%%%!!!!%?%%?!%%%%??!!!%?!?!!%%%?%!!%!%%??%%%%%%!%??%!%%!?!%%!%!%!%%%%!!!%?!%!!%%!?%%!??!!%%%%!?!%?%%!?!%%!?%%!!?!%%%%%!%%%?!%!?!?!%?%%%%!%%?%!%??!!!%%!?%%%%!!%!%!%%%!%%%%!!%%%!%%?%%!%!!%?%??%?%!%!%!!?%!%?%!%%%%%%!%!!?%%!%!!!%!%?%!%!%%!%!%%??!%?%?!%!%!%??%%???%%?!?!%%!%%!!%!?%!!!%!%%!!%??!!%%%%%%%%%%?%%%%!%!%%!%?%?!!%!%?%!%?%!%?%%%%%%!%%!?%%?%??!?!?%%!%%!?%?%%%%!!!?%%%%%%%%!%%%%%%%!?%%%%!%%!!!!!%%?%??%?!!%!%?!%%!%!%%%!%%!%%%?%!%%%%?%%%%?%!%%%!%%?%?%!!%%??%%%!%%%!?!%?!%%%%%!%%%%%?%%!!!!%%%!%?%!%%!??!!%??%!!!%!?%?%%%%%%%%%!!?%!%?%%??%?%%%??%%%%%!%%?!?%%%?%!%?!%!%!??%!??%!%!?%??!%??%!%%%!%%?%%?%!!!%!!!!%?!?%?!%!!!%%!%!%!!!%?!!%%!%?!%%?%%%%%%%%!%?!%!!%!%!!!%%%%!%%%!?%%%?!?%?%?%%%%%%%!%!%%!?%?%%%!%%%!%%!%%%%!!!!!%!?%?%%!!!%!?%!%%%!%!!?%!%%%%?%%%%!%%?!%!%?%!!!%!%?%%!%%!%?%?!??!%%?%???!%%%%!!?!%%!?!!?%!!%!!!%%%%%?!?%%%!?%%!%?!%%!!%!?%%!!!%!!%%!%%%!??%%%?%!%!%%%%!%%%%%%%%%%!!%?%%%?!%%!%%!!%!%%?%%!%%?%%!!%!!!%%%!!!?%%?!!%%!!?!?%%!!!%%!%%?!!?!!!!%%?!?%%??%!!??!!!%?%%!%?%%%%!%!!%%!%%!%!%%!%!!%!%%!%!!?%%?%!%%%%?%!%%%%??!!??%?%%!?!%%!%%!?%%!!?%%!!?%%!!!%%?!%%%??!%%%!%%!%??%%%%!!%%%!!%%%!?!%%!!%!!%!??!%!!!%!!%?!?%%!!%%%%!!%!!?%!%%?!%!%%!%!!%!%%!%!!?!!%!??!!%%???%!%!!%!!%%!??%%?!!%!!%%%%?!??%%!!%%%!?%!%%%%!!!%%!%!!!!?%!!!!%?%!%!%%?!%?%!%!?!%!%%%%!%!%!%%?%%!!%%%!!!%%?!%%?%%%!?!!!!%?!%%!!%%%?!??!%%!!%%%%!!%%!!%!%?!!!%?%!%?%%!!%%!??%!%%%!%%%!!?!!%%!%%!??%%%??%!%%!%?%%?%%%%%%?%??!?%!%%!%%?!!%%!%?!?!%?%%?%%%!!%!!%!%%%!!!%?%?%%?%!%!!!!%%%!%%!%%%%%%%!%%%?%%%?!%!%%?%%?!!%!%!%!!%!%%%%!%!%%?!%%%%%%?%!%%%???%%%!%!%%%%%!?%!??!!%!?!%%%%!%%%?%%!%%?%?%?%%%%%%%!%??%%?%?%%%!%!%%%!%!%!%%%%!!!%%!%?%?%%?!!!!%%!%%?!?%?!%%%%!!!%%%?%%%!!%?%%!%%%%%%!!%%%%%!%%%%%!?!%?%?!?%%!%!%%?!!%%%!%!!%%%?!%%?%!!!!!%%!!?!%!%%%%!%%?%%%%!%%!%%!!?%%!!%!!!%?%!%%?%!%??%%%!!!??%%?!%%%?%!%%?%%%!!%!%%%!?!%%%!?!?!!%%%%?%?!!!?%%!%?%%?%%%?%!%%!?!%!!?!??!!!%%!%%!!%%!!%!!%!%???!?%%%%!!!?%%!!%%%%!!%!%%%!??%%%%%!%%!%%?%%%%?%%%%?!!%%!%!%!%%%%!%!%?%%%!%%?%%??!!!%%!%%!!?%!!!%!%!%?!%!!%!%%!!%!%%!!%!%!%!!%!%!!!%%%%%%!%%%%%!%!%%!%%%!%??%%!%!!%?%%!%!!!%%?!%%%%%%!%%!%%%?!!%?%%%??!!!!!!??%!!?!%%%!??!!!%!%%!!!!%%%%%%%!%?%!%?!%!%%%%%%!%%%?%%!%?%?%!%%?%!?%%!!%!%!?%%%%%!?!%%?%?%??%%%%!?%?!!!!!%%%%?%%?%!!!!%??%?!!%!!%?!!%%%%!%?%?!!!!!!!!?%%%%%%?%?!%!?!?%%%%!%!%!!?%!%!%%!!%%%!%!!?%%!%%!%%%!!!%%?%%%%!%%!!!!?%%!!%!%%!%!%?%%%!%??%%%!?%?%!!%?!?%!%%!!%%?%%%%%!%!%!!%!%?%%!!!%?!%%!?%%%%%!%??!?%!!!?%?!%%?%%%%%%%?%%?%!?!!%%%!?!%%!%%!!%%%!!%!?!%!%???%!!!%!!?%!!%?%!%!!%!!%!!%?!?!!%!!!!?!?%%%%?!!?!?!!!%%%%!!!!!?!!!%%?%?!%%?!?%%%?!%?!%!%%%%%%!?%%!!!?%!??!?%!!!!!!!%?%!?!!%?!?%%%%%%!!!%%?!%!!?????!!%%%%%!!!?%%?!!%%%!%%%?%%%?%?%!!%!%%%%??!%%%!%?%!!%%%%?!!%%%%%!%?%%%!%%!?%%!?%!?%%!!?!?%!%%%%%!!%!??%%?!?%??%?!!%!!!!%!!%%%??!!%%!?!?!%%!!%%?%%!!%!%!!!!!!%%%?%!%%!?!!?!%!%%%???%%??%?!%!!%%!%%?%!%!!?!%!%?%!%!%%%?!!!%%!%%%%%%%%%%%%?%%%%%!!!%%%?%%!%!?!??!?%!!?%%!?%%%!%!??!%%%%%!??!%%?!%%%!!!%!%!?%!%%%?!%%??!!%%%?!%!!?!?!!?%%!%!%?%%!!?%%!!%!????!%!!!%?%?%%?%%?%!!%%!%%%%?%%!!!%?%?%!!!%!%??%%%?%%?!!%??!%%!%!!!!%!%?%%%!%!%%%!?!%%%!%!!%!%?!!!%%?%%!??!!!%%%?%%!%%%%!!!!%?%!?%%%%%%?!!!!%!!!%?%%!%%!!!%?%?%!%%?%!%?!!!%!?%!%!%!%!??!?%%!!%!%!%%%?!!?!%!??%%%!%%?!%??!!??!!?!!%%%!!%%%%!?%%???%!%%%%?!%%!!%%!!?!%?%%!!!%%??%!!%%%%%%%%%?!!?%!!%%!??%?%%?!%?%%!%%!%!%%%%?!%%%!?%%!%!%!!!%!!%%%%!%!%!%%%%%%%!!!%%??%%%!?%%%!!!%!!%%%!!%?!%!!%%%%%?!!!!!!!%%!!%?%!%%?%%%%!%!!!!!?%!!%!%!%%!?!?!%%%!!%%%%!%%!!?%!!%!?!!!%!?%%%!!%!%!%%!?!%!?%%!!!%!%!!%%!%%!%?!%%%!!%!%%!%%%%?%!%!%%%%?%%%!!%%%?%!!%!?!%%%!!!%%%?%!%!%%!%%!!!%%?%!?%%!%%!!!!%%%%!%!%!%%%%!!%%?%!!%%%%!%?!?!!%!%%%%!?%!!%%!!%%%%%!%!%?%?%%%%%!%%%!%%%%%%%?%!%?!%%??!?!%%%%%!?%%??%%!?!???%%%?%!!%!%!!%%%%!%?!%%%!!!%%%%!%%%??!!%!%!%%!%!%%%???%!!%%?%!%%!!%%!?%%%%%%!%!??%%%?!%%%%!%?%%!!!!?%%%!?!?!%?!%%!!?%%%%%%??%%%%?%%?!?%!%%%!%%%?%!%??%%%%?!%!??%%!!!?!!%%%?%!%%%%!!!%?!!%?%%?%!%%%?!!!%%%%?%%?!!%%%%%%%?!!%%%%%?!%!%!%%%%%!%%%%!!%%?%?%%%!!!??%!!%!%%%%%!!!%!%%%%%??%!!?%?%!%!%%!?%?%%!?!%!%%?%%%?%!!!?%!%!%?!!?%%?%!%!?!%%!???%?!!%%??%!%%?%%%!!%?%!!%!%%%%!!%?%%?%%%!!%!!%!%?!!%!%!!%%%?!?%!%?!!?%%!!!!%?!%?!?%%%%%?!!?!!%%%?%%!%?%%%%%%%!%!%%?!!%%!%%%!%!%?%!%!%%%?%%?%!%!!%%%%%%!!%!%?%%!%!!?!!!%?!?!!%%!%!!!?!!%?%!!%%?%%%%%%!%%%?!%%?!!?%%%?!%%?%?%%???%%!%!!!!%%%%??%%!?!%!!%%!!!!?%!!!%%!!%%!?%%%???!!%%!?%%%%%!!%%%%%%!!%%%%!%?!%%???%!!!%%!%!%%?!%%?%%%%?%%?%%!?%!%%%!%%%???%%?%!!!!!%!%!!!%?%?!%%%!%%%%%!!%%%!%?%!%!%?%!!!%%!!!!%?!%%%%!%?%?!%?%%%%%!?%%%%?%%?!%!%%!%?!!?%%!!%%!!%%%??!%%?!%%%!!%?%%!?%!%%?!!%!!?%!!!?%?!%!%!!%!%!!%!%?%?%%!%%%!%%!!%??%%%%?%%%!%%%!%%?%%!%%%!!%%?%%!%!%!%%%?!%%%%%?!?%!!?!?!!%%%%?!%??!!!!!?%%!%!!%%?!!%%%!!%%%%!%%%%!%%%!!%!%%%%%!!!!%%?!?%?!%%!%%?!!?!%!%%!!!%%?!!!!?%!!%%%!%!?%%!!%%%%%%%%!!!%%?%%!%%!%%%?%!%%%!%%%!%!!%%%%!%%?%%%%?%?%%!%%%%!%%!%%!%?!!%%!!%?%!!%%%?%?%!%!%!?%?!%!!?%%??!%!%!%%%!%%%%!%!%?!!%%%%?!%%%%%%%!%?%?%%%%%%!%!!%%!!!%!?%%?%?%!?%%%%!%!%?!!%%?!!%!?!%%??!!!%!%%%%%???!%%!!?%%%%!%%%%!%?%??%%!%!%%!!!%!!%%%%%%%%%%?!%%%%%%%%%!?%%!%!%%%%!?!%!%%!%%%?%%?%%!?%!%!%!%%%!%%!!!?%!%%%%!!!!!!%%%%%%!%%%%%!%%%?!?!%%%!%!?%!!!!!%!%!!%!!!!%?%!%!%%%!?%%%!%!?%!!%!%%%?!?%%%!%?%!!?%!%%??%%?!%%%??!!!!!%!%%%?!?%?!!%%??%%!!%%%!%??!%!?%?!!%%%%?%%!%%%!!!%!%!%!%%%%%?%%!%%%!%!%%!%%!%?%%!!%?%%%%%!%%?!!%%%!%%!%%%?!%%!!%%%!%%!?%!%!%!%!%?%!!!%!%%%!!?%??%!%!%?%?%%!?!!!%%%%!%!?%!%?%%!%??!%!!%%!%%!%%?!%!!!?!%!%%!!%%??%%%!%!??%!??%%%!%!%%%%%%%%%%%%%?%!%%%?!%%?!!%%?%!%!%%%!%!%%!!!%%%!%!%%?%%?!!?!%?!%%!?%%!?!!%!%%!?%!!%!%!%%!!?%!??%%?!%!%%!%%?!%!!%?%!%!%!%%!!%%!!!!?%%!!?%%?%!?!?%!%!%!!%%!!%%!%%%%%%%%!?!%%%%%?%%?!!!%%%!!%!%??%!?%!!%%%%%%%!%????!!%!!!%%!%%%%!%%%%!%!!!!%!%%%?%%%%%%!%%%!%%%%%!%?%!%%%%%!??%?%!!%?!%!!%%!!??%!%?!%?%%%%!??%??!%!??%?!?%%%?!!!%!%!?%!%%%!?%!%%!%?%!!%%%%%!?%%?!%!%%?%%!%!!!%!%??!?%%??%!?%!%%!%%?!!%%%???!!%%%!!!!%!%%%%%!%!!%%%!!!%!?%?%!!!!%%%%!%%%%%%?%?!!!%%!!%!%!%%!%?%%!?%!%%!%!??%%?%!%!%%%%!!!!%%!%!!!?%%%%%%%!?%%%%%%%%!!%%!!!!%%!%%%%!%%!%%!%%!%%?%%%!%%!?%!%%%%!%%!!%%%!!!?!?%!!!!%%%?%%%!%%%%!%%%!?%%%%!?!??!%%%%%??!%%%!?%%%!!%%!%%%%%!%!%!!?%!%%%!??%!%%?%?%%%%%???!%%!?%%?!%%%!%!?%%!!!??!%!!?%!%?!%%%%%%%?%!%%%%!?%?%%%!!%!!!%%!!%?%%%%?!!!%!!!%%!%!!%%%%??%%%?%%%%%%%!!!!!?%%%%%%%%%!!!%?%%!%!%%!%%?!%%!%%%!%!!%%?!%%?%?%!??!!%?%%%?!%%%!%%%!!%%?%?%%?!%!%%!?!%%%!%?%?%!?!%!%!%!%%?%!%!%?%%%%!?%%!!%?%%!!?!%%?%!!%!?!%!!?!%%%!!%??%%%!%%!?!!%%%%????%!%%%%?!!%%%!!%!!!%%%%!%%!?%!??%!%%?!!!!?%%%%%?%%???%%!!?!%%%%%%!!!?%%%%%%!%!%!%!%%%!%%!%%%?%?%%%%!?!!!%?!%!!%%%!!%?%?%?!?%%!%!!%%?%%%!!!!?!?!!?!?%!!!!%%%%%!%%%!!%!%%%!?%!???%%%%%%!%!!?%!!!%%%%%!!%%%!%%!!?%%!!!?%%%%%%!!?!%!%%%!%!%%%%!%%!%%%!%%%!%%!!%%!%%%?%%%!%!?!%?!!%%?%?%!%!?!%%%!%%%%%!!%!??!!%%%!!?!%%%%!%?%%!?%%%?%%%!!?!?%%!%??%!%%!%!??%%%!%?%!!%%%%%?%?!%!%?!%!?%!!!%!?%!%!?!!%?%!%%!%%!??%%!%!%%?!!%%%?%??%%?%%?%%!??%%%?%%!!%!%!%!!%%%%%%%%%?%!?!%%%%%%%!??!%%!!%%!!%!!%?!!%%?!!%!!!!%%%??!%?!%%%%%%!!?!%!%!%?!!%?!!%?!%!!!%%%%?!!?%%!!!!%%%%%!!?%%%%?!%%%?!!%!!%?%!!%%?%%!?%%%%!%?!%?!!%%%%%%%??!!!%%%!?!!%!%?%!?!%?!%!%!%!%%%?%%!%!%??!%!!%!%%%!%%!?%%%!%!%%?!!!%%!%?!!!!?!%%%!%%%!!!?!?!%!!%%!!?!%!%!%??%!!??%!!!!%?%!!?!%%%%!!%?%!%?%%%!%%%%%%%%!??%%%!!!%!%!%%?%!%%%?!!?!!?!!!%!!%!%!%%!%%%%%%%!%%!!%%?%%%%?%!!%!%%%!!%!%%!!!%%?!%%!%%%%!%?!%%?%!?%?!!%?!%!%!%?%%%%!%%%%??%%%!%%%!!?!!!%%%%??%%?!%%?!??!%%!??%%?%!%%!!?%%%%%%?%%%!!?%%%??%%%!%%%!%!!!%%?%%%!!!!%%?%?!%%%!!!!%!%%!!!%!%!%%!?%%%%!%?%!!!??!%?%!%?%!%%!%!!%%!?!%%%%%?%!!%!%%!%!%%%!!?%!%%%%%%%%??%?!%!%%%%%%?%!%%%!%%!%%%%%%?!?%!!!%!!%%%!??%%%%%%?%%?!?!!%!%!!%%!%!%%%!%!!%?!!%!%%?!!!%%%?%!!%%%!%?!%%!!!%?%?%?%!!!%%?!%%%%!%!!?%%%!%!%!%?%!!!%%!!%!%!!!!!%!%%%!%?!%%?!%%?%!%!!%%%!%%!%?%??!!%%%%%!!%?%%!!%%%?%!!%%%??%%%?!?%!%%!%%%!%%%%?%!?%?%!%!%?%?%!!??!%?%%%%?%!%%%?%%%!!?!%!%%%%?%%%!?!%%%%?%?%%%!!!%?%%?!?!%!!!%%%%!%?%%??%?%%??%!!%%!!!!!%!%!!%?!%!!!!?%%%!!!!%?!%!%!!%%!%%??!!??!?%???%%!%%?!%!!%!%%?!%!%!?%?!!!??%%?!%?%!%%%%!?!%%?%!%%%%%%%!%%!?!%!!!!??%!!!!!?%!%!%%?!%?%!!%%%%%%%?%%!!%!%?%?%!%!!%%?!?!!?%%!%!!%%!!%%%%%%%%%%%%!%%!?%%!%%?%%!%!%%!%%!!!%%!!!%%%!%%!%!!!!?%!!!%%!%?!?!%%%!!%%%%%%!%?%%%%%%?!%%!%?%?!?!%?%!%!%%%%%!%?!%?%!%%%?%?!%%!??!%!??!%%!?%?%!!?!!%??%%!%!!%!%?!%?%!!%!%%!%%%!!%!!%%!%?%!%!!%!%?!!%!%!%!%%%%!%!?!?%%!?%%%%!!?!??%!%!!%!!!%!%%?%!!%!%%?!?%!%!%!%%%%!!%?!!?%!%%%%!%?%!%?%?%%?%?%%%?!%!?%!%%!?%??%%%%%!!?!%%!!?%%%!!%?%!%%?!!%%?%!%%?%!!%!%!!!!%!?!?%%!?!?%!!!?%!%%%?%!?%%!%%%!%%%!!!%?!%%%%%%%!!%?!!?!!%%%%?%!!%%!?!!%!?%?%%%?!%%%%%%!???!%%%%!!?!!!%%!!!%??%?%%%%%??!%!?!%%!%?!%!??%%%%%%!%!%%!%!!%%!%!?!!%%%%%%%!!?%%%%!%%?!!!!!%%!%%%%?!%!!!?%!%%%%?!!%%!!%!%!??%!?%%%%?!?%%%!?%!??%%!??!%%%%%?!!!%%%%%!%%%%%%?!!!%%%%?!!%!!%%%!!%%!%!!!!?!%?!%%%??%!%!%?%!%!%!%%?!?%%!%!!!?%!!?%%%!%!%%?!?%%!%!%%%%%%?%???%%!%%!%!!?!%%!?!%!%?%%!?%%!%!!!%!?%!%?!%!!??%%%!!?!%%%?%?%?%%?%!%!!%%%!%%!%!!!!%!!%%%%%%!%%%!%%%%!%%%%%%!!?%%%%%%%%?%!%%!!!%??%%!?%!%%!%!!%!??!%?%?%!%?!%%!%!!%!%%%%%%!?%!!!%%!!!??!%%?!!!!!!!%?!%%!%?%?!%%?%%%!!?%?%!%!!!!!!%%%!!!%%!!?%!%!?%%!!!!%!!%%!%!%%%!%!!?%!!%%%%?!!!%?%%!!%!!?%?%?%%%%!%!?%?!%?%!!!%%?%%!??%!!%%!%%%%%!!%%%?%%%!!?%%%!%?!%%%!?!!%%%%!!!%!%%%%!%!%%%%!!%%!%%%%!%?%%?%!!!%?%%!%!!!?!!!%?!%%?!!!%%%%!!?!?%!%%%%!%%%!!?%%!!!!%%?%%%%%!!!%%?!!%?%%%!!!%%%%%%?!%?!!!%%!%%%%!!%!!%%%%%!?%%!!%%%%%%%%?%%%%%%!?%%!!!!%!%%%!%!?!!!%?!%%?!!?%%%%%%!%!?%%?!%?!!%!?%%!?%%??!%??!!%%!!%!?%!%!?%%!!?!!?%!?%!?!?!%%%!%!!%!%!!??!!%%%?%!%%%!%!!!%!%??%!!!%?%?%!?!%%!%!!%%%%%!!%?%%?%%%!?!%!%%%%!%?%%!?%%?!?%%%%!%!?%%%%%?!!?!!%!!%%!?!!%%%%%??%!%??!%%!!%??!?%!%!%!%%%!?%!!?%!!%%%%%%%%%!!!%!%%?!!%%!?!%!%%%%!???!?%!!%%%!?!%?!%?!?%%!%!!!?%%%?!%%%%??%?!%%%%??!%%%?!%%?%%%?%%%!%%%?%!?%!!%?!%%!%!%?%%%%?%%%!??%!!!%!!!%%%%%%?%%%!!!!?%%%%!?%!%%??!%%?%!!%%?%!%!%?!!%!%!?!%?!%!?!%?%%!!!?%!!!%!?!!%?!%?!!%%%!!%?!?!%!%?!%?!?%!%!!??!!!???%!%%!%!%??!%!!?!%?%!!!%%%%%!%%%%!!%!!!!!?%%?!!!%%?%!!%%!?%%%%?%!%?%!%%?!%%%%%?!?!%!%?!%%!!%%%!%!?%!%%?%!?!%%%%%!%%?%%!!!?!%?%%%%%%?!!%%%%!%%%%%%%%%%!?%%!%%!!%?%?%%!%%!%!!!%%%%%!!!!%%%!!%?!%%%??%!?%%%?%%%!%?%%%!!!%%%!!%%!!!%!!??!%!!!%?%!!%%%%!%%%?!!%!%?%%!%%%!!?!!%%%%!%%%!!%%!?!%!%?%!%%%%!!%%%%!!?%%%%%!%?%%%!%!!%%!?!!!?!?%?!!%!%%!!%%!%%!!%?!%!%%%?%?%%!%!!%??%%!!!!!%!%?%%%!?%%%!?!?%?!%%!!!??%%!%%??!!%%%%%!!%!!%%?!!!!??%%!!!%%%%!%%!!%?%%!!?!%?%!?%!%%%!!!%!!?%%%!%?%?%%?!%%%%!%%!%!?!?%%?%?!??%%%?%%%!%%?!%?!?%!%%%!%??!?!!%%!%!%%%%%%!!??!??%%%%%%!!%%%!!%%!%%%!%!%!%%%!?%%%!!%!%%??!%%!%?%!?%%%%%!?!!!!!!%?%%%!?%!%!%!!!%%!!%%!%!%!!%%%!%%!%!!%%%%%%%!%??!?!?!%!?%%??%!!!!%%!!!?%!!!!%%!%?%!%%%?%%%%%!%%!!%%%!?!!%!!!!%%!!%%??%!%%%?%%%%!?%?!?%?%!!%%%%%!%%%!!%%?!%%%!!%%!!%!?%%?!%%%!!?%%?%%?%%!!%%!%%!?%!%!?!!?!%!!%%!!%%%%!%%%!%%%%??%!%%%!%???%%!%%%!%?!!!%??%!%%%%!%%%%?%!?!%%?!!%%%%!%%%!!?!%%%!?%!%%??%!?%%%!%?!%!%!!?%?!%!!!%%!%?%!!!!!%%%%%%%%%%%%!%!%?!%??%?%??%%%!%%%%%??%!%%???!!!%!%!?%%%!!%?%!%%%%?%?%%!???%!!!%%%%!%%!!%%%!%!!!%?%!%%%!!%!!%%!%%%!?%!%!!%!%%!%?!?!!!!!%!%%%?%%%%%%%!????!%??!!!%%%%!!!%%%!%?!!%!?%%!%%!%%!!%?!!%%?!%%!!%%%?!!??%!%?%!%%!%%?!?%%%%%?%!%%%!!%!%%?!%%!?!!!!!!?%%!%!%!%!%??!?!%?%%?!!%!%%?%!%%%%%!%%?%%!%%%??%%%???%%%%%%%%!%%!??!%!%!%?%%%%!%%%?%%!?%%%?!%%%%!?%%%?!%?%%!?%!?%%!%%%!%%!!%!!%%!%!!%%?%?%%%%%?%!%%!!!%%?%%%!%%%%!!!!!???!%?%%!!!%!!%?!!!%?!%!?%%%!!%!!!%!?%%?%?!?%%%%?!%%%%!%?!%%%%%!%%?%!!%%%%%%%%!!%!%!%%%!!%%%%%%!%!!%%?!!%%%%!%%%!!%%%%!%%%!!!%%!%!!%%%%%!%%!!?%%%!%!?%%%%%!?%%!%%%?!%!%!%??%?!!??%%%%%%!%%!!%%!!!%%!%!!!?%%?%%%%%%??!!?!%?!?%!%%%%%!?%%??%!!%!??!%%%!%%?!?!!%%!%%?%!%%%%%%!!!!!%%?!!?!%%!!!%%%%%%!!%!%%!?!??%%%%?%!%%%%!!?%%??%??!!%%!%%!?%%%!%%%%%%?!?!!%!%%!!!?%%?%%!%!!%%%?%!!%%%%%%?!!!%!!%!!?%%%%!?!?!%!%%!%!%!%!%!%!%%!%!%!!!%!%??%!!!!%?!!%%!!?%%!!?%!??!%!%%?%%?%!?%??!%!!?%??%%!!%?!?%!!?%?%%%%!%%!!??%?%!%%%%%%%%%%%%%%??%!!???!!?%!%??!!%%%!!!%?!%!!%!?%?%!%?%???%!!???%!%%%??!%!%?%%!%!%%%!?%?%!!%%?%%?!!%%%%?!%?!!!%!!%%%%%%?%%%%!%!?!%??%?%!%!%!%%!?%%%%?!%!!%?!%!!!%%%%%%!%!%%!%!!!!%?!!!%%%%%!?!??%!?%%%%!??%%!%!!!!?!%!%%%%%%%!%%%%!%!%?!%%?%%%%!?%%%%?%%%!%?%%!%%%%!%!!?!%?%!!%!?%?%%%?%%%!??%!?!?%!%!%!%%%%%!%%!?!%?%!%%%%%%!!!!?%?!%!%!!!?%!%%%%!!%%%!?!?%%%%!%!%%!%%%!%?%!!!!!%%!%%%!!!?%%%?%%%?%%%%??!%%!%?%%%%!!!!!%!!%%%%%!!!!?!!%!%!!!%!!%%%!%%%%!!%!?!%!%??!!%%%?%?!??!%!%!%!!??%%?%!%!%%%?%%!%%!!!!%%??%%!?!%%!%%%%!%%%%?%?%%%%%?%%!!!%!%%%%?%!%%%%%?!%%!!%!%!!%?!%%%??!?%%%%!?%%%!?%%!!?%??%?!?%%!%!%%%%%%!%%%%!%%%!!?%%%%%!%!%%%!%!!!!!!!%%%%%?!%%!%%?!%%%%%%?%?!%%%%!!?%!!%?%?!%%%!%?%!!!%??!%!?%%%!!%!??!?%%!?%%%%!!%!!!?!%%%%!!%%%!%!%!%?%%%%!?%%!?!%%%%%%%!!!%!!!%%%%%?%!%!?!!?!%%%?%!%!%!!%?%%%%?!?!!!!!!!%!!%%!!%%!%%%%?%%%%%%!%%%%%%?!??%!%%%%%%!%!%%%!%%!%%??%!!!!?%?!!!!%!?%!%!!%!%%%!!%%?%%!!%!!%%%?%?!%%!!%%%!!?!!%%%%%?%%%??%??%%%%!?%!%!?!!%%%%!%%%%%%%%?%!%%%%?%!!%%%!?%?!%?!%%!?!%%%%%%!?!%%!%!%!!?%!!%%!!!!%%?!%!%%!!%%!%!%%!!?%!!%!??!!?%%%!%%%!%!!%%?%!%%!?%%%??!%?!%%%?%%%%!%%!%%%!!?%!%!?%!?%%?!%!!!%!%%?%!%!!?!%%!!!%%%?!%%%!!!!!??%%?%!%!%%%%%!?%!!!%?%%%%%%%!!?!%!%%%!!%%!%!%%!!!%!!%%%%!??!%%%%!!%!!!!!%?!!!%%%!!?%!%!??%%!!!%%!!?%!%%!!!!%%%!!?%!%%%?!%?%!%%%?%!%%!%!?%%!%?%!?%!?!%!?%%?%%!%%%%%%%!??%%%%%?!?!!?!!%!%%!%%!%!%???%!?%?%%%%%%!%%!?%%%!!%!%!%!?%??%?%%?%!%%??!%%!%%%!%!%%!???%!!%%?!!??%!%?%%!??%%%?!%%%?!%%!!!%%?%!%%?%??%%%!?%!!%!!%%!%%%!!%?%!?!!!%?!%?!%%%%%?!!%%!?!!!%%?%!%%%%?%%!%%?%%%%?%!!%!%%%%!!!%%%%%!??%?%%!?%%%!%!?!%%%%?%%%!?!%!?!%?%??%%!%!!!!%%?%?!?%%!%%!%!%?%?%%!%%%%%%%%%%?%!??%%!%?!?!%%%?!%!!!%%%!%!!%!?%!!%%%!%%%%!!%!!!!?!!?!%!%??!%!!!?!%!!?%%%?%!!!%?!?%%%%!%%%?%!%!%!%!%%!!%!%%!!?%%!%%?%%%%%!%%?%%!%%%!%!!!%%%%%%%%???%%?!%!?!!%%%!?!%%%%%%?!%?!???%!%!?%%!%?!!%!%?!%%!!%%!!%!%?%%!%%%?%!%!?%%%!!%!!%%%%?!!!!%!!!?!%%!!!%%%%?%?%%?%%%%!!%%%?%?%!%!%?%!%!!!%!?!%!%?!!!%%%%?%%%!%%%%!%!%%%%?%!%!!?!!!!%!%%!!?%%%%%%%!?%%!%%%%!%?%%!!%!%%%!?!?%!%%%!%%!%!!%%!%%!%!!?!%%%!%%%%%%%%!%%?%%!!!!!?%!%%%!???%?%%!%%%%!%%?!%%!!!%%%%%%???%%?%%!%!!!!%!%!%!!%!%%!%%!?%!%%!!?%!?%%%%%%%!%!!?!!?%!!%%!?%%!%!?!%%%!?%?!!!!%?!!%%%?%!!!%%!%%%!!%!?!!%?!!%!!%?%?!!?%%%%!%!%%?!!%!?%%!%!%%?%!%!!?%!%!!%%!!?!%!%!!%%%%!!!!!%!%!?%%?%!%%!!?!%%?%%!????!%?!!%%%!%%%%%%!%!%%%%?!!?!!%%!%!!!%%%%!%!!%?%!%?%?%%%??%%?!!!?%!%!%%!%%!%?%%!%!!%%??%%!!?%%%%??!%?%%%%%!%%!!%?%?!!??%%%!%!!!!%!!?%%%%%?%!%!%%%%??!%%%?!%%%?%!!%!!!!%!!!?%%!?%?!?%%%!%%%%%%%?!%%!%%!%%%!!%??%%!!%%??%!!%!%%%!%?%!!?%??%%%?!%!%%?%!%?%!!!?%%%%!???!!!!%!%?!!!%%!%%?%?%%?!%?!!!!?!!%!!%??!%!!%!!??!!%%%%!!%!!%!!%%%%%!%?%%!%%%%!!%%%%%%%!%%%!!%!?%?%%%%!?!!%?%%%?%%?%%%%!%%%%%%?%%%%%?!%!!%%!%%%!%%%!%!?%%%%?%!!%!%?!%?!!%!%!%%%%!?!!?!?%!%%?%!%!%%!%%%%%%?%!!?%?!!!!?!!%!!%%?!!?%!%%!%!%?%%?!%%!?!?!%%%%%%!%%%%%!?!!!!%%?%???!%!%?!?%%%%%?!%!!!%%?!%!!%!!%%!!!%!%%%%%%?!??%!%%%!%!?%?%!!?!%?!%%%??%%%%%%!?!%!%%%%%!%%??%!%!%!!%!%%%!!%?%%%!?%%!%!%!%%??%?%!!???!%%%?!!!%%%!!%%%?%%%%%!!%?%??!!%!%%!?!%%%!%!%%%?%%%!%!%!%%%%!%%!%%%%%!!?!!%%%?!%!!!!%?%%%%?!%!!!?%!!?%%?%%!!!!%%%%!%?!%!%?!%!!!!!!?!%!?%%%?%%%%!%?%%?%%%?%%%??%?%%!!%%!%?!%%%!!!%!?%!%%!!?!!%%??%?!%%!%!!?!!%??!!!%%%?!%?%%%!!?%%?!??%!%%%!%?%%!?!%%!!%%%!%!!?!?%!%!!%?!%%!%!%%%?%%!%?%%%!%%%%!%?!?!!%%??!!%!%!%%!!!%%%%%%!%%%!!%%!!%%%!!%%!!!%%?!????!!!??%%%?%?%%?!!%!!??%!%%?%!!%%?%!!%?%?%%%%!?!%%%%%?!??!!?%!?!%!?%!?%!???%!%%!%!!?!!%%%!%%!%!!%%!!%%!%%!%%?%%!%!%!?%!%??%!%!?%%!%?%!%!!!!?%%!%?!%!!?%!%%%!%?!%?!!%%?!!!%?%!%%!!%%%%%!%%%?!?!?%!%?%!%%%%!!%?!!%?!%%!%!!!%!%%?!!?!%?%%%!%!%%?%!%??!??%%%%!!?%!%%%!%%???!??!%!%%??!%!!%%??%!!%!%!!%!%%%!!%!%!%?!??!%%%%%?!!!%??!!%%%?!%!%%%%%%!%%!%%?!%%?%%%?!%%!!%%%%!!%??%?%%?!%%!?!%%%%!%%!?%??%%%%%?%%???%!%%!!%%%%!!%!!%%!%!!!%!%%%%%!!!%?!%%!%%%!!!!!%%%!%!!!!%?%%%%%%%!!!%!%?!%%?!?%%!!%!%!!%!?%!!%!?%!%%%?%%?%%!%!?!?%!!%%!!%%!?%%%?!!!!%!%%?%%!??%!?%?%!%%%!%!??%??!!%%%%%?%%%%?!??!?%!%%?%%%!%!%!%%%!!?!!%!!%!!%%%%%%!!%?%!?!?!!!%!%!??%!%!%%%%%%!!%%%%%%%%?%!%%?!%!%!!%?!!%??%?%%%?!?!%?%%!%!%%%?%!!%%%%!!!??%?!?!!?%!?!!%%%%%!!?%%!%!!!%!!!?%!%%!%!?!!%?%%?!!!%%%%!%?%%??!%%%%!?%%%%%!!!?%!%%%!%%%!%!?!!%%?%%!%%?%!%%%!%!%?%%%%??!%!?%!?!%%!!%%?%%!!%%!!%?%!%%!%%%?%?%!!!?%!%!%!!%%!%%%%%!?%%!!!%!!??!?!%!?%??%?%%%%!%%?%%!%!%!%!%%%!%!%?!%%%?!!%!?%%%%?!%!%!!!!?%%%%!%?!!!!%%%%!%!!%%%%%?!!??%%%??%?!%?%!!!%%%!%%!!!?!!%%%!%%?!%!!?%%%%%!%?%!%!%?%!?%?!!??%!%%!%?%%%%%%!%%%!%!%%!%%!%%!%%?!!!%%%%%%!??!%?%!%%%!?%!!!%!%?%%%!!%!%?!?%?!%%!?!!%!!%!!!%%%%%!%%%%?%!%%%%?%!%%%?%!%!!?!?%%%%!?%%%%!%%%!!!?%?%!?!!%%?%?!%?!?!!%%!!??%%%%!!!%!!%%%%%%%%%!!%%!%!%%??!%%!!%!%%%?%%!?%%%!!!!%!%!!!%?!!!!!%%!!%%!?!!!?%!%%%%%!%!!%?%!??!!%!%%!?!!%!%?%%!?!%%!%%!%!%!%!%%%!%!%%%%%!%%!%%!!!%!?!!%!%%%%%?%%%%%%%%%!%?!!%%%%!%!%%???!%!!!%!!%?%!%%%%!!%!%%!%!%%%%!%%!?%?%%!%!%%%????%!!?%!!%%%?%%?!??%%%%%!%!%!%?!%%??%%%!!!%!%!%%!!!%%!%!%!!%%!!!%%!%%?!%?%%%!%%!?!%!?%%?%!?%!%%!%%%??!%%%%!%!?!%%%!?%?%%%!%!%!!%!?!%?%%%!!?!%!!%!%?!!%%%%!%%%%!%%%!%?%%??%%!?!%%%%%!%!!?%?!??%%%?%%%%!?!?%!%!!%!%!%!%%%%!!%%?%%!!!??%!%!!%%%%%%%!%!%!%!%%?%%%%%?%!?%?%%!!%!?%%%%%%!!?!!!?%%%!!%%!!!%%%?%%%%%!%%!%%!%%!?!%%%%%?%!?!%?!!%%%!!%?!??%!%!!%?%%?!%?%!!!!%!%!%!%%!!!!!!!!%%%%%!?%%??%%!%%?%%!%%%!%%%%%!%!%%%?%!%%?%%%!?%!?%%%!?%%%%%%%%!!!!!%%!!!%%?%?%%!%%%??%!!%??%%%%!!!?%%?%!!%!!%%!%%!%!!!!%%%%%!!??%%%!%%%!!!!%?%%%!%??!?%%%%%!?!%%!%%%!%!%!%!!%!%%?!%%!?!%!??%!?%?%?!%%%!%!!?%!?!%!?!%%%!??%!%!%!%!%?!!%!!!%%?%!%?%!%%!!?!!!%!!!%?%%?!%!!%%%%%%!!%%!?%!?!%%%!!!!%?%!%%!!%%%%!?!%%?%!!%%!%%%?!%!?%!%!!!%%??%!!?!%%%%!!!%%!%?%!!?%!%!%!!%!%!%!!!%!%!%!%!%?%%%%!%%!!!%??%!%%!%!%!?%%!%!?!%%?!%?!?%?%!%%%?!%?%!!%?!%%%%%?%!!%%%!%!%!%??%!%!?%%!!%?%%!!!%%%!?%%%%%!%%%%!%?!!%%%%?%!!!%%?%%%!%!!%%!?!?%%!!!!??!%%?!%%%%%?!%%%%?%%!!%%%!!?%?!%%%!%%!!!%%%%%%!%%?!%!%!%!!!??%%!??!%%!%%!%!%!??%?!%%!!!%!%?!!!!?!%?%!?!%%%%%!%???%%%%!!%%%%?%%!??!%!!%%??%%%%%!!?!%?!!%%%%??!%%%%%!?%%!%!%!!%!%!!%%!%%?%%%%!%!!?%%%!!!%%%?!?%%%%%%%%?%!!!!%%%%%?!!%%!%%%%!%!?%%%!?!%?!%?%%!%%%!!??%!?!??%!!%?%%%%%%!!%%!%??%%!%!!%%%%%?!!%??!?!%%!!%!!?%!!%!!%!%!!!%!!%?%!%!!%%?%%?%%!%!%!!??%?%%!%!%%!?!!%%!%%!!%%%%%?%!!%?%!?%!%%%!%%!?%%%%!%?!%!?%%?!%%%%!%%%?%%%!!!%%!%!!!%%%?%%%!!%%???!!%!%%%!!%?%!!%!%%%%?!%%!?!%%!%%!%%!!%!!!!!%%%%%?!%%%%!%??%%?!!!%?!?%!!!!%%%?!!%%?!!%%%!%!!%!%!!!!%!?%?!?%%%%%!?%%!!%%%!?%%!%%?%%%!%!!%%?!%!%%!%%%?%?%?!!%!!%%%!?%%%??!!%!%?%!!!??%%%!%%%%%!!!?%%%!!!%!!%%!!%%?%?%%?%%?%%%%%?!?%%%%??!%%!%%?%!!%?!!??!%%%%%%!%%?!?%?%?%%!!%!!%!%!%!!!!!%%!!?%!!%%%%!!%?%!?%!%!%?%!??%%!!!?!!!?%!!?!!!!!!%%%%!?%%!?!??%%%!!!??!%?!%???!%%%!?%!%!!%!%%%%!%??!?!%%%!!!%%%?%!%!?%!!%%!!?!%!!!%!?%!%%%%%!!?%%!!%?%?%%%%%%!%!%?%%%%%!%?%!??%%%%%!%%%%%%!?%%??!???%%!??%%!!%!%?%%!%?%%!!!!%!!%?!%!%%%%!!%!%%?%%%!!%?%!!!%?!!%%%%!!?!%!!?%?%%%%!!%?!%?!!?!!?%%%!?!!!!?!?%%!!%%%%%!!!%%??%%%%%!%?!?!!%%!!!%?!?%%%%!%!%%!%%%%%%!!?%%%%%%%%%%%%%!?%%!?%%%?!%?%%?%%%%%!!?!?%%?!!%?%!%?%!%%!?%%?!??%%%!!!%?%%!%!!%%%!%%%!?!?%?!%!!?%??%%!?!%%?!!!%!!!%!%!?%%%%!?!!%!!???%%??%!!?%%%%!%?%%%!!!?%!%%%%!!?!%%!!!!!%?%%%%!!?%%%%%????!?%%!?!!%?!%!?%!%%?%%!!%%!%%%!%%%%%!%!!%%?%!%%!?!%?%!%%%%?%%%%%!?%!!????!!!!!%%%!%%%?!!??%%%?%!%!%%%%%%%%%!!%%%!!!%!%%?%%!%!!%?%?!?!?%!!?%!!%!!%!%!%?!%%?!%%!!%%????%%!%!!%%%!?!?%%%!%%%%%!!!%%%%%%%??%!?%!!%?!?%!%!%%%%%??!%!%%!!??%%%%!!??%!!%?!%!%%!%?%%?!!!!!?%%?%%%%%%??!?!?%%?%%?!%!%%%%!!%!?!!%%%!!%?%?%%!%%%%%%!?!!!%%%%!?%!!%?!%??!%%!?%!%!%%!%!!!!?!%!%!%?!!?%!!!!%%?%?!%%!%%!%%%%!%%%!%%!%%%%%!!!!!!?%?!?!%!%!!%?%!?!%!?%!?%!%%%!%?!%!!%%%?!?!%!!!%%!%%%!!!%%??%!%!%%!%??%!?%%??!!!%?%%%!%!%%%%%%?!!%!!!%!%!%!%%%!%%!%%!!??%!%%%?!%%!%%!%%?!%%??!!!!%!%!!!%!!!!%!%%!%%?!!%%?!%%!%%%%%%%!!%!%%%!%%%%%!%?%?%?!!?%%?%%%?%%%%%!?%!%%%!!!%!%!%?%%%%!!!%%%%!?%?!??%!%!?%!%!%%%!%!???%!%%%%%!!%%%?%%%?%%!?%?!?%!!%!%%?%?%?!%!!%%%!!!?%%!%?%%%!?%!!%!??!%%%!!!%%%%%%%%!!?!%!%!%!%!%!!?%!!%%%!?%%!!!!!!!!!!%?%%%?!!%??%%%!!%%%!?!!%!%%!%%%?!%!%!%!%%%%??%%!!!!%!%%%%?%%!%%%!!?%%!%!!!!%!?!%%%%%%!!??!!!%!%?%%%!!%!%%%!%?%%%%%%%%?%%%!%%%!%!%%!%%!!??!%??!%!!!%!%%!!!?%%%%%%%????%?!%%%%%!%!??!!%%?%%%!??%%!%%%!%%?%!!%%!%!!!%!!!!%%!%%%%%%%%%!!%%!%%%%!%%%%?%!!?%!%%!%!%?%%%%!?%%%!!%!%%%%!%%!?!%%!%%%!?%%??%!%?%%%!%!!!?!%!%%!%!%!!%%!%%%!!!%?!%!!???%%%%!?%%!?!%!%!%!%?%%!?%!%!%%!!?%%??!%!%!?%%%%%%%%?%!%?%??%%!!!%???!%?!?%?!%!?!%!!!%??!!?%%!!%%!%%%%!%!%%%%%%%%%!%!%!!!!??%%?!%??%!?!!%!!????!!?%!!!!%?%!!%!%%%?!?%%!%!!!!%%!%%%%%!!?!%!%!%%%?%%%!%%?%!!!%%!%%%!%?!!%%%!%%!%%%!?!%!%?%!?!%!%!!%%%!%%!??%%%!!!!!%?%%%?%%%%!!%%!%%!%??%%%!%%!?!!%%%?%%%!!!?%?!%%!%%%!?%%%%%%%%%%!?!%!?!!%%!%%%!%%%%!?!%%%%%!%%%%!%%%!%%%%%%%?%%%!%%%!!?%!%%?%%!!%%%!%%?%!%%!%%%%!%!%!%!%%!%!????!!?!%?%!%%!%!%!?!%%!!%%!!%%%%%%?%%%%%%?%!!%!%?!??%%?%%%!??!!?!?!!%!%%%?!!?%??!%%%!!?%%%??%%%??!%%?%?!%!%!%%?%%?!%%!%%?!%%!?%?%%%%%?!!%%!%!%%%%!!%%!%!%!!%%%%!!!?%%%!!!%!!%%%%!?!!!%%%%%%?%%%?%?%?%??%!%?%%!!%!%!!%??%%%%%%%!%?!%!%%!!%?%!%?%?!!%%%%!%%!%!!%%!%%%!??!!!!%!%%%?%%!%%%!%%%%%%%%!%?%%%!!%?!%%%%%!%!!%?%!%%%%??!%%%?%%%!!!!?!%!!!!!%%%??!%!!!!!%!!?!%%%?!%!!%%?!?%%%?%?!%%?%!!%!!%%!!%?!%!%%?%%!%%!%?!!%!%?!?%%%!!%%?%?!%!%!%!?%%%%%??%!%%!%?!%%!%%%%!%?%%%!%!%%%!%%!%%%%!?%%!%!?!!?%?!%?%%!%!%%!%%%%?%%%%%%%!?%%%?%%%!%!!!!!%!%%!%%!%!!%!!%%%!%!!%?%%%!?%!!!!!%%!!!?%%!!%%%%?!!!%?!!%%%!??!%%%%%%%%!%!?%%!%%!%%!!%!?%??%%%%%?!%%!!%!!?%!?%%%!%%%%!!?!%!%%!%%%!?%?%!!?%?%!!!%?!!?!%?!?%!%%!%!%%%?%!%%%%!%%%%%%!%%!!%!%%%?%!!?!%%%%%%%!?%%%??%!%!!%!?!%!%?!!%!%???%%!%%!%%!?%!!!!%!%%%!!?!%!%%%%%!%!!%?%!%%!!%!%%%%!!!!%%%%!!?!!!!%?%%!!%?%???%!!!!%%%%%!%!%%%%%?%?%%%?!%?!!?!!!?%!%%%%%?%%!!%%%%%!%!%??%%!!%?%%%%%%%!!?!!?%%%?%%%?!!??%%?!%%?!%!%!%%%!!!%?!??!%%?%%%!%!!%%!!!%%%%%!%%%%!!%%!%%%??%!?!%%!%!!!%?!?!%!!!%?!%!%!%!%!!?!?!%%!!!?%%?%%!%!%%!%??!%!%%!!!!?%?%%!%!!!!%?%!%%%%!!%?%?%%%%%%%!%%!%%!%?!%?!%%?%%!%!!!!!!%%%?%!%%!%%%%??%?%%!!%!%%!%?!!%?%%%%!?!!%%!%%?!!%%%%%!!%%??%!!%!!%%!%!%!!!!%!%%%%!!!%!!!!%?!??!!!%!%%?%!%?%!%??!!%!%!??%?!%?%%%%!!%%!!!!!!!!%%%%%!!%?!%%%%%%?%!%?%%%%%%%%%?%%%?!!%?%%!!!!%?%??%%!!%%%%!!?%%!%%?!!?!!%%%??!%%?%%%!%%%!%!!%%%!!%%%%?%%%?%%%!%!!!%%!?%%?!%%?%%%!?%?!%%!!%?%%%%!%%?!!%!!%%%!!%!%%%%!!%!%?%!%%!%!%?!%!%%!%??%!%?%!%%!%!!%%%%!!?%%%%%%!?!%%!%%??!%!%!!%%%%%%%?%!!?%%!!%%!%!??%%%!%?%%!?!?%%%!%%?!%%%%!%!%%%%!?!?!?%%!??!?!%!!%!%!!%?%?%!%!%?%%!!!!%!?!%%%?%%!!%!?%%!?%%%%!?%%%%%%%%%%!!%%!!%%%??%%%!!?!!%?!!%%%!!%%%!?!?%%?%%!%!%!!!%?%?!%%%!%!!!%!?%!%!!%%!!%!%%?%%!%%?%!%%?%%!%?%!%%%?%!!%%!%!!%!!?%%%!!%%!!?%?%%!%%!!!%!!%?%%!%!%%!!!!%%%%%!%?%?!?%%%%%%?%%%%%%!%%!?!%?%!!!%%!%!!%%%%%%!%!%!%?%%%?%!%%!%!%?%%!!%?!?!!!%?!?!%%!??%!!%%%%%%%%%%%?%%!%%%%?%%!%%!%%%!!!%%?!??!%!%%%%!!%!!!??%!!!!?%!!!!%!!!%%%!!!%%!%??!?!?%!%!%%!%%%!!%!!!?%%%?!?!!%!!%!%%?!%!%?!!!!!!!%??%%?!%%!%!!%?%%!%?%!%%%%!%!?%%%%!!%!!%%?%!!%!%%%%!%?%%%!?!%%%!!!%!!%%!%?%?%%%!%?%!!%?!%!!?!!%%%!!!!%!!%!!!%!%%!%!?!%!!!%%%!%%?%%%!%?%%%%!%?!?!%?!?%!%%!%?!?!%%?%%!%%%!%%?!!!%!%%%!%!?!%!?!%?%%%%?%!%?%?!%%??%!%%!%%!?%!??%%!%%%%%?!!?!!!!%!!%!??%!!!!%%?!%!!??!??%!%%?%?%%???!%%!%?!!%%!!%!%!%%!%%%%?%?%%%%!%%%!!!%%!%!%!!%%%!!!%%!%%%%!!%!%?%!?%?%?%?%%%%%??!%!?!%%%!!!!%!?!%%!?%!%%%??%%!%%%!%%%%%!?!?%%%!%?!%!%%%%%!%!%%!!%!%%%?%!%%%%%%%%%!%%%%!%%%%%!?!??!%%!?%%?%!%%%???!!??!?%%!!!%%!%%?!%?!?%!%?%?%%!!!%!!!!%%%%%%%!!%%!%?!?%!!!%%%%%%%!%%%%!?%!?%%%!%%%%%%??%%!?%%?!?%?%%%%!%?!?!?!??%%%%??%?%%%%%!!!!%!?%?!?%?%%!%%%!!!%%%%?!!!??%!%%%%%!!!%?%!?!%!?%!!%%!%?%!!%%%%%%!%!%%%%%%!?!??%%%!%%%?%!%%%%?%?%?%!!?!!?!!%%??%?%%!%!!?!%!?%%%%!!%%%??%!???%%%%%%%!!%%!!%!!?%%%%?%!%!%?!!%%%%!?%%%%?%%!?!%%%%%%!!!!%%%%!%%!%!?!!!%%!?%?!!%%!%!%!!%%!%?%!%!%%%!%%%%!%!%%?%!!%!%%?!%%!%!%%!??%%%%%?%?%%%%%?!!%%%?%?!%%%%!!?!!!%%!??!%%!%!!%!%!?!!?!!!?!!!%%?%%%%!!!!%?!!!%%%%!%%!?%%%%!!!!?%%!%!!!%!%!%%!!!%%??%!%?%!!!%%?!%%%%!!?%%%???%%!%%?%%%%!?%%%!?%%?!%?%%%%!%!?%?!???%?!!%%%???!!%%%!%%%%%!?!%%!!%!!?!!%%!%?%!%!?!%!%%?!%%!%%!!%?%%%%%%%%%%!!%%!%%%??%%??%?!%???!%%%!!!%%%%%!!%%%%?!%?!%!%!!!!!!!%!%!%!%!%!%!%%!%!!??%??%%%!%!!%!!%!%%%%!%!%%%%%!%%%!%?!%%?%%%!%???!%%%%?%%%?%!??%%%!!%!!?!%!%%!%%??%%%!!!%?!%!%%!%!!%%%%!!%!!!%%!?%%!!%!!%?%???!%%!!%!%%?%?!!%!!!%!%%%!%!!!%%!?%%!?%!?%%!%%%%?%!%%%%%%!?!%?!%%%%%%?%!%%!%!%!%%!%!??!%%%%%%?!%%!%!!?%%%!%%%!!%!!%%%%%%%%???%?!!%%?%!!!!%%%?!%!?!%%!?%?%!!%%!%%?%?%!%%!!?%!%%!%%%?!%!%?%%!!!%!!%!%?!%!%%%%%%%%%%?%!?!%%!%?!?%%%%%%%%!%?%!!%%!!?%?%!?%!%%!%%%%!%%!!%!%%%%!%!%%!!!%!%%%!%?%!?%%%%!%?!??%%%?%%%%?%%!%%?!?!%%%%%%!%%!?!!%!%!!%!!%%?%!%%!?%%!%%%?%%!%?!%%?%%%?%!?!%?%%!?%!!?!!!%%%?%!?!!%?%%?%!?%??%%!%%?!?!%!%!?%%%%!!?%?%%!!?%%%!%%!!!!!%%%!!%%!%%%!!%%%?%%%!%!!%!%?%%%%%%!!?%!!%%%!?!!%%%!%?!!?!!!%!!?%%!%%?%%?!%?%!%%?%%?!!!%?%!%%?!!%%%%%!%%??!%?%%!%%?%???%%%!?!!%%!%%%?%%%!%!%%%!%!%%!!%!!%!%%?!%?!%%!%!%!!!!!!!!%!!??!%%%!!%%?!%%?%?!%%%?%%%%%?!%!%!%%%!!!%%%%!?%!!%!%!%!%%!?!%%%%?!!!!!!?!!?%?%%!!%%%%%%%%?!%??!!?!?%??%!%!%%%%%%!!%!%%!??%%%%!%!%%%?%%!???%%%!??%%%%%%%%%%%!%??%%!%!%?%%?!%%%!%?!%%%%%%%!%%%%%%%!%%!%?%%??%%%?!%%%%!%?%%%!!%!%!%!%!!?!%!!!%%?!!%?%%%!??%?%?!!!%?%%%!%!%%!?%!%%%%?!%%!%!?%!!?!%!!!!%?%%%?%%!!%%%!??!%%!?!!!!%%%?%%%%%!?%!!%%%!!?!?!?%%!%!%!!!?%!%%!%?!!%?%%%!%?!?%!!?!%!%!!!%!?!!?%??%?%%!%%!%!?!%%%%%!!!?!%%?%%%%%%%!%?%?%!%!!?%%!!!!%???!!?!%!!!%?!%%!?!!%?%!%!?!?%%!%%?!%!%!%%!!!!!!%!%%%%%%%%!!%!%%!%!%?%?!!%%%??%!!?!!%!%?%%!!!%!?!!%%%!!%%!%!?%!%%!!!%%%!%%!?%%!%%?%%%!%!!%!!%%!%!%!!?!!%%?!%%%!!?%?!%!!%?!!%!?!!%!%?!!!?%?%?%???%!!%!%%!%!%!%%%!%%%?%%%%!?%%!!!?!!?!!%%%%%?%%?%%!????%?%!%%%%!?%!!%%%%%!%%%??!!?!%%%?%??%%?%%%%%%!!!?%!!!!!%%!%!?!%!!%!%!%%%?%%!%%%%?%%%%!!?%%%!%??%%%!%%!!%%?%%%%%!?!%%%%!%%%??%%?%%%%?!!!!%%!%!%%!!%?!?%%!!!?%?!!?!%%?!!%!?!%%%%!?%?!%?%%!%%?!!%!!?%!%%!!%%!%?!%%?%!??%%%%!??!%%%%%!%%%?%%%!%!%!?!!?%%!!%!!?!%?!?!!%!%!!???!%%!%!%%!!%!!?%%!!%?!!%%%%?%!!%?%??!%!%%%!!%!%%%?%%?!%?%!!?%%?%%%%%!%%!%!%!%?!!!?!!!!%?%%%!!!!!??%%?!%%!?!%%!%!%?!%%?%%!%?%%?%%%!!%%%%%%?%%!?%%%?!%%%?%!%%%%%!!!%%%!!!?%?!!%%!!!!%!!??%!%%?!!!%!!%%%?%%%%%%!!!%%!%!%%%%%%!%!%%!!!!%?%???!%?%!?!!?!%!!%?%%%%%!?%%?!?%%%!%!!!%!%!%%!!%%%%%%%?%%%%!%?%!?%%%%%!%%%?%%%!!!%%?%!%%%?%%!!!?!%%!!%%%!%!%!?%!!!%%%!?%%?!%!!%??!!!!!!!%!%%%%!%%!%%!!%?!!%%!!%%%%!%%!?!?%!!!%%%%%%?!!%%%%%%!%%%%?!%!%?%%%%!!%?%%%!%%%%?!%!%%!!!!!!!%!%%?%%%!%%%%!!????!%?!%?!%?%?!!%!?%%!%!%%!!!??!!%!!!!!?!%%%!%?!%!?%?%?%!!%%%?%%!!%%!%!!!%?%??!?%%%%!!?%%%%%??!!?!!%%%?%%%?%!?%!%%%?%??%?!%!?%%%!?%?%%!%!%!%??!!!%%!?!???%!!?%!%%!!%!%%!!%%%%%%!%%%%%%!%%%?%?!%?%!%?%%?%?!%!%?%%%!%%%%%?%?!!!%?!%%!!%!?!%!!%%!!%%%%%!!?%!%??!%!!%!%%%!!!!%!%!%?%!%!!!%%%%!%%%%!%?!%!%%%%%%%!!!%!!!%%!!%?!!%!!!!%!%%%%!%?%%!?!?!%%%%%!%%%%!!?%%!!%%%%?%!!%%!%%%%%!%%?!?%?%!?%%?%%%!?%!%?!%%%%%%%%%%!%%%!!%!%!?!?!!!%%%!%?!%??!!%!%!%%%%%%%%%%%%!%%!%%%!!%?!%%%!%%!%%!?%%%%%!!%!%?%!?%?!!!!!%!%!%!?%%%%%!?!!?%!%?%?!%?%%?!%?%%?!!%!%%%!%%%%%!!!!!?%%!??!!%%%%!%%%!!%!%?!?%!?%?%!!?%!%?%!!%??!%%?%!%%%%%%%%%!%!%!?!??!%!!%!!!!%?%?!?!%%%%%%!?%%!!%!!!%%!%!!?%!%?!%%!%!!%!!%%!%!%!%!%%%!%??%!?%%!!!%?!%%!%!%%%!%%%%%%%!!!%!%%%!!!?!!%!%?!!%%!!%%!%%!!%?!!%!%?%!??!?!%!%%%!!?!%%!%%??%%!%%%%%??%!!%?!%%?%!!!%%%%!%!!!%!?!!%?%%%!!!%%?!%%?%?%?!%%%%%%!!%%!%!??%%!%!!?!??%%%???!%!??!!!!!%%%%%%%%!%!!%?%%!!%%?!?%%!?%!%%?!?!!?%!%?%%!%%%%%%!%%%!%%!%%!%%%!?!%%%%%!%%!%!!%?%%%%!!?%%!%%!%!%%!!%!??!%%!!%%%?!%?!%%!?!%!!!%%%!%?%%%!%!%%%%%%!%%!%%!!?!!%?%%%??!%%!!!%?!%%%!%!!!?%%?%!%!?%%%%!%!!!!?%!!%?%!!!?%%!%%!%%%!%?!%!?%?!%!%%??!!%!%%%?%??!%???%%%%%%!%%?%?%%%%%!%!?!!??%!%!%!!%?%?%%%?%?%??%!!!?%%%!?!!!%%!!!!%%%%%!!%!%%!%!!%?%%?!!?!?!?%%?%%%%%%%!?!!!!%%%!%%%%!%%?%?%???%%!%%%!!%?%%!!%!??!!%%%!%!%%%!%%%!!?!?%!%%%!?%%!%?%!??%%?!%%!%!!%!%!!%%%%%%%%%??!%%!!%?!!%!%?!!%!%%!%%%!%%?!!!%!%%?!!%%!!!%!!%!%!?!!!%!!?!!!%??!%%!?%%%?%?%!%?%!?%%!%%%%!%%!!!%%%?%!%!!%%%%%!%%%%%%%%%!%!!?%!%!%%%%!!%?%?%?%%?!%%%%!%!!!%%%%!!?!?%%??!!%!?!!%?%!!%%%!%%%%%!!%%%!%!%!%?%!!%!!%!!%%%%!%%!%%!%!%!!%?!!%!%%%%%%%!%%!%%%?%%%%!!!%%?!!%%??%??!!!%%!!!%??!%%%!%%%!??!!%%%%?%!!!??%%!%?!%%?%%!!!%%%!!%!%%%?!%!!!%%%%!???!%!!?%!?%!?!!%%!%%!?%!%%!?!!?!%!%?!!%%%%!%%??%!!%!%!%%%!%?!%!%%%!?!?%!!%!!??!%!!%%%!!%!?!!!%%!%%?!?%!%?%%??%%%?!!?!!?%!%!!%!%!%%?%??!%%%%!?!%!!?%?!!!%%%%!%?!!%!!%!!%%%%%!?%?!%!!!!%%?%%%%!%!%%!!%!!%%?%!%!!!%%%%%?!%!%%%%!%!!%%%%?!%%%%!%%%%%%%?%%%%%%?%%!?!%%!!%%!?%%!?%%!%?%%!!%%?%!%%%!!%%%%%%%%!!%%!%%%!%%??%!%!?!??!%%!!!%?!%%!%%%!!%%%%!?%?%%!?%!?%%?!%?%??!?%?%?!%!!?!%%%%%?%%%%%%%?!%%%!!?!!%%??%!%!%!?%%?%!%%%?!!?%%%%!%%%%!?%%!%!%!?!%%!?%%!!%%%!%?%%!%?%%%!!!%%%!%?%%?!%!%!%!!%%%!!%%%??!!%%%!%%?!%!?%%%%?%!!%?%%!%!%%%!?!%?!%%%%%?%%%%??!%?%!!!!!!!!%?!!!%%!!%%%!!!!%!%?%!!%?%%%%?%??!%%%!%!%%?%%!!%%!!%!%%%%%?!?!!%%!%?%%%!?%!?%%!!%%%%!%%??%??!!!%%!??%!!%%!?%!?!%%%%!!?!%%!??%?%??%%%!?%?!!?!%%!%!%%!%%!%!?%?%%!%!!%%%!%???%?%%!?!!%!!%!!!?!%%?%%!%!!?%!%?%?%%!??!!?!!!%?%%?!!?%%%!%?!%%!%!!!%!%?%%!%%%%%!%%!!%!%%!%?!!!%?%!??%!%%%%%%%%%?!!!?%%?%%%%!!%!%!%%!!%%?%?!%?!%%%%?%%!%!%%%%!%?%%%?%!%%%??!%%%%%!??!?%%?%??!?%!!!%!%!%%!!%%!%!!!!?%%!!!%!%%%%!!!%%!!!!%%!?%%!%%!%%!??%%%%!%%%!!%!!?%!?!%?!%!?!%%!!%!%%???!%??!%!!%!%!%!??%?%!%!?%%!!%?%!%%%!%!!%%%?%%%!!%%!%%%%??%%!!!?!%%%!%!%!%!?%%%?!%????%!?%!%%%?!??!!%!%%?!?%%%!!??!??!%!!%%%!?%%%?!%!!!!%?!!!!%?%!%?%!??%!%!%!%?%!%%!%%%?%%%!%!?!%%!%%%%!!?%%%%?%%%!%?!%!!%%?!%?!%%%%%%%%%?%!%%!%?%?!!!%%%%!%!%??%?!%!?!!%???%%!%%!!%%!%%%?!%%!!%%%?%??%!%%%%%!!%%?%%!%!%!?%!?%%!%%%!%!%?%!%%!!%!%?!%??%%%!%!!!%%!%%%?%%!%%%?%%?%%%!!%!!%!%!!?!%?!%?!!!!%%%!!%%%%%%!!%!??!%%!?%%!%%%??%!!%!!%?!?%!%%%%%?%?%%%%%?%!!%%!%%!%?%!%!!%!%!?!!%%%%!%%!%!!%?!%!%!?%%%!%!%%!%?%%%%%%!%!!?!?!!%!!!%%??%%?%%!??%%%!!?%%%!!%?!%%!!%%%%??%%%?%%!!%%%%?!?%%!%%%!%%!?!?!%!%%??%%%!%!%%%%!!!!%!?%%!!?!?%?%%%%!%!%%!?%%%!%%%%!??%!!%!?%!?%%!%%%%%%%%%%%!%%!%%!!%!%?%!!%?!!%!%?!!%%!!?%?%%%%%%%?%!%%??%%!?%%!%%!%%%%%?!!%%!%!%!!%???!!%!%!??!%?!!%%%?%?%!!%%??%!!%!%!?%?!?%%?%%%%!%!%%!!!%!!!!%%%%%!%!%!%%!???!%!%%!%%!!%%!?%!?!!%!!!%!%%%%%%%%%!%!?%!%!%?!!?!?!!%%%!%%!%%?!%%!%!%%%!%!?%?!!%??!?!?!%%?%%%!%??%%!!!!!!!!!?!!%%%!%%%%!%!??%%!!%!?%?%?%?%?%!%%?!%!!!!%!%???!!?!?%!%%%%?!%!!%!%%!!!!!%%%!?!%!%%!?!??%%%%?!%!!%%!!!!%%??!%!!!!!%%!?%!!?%%%?!!%%%%%%%??!%!%%%%%?%%%%!%%!!%%!%%!!%!?%!%!%%%!!?%%%%?%%!%%?!??!%%%?!!?%!%!%%%!!%!?%%!!?%!%%?%?!??%%?%%!%%%?%!%%%%??!!!%!%%!%!%!?!%%%%%!%%?!!?%%%?!?%%?!%!!%?!!%%%%?%%%!%!!%!!%!!%%!%%%!%%%!%!!!%!!%!%%%?!!%%%?!!?%!!%%!!%%%%%!?!!%%!%!%?%%!!%%!!!!%%%%?%%%%%!%%!!!%!%%%?!!%?%%%!%%%!%%%%%%%%%%!?%%%%?!%!?!%!%%%!!%!!%%%!%%%!%?!%%!!%%?%!%%!%%%!%!%%%!!%!%%?%%!%%!%%%?%%!%!!%%%!%?!%%%!%%%%%!?!!?%%!?!!!%%?%?%%%!?%?%!!?!%!%%%%%%%!%%%%%%!!!!!%%??!!??!%!%???%?%%%!!%!%%?!?%?%%%!%%%!!!%!!%%!!!%!????!%???%!!?!%%?%!!%%%!%?%!?%!%%%!!%%?%!%%!??!!%!!!%%!!!%!%?!!%%%!!%%%!!?%!!%%%!!??!%!%%%%!!%%%%%!%%?!%?%!%%!!%??%%!!%%?!%%%!!!!!%%%!%%?!?%!!?%%!%%%!%?%%%!!!?%%!!!?%%%?!%%%!!!!%?!%%%!!%%%!!%%%%!%%?%%?%!?%%!!%?%?%%%!%%%!?!%%%?%%!!%!%%!!%?!%%?!!?%%%?!!!!%%?%!?%%%?%!%!!%?%%%??%%%!%%!%?%!!!!%%%!?%%%%!?%%?%!%!!%%!%%%%?%%!%%!%!?%!%?%%?%?%%!!!!!%!%!!?!?%!%!%%%%%%!%%%!%%%!!?%!%!%%!%%!?%%%!?%!%!!?%%?!?%?!%!!?%%%?%!?%!?%%%%%!?!%%!!!%%!%?!%%%!%%!%%%%%%%%!!!!!%!%%!!%%%!%%%%%?!%%%%%!%%!!!%!!%%%!!%%?%!%%%!%!!!!%%%!%%%!!%???!?%%?%!%%!!%?!?!?%?!%%?!!?!?!%!%%!!%!%???%!%!?%?%!!?!%%!%%%?%%!%%!%!??!%!!%?%!%!%%%!?%?%!?!?!%%!!%!?%%???%%!%%%%!?!%?%!!%%%!!?%%%%?!!%%%!%%%%%?%!%%!!?%!?%%%!!?%??%%?%?!%!?!??!%%%%!??!?!!?%!%!!?!%%%?!%?%%%!!!%%!!!?%%%%!!?!%%%!?%!?%%%%!!%!!!%%!%%!%%%%!?%!%?%!!?!%%%!%!%!?!?%!?%%%?!!!%?!%%%!%%%??!?%!%%!%%?%%%%%%!%%!?%%%??!?%%%%%!%%%%!!%!%?%%?%%?!%%%%?%%%%?!%?%%!%%%%%!%%%!?%?!%!?%!!!!%!!%%%%%!%%%%%!!%!%?%!%!!%?%%?%%%%!!?%%%?!!!%!%%%%?%?!%?!!!!!!%?!%%%!%%!!%?%%%?!?!!%%%%%%%?!!%%%!!%!?%!?!%!%!!%!%!%%%?!!!!%%?%!!%!!%?%%?!%?%!%!%!!%!%?!%%%!%%?!%!?!!%%%%!%%!!%%%%!!%!%!!%?!%!%%%????%?!%%%%%%%!%%%%%%?!!?!???%%%%!%!!!!%!%%!?%!!%!%?%!?%%!%%%?%!!%%%%%%?%?!!%%?%%?!%%%%!!?!!!%%!!!?%%%%?!!??!?!?%%!%%%%%%!!%!%!%?!%%?%???%?!%%%%%!%%%?%%%!!%%!%%%%%!%%%%%%!!!!?!%!%!!!%%%%??!?%!!%!!%?%%%?!?!!!%??%?%!%%%%!%%%!?%%%!%%!%!%%%!%?%%?%!%%!%%%%??!%!%?!%%!!%!!?%%%%%?%%%?%?!%%?%%?%?!!!!%%%%%%%%%%%!%%%?!%!??!!!%!%!%%%%%%%%%%!%%!%%!%%!?%!!%%!%%%!!!!!?%%!?%?%%?%?!!?%%!?%!%%%!!?%%%%%?%%%?!%!%?!!%!%!%%?%?!!!%%!!%??!?%%%!%?%%!%?%!%?%%!%%!?!%%%?%?%!!%?%%%?!!!%%%!?%%%%!??%?%!%%%%%%%!%!!?%%%?%%%%!%%!!%??%%%???%!?%!??%%%!%%%!%!%%%??%!!%%%!!!%!!?!!!!!%%%?!!?!!%!%%!%%!%!%%!%?!%%!!!!??%%!!!%%%%%%??!!%%%%%!%!!!%%?%%%%%!!!!%%!%!%?%%??%?%%%%!%??%%%%%%%!%%?%%%%%%%!%!!!%%?!!%%!%%?!%%%%!!!?!!!!!%%?!?!??!%%%!??%%%?%!%%%?%%%!!!%%%!!!?%?%?!%!%!%%!?%%!?%%!%%!%!%!!!%?%?!%%%!?%%%?!?%%?%!?%!%%!!%!!%?!!!!%?%%!%%%!?%!%!!%%%!!!%%%!%%%%%%%%%?!!!!?%%%%?!?%??%%?%!!!%!?%%!!!%?%!!%%%?!!%%!!%?%?%!%!%%%!!%!%!%?%%%%?!?%%?%!%!%!!?%%%!?%?%!?!%!!%!%%%%?%%%!!!!!%%%!%!!%%%!%%%%%!?%?!%%!??%%%!!?%%?!?!!%?%%!!?%%!%??!%!%%!%!%!%?!%!!%!!!?%%!?%?!%%%?%%%%!%%!!%?%?%!?!%!!%!%!%%%%!%%?%%%!??!%%!!!%??%!%%%??%%?!%!%?%!!?%%!?%%?%?%%!!%%!?%%%!%%??%%%!!%?!%??%%%?%?%!%%%!?%!%?%!%%%?%%!??!%%%%!?%!%!!%?%%%%!!%?%%%%!!!%%%%??!%%%%%!%%!%%%%!%!!%%!%%?%%?%?%?%%?%!!!%%%!%%!%?!%%?%!%!%!!%!%%!%%?!!!%%%%!??!!?%??%!%?%%?!%%%%!%!!%?!%%%%%%!%%!?!!!%!%!!%%!!%%!%!!%%%%%%!!%!%%%!!?!%!%%!?!%%!%!%%%%%%%??%%%%%??%%%%!%!!?%%%?!!%%%%%%%?%%!%%!?!%?%!!!???!!??%!??!!?!%%%?!%%!?%%%%?%!%??!??%?%%%!%!%%%%%%?%!%%!?%?%??%!!%%%!%%%%%%!!%!!?%%%?%%?!!!%!?%%%%!%!!?%%%!?%%%??!%%?%!%!?%!%!%%?%!!%%%%!%!!!?%%?%!!%%!%%!!%!?%%%!%!%%?!??!%%!?%!%%%%%%%?!%!?!?%%%!%%%!%!%%?!!?%%%%!%%%!%!!!!!!!%?%%?%!%%!!!%%%%!!?!?!%?!?%!!%%!%%!%%?!!%%%!!%%%%???!!?%%!!%?%%%!??%?%!%%%!?%%?%%?%!!!!%?%?!%%%%!!%%%!!!%!?!!?%!%%!%%!%!!?%!?%?!%%??%%!?%%%!!!!!%%%%%!%!%?%%!!?%!%!!%%%%!%%%?%!!%?!%?%%%%!%%%%!%%%?%%!!!!%%%!!%!%%!?%%!?%%%?%!!%%%?%?!%!%!!%%%!%%%!!?!?%!!%%%%?%!!%!%%!!%!!%%!!!%%!%%%!%%%%!!?!%!?!!?%%%!%%!%?!!!!%%%!!!!!%?!%%?%%!%%%??!?%?%%%!?!?!!%!%!%%%!!?%%%!%%!%?%!%?%%!?%??!%?%%!%%%!%!!%%%%%??%!!%!?!?!%%%!!%!?!?%!%%?!!%%%!!%%!%%%%?%?%%%%%%%%%!%%!%!!??!%%!?!!%%!!!!!?!%%!%%?%%%!!%!%%%%%!?!!!!!%%?%!!!%%%!?!%!!!!!!%%?%?!?%%!%!!%!!%!%%%?%%%!%%%%?!%%!!%?!%?%!%?!%%%%!??%?%!%%!!%%%!%?%%!%%%%%!!!%%!!%%!%!%%?!%%%!%%!%?%?!?!!%%?!%%!!???%!!%?!!%?%!%!%!%?!!!%%%!%%%%!!%!%!%!%!!%%!!%!?%%%?!??!!%%??%?%%!!%!%!!%!%?!%!%?!!%!%?%!%?!?%%%%!!%%%%!%%!%%?!??!!%!!!!%?%!??%!!%%!%?%%??%%!!?%%!%%?%!?%%%?%?%%!?!!%!!!!%%?%%?!!%%%%%!%%%!!!!%!!!%!?%%%!!?%?%?%%%!%???%%%%%%%!!%!%!!%??!!?%%?!?%%!%%%%%??!!!!%?%?!?!%!%%!%!?%?!!%%!!%%!%%!%?!?%!%%%%!%!!%!?%%!%%%%!!!%%!?!%??!%%!%!%?%%%%%!!!!%!%%??!!%%??!%!?!%%!%%%??%%!%!%!!%%%%!%!%%!%?!?!!!%%%%%%%%!?!%!%?%%%%%%!!%%%!%%?????%!!%%!%%!!%%%%%%%%!%%%%%?%%%!%%!!%%!!!%%!!%!%!%%?%!%%!%%%%%%%%?%!%!%?!?!%%%%%?!!%%%%!%%%%!!%%????%%!?!!!?!%!!%%!!%%%%%%!?%!%%?%%!%!%!%%%!%!%%!%%!%%?%%%?%%?%%??%%%!?!!!%??!%?%%?%%%!?!%%?%%?%!???%%%!!%!!%%%!%!!?%!!!!!??!%%???!%!!?%!%?!!%?%%!!!%%!%!?!!??%%?%%%%%?%%%%%?!!%%?%%?%%%!?!%!!%%%%%!%?!%?%%!%%%?!%%!!%%%%%!!!!%%!%%%%%!%!!%!%%?!%!!%!???!%%!?%%??!!%%%!%%%??%!!%%%?!??!!!!?%%%!?%%%?%%!%!%?%!%?!!%%!%%%!%%%%!%%!?%%!!!!%!?%%%!%%%!%%%!%!%!!?!%%%%%%!!%!%??!?%%%%!?%!%??!%%!?%%%!??%!!%!%%?%%%%%!%%%!!!?!!!%!%!!!%%?!%?%!%%%%%%?!?%%%%!%!%%?!!%%!%%%%?%!???!%!%%%%?!!!?%%!%!?!!!!%!?%%%%?!%!?!?%%%%!??!!?%?%%%!!?!?%!!?%!??%!%!%!?!%!!!!%!!%%%?%!%?%%%!?%%%!%?%!!!%!?%!%%!!!%?%%%%?%?%?%%!%!!%!%!%%?%%!?%???%%!%!!?!!%!%!?%!!!!%!%%%!%?!%!!!%%!%!?%!%%%!%%!%!??%%!%!%%!!?%%!%%%!!!%!!?%!!!?!%%%%?%!!%%%%!!!!%!!!!%!%%%%%!!%!!!%%%%!%%%??%!%!?%%?%%%%%%!!?%%?%%%!?%!%%!%??%%%!%%!?%%?%%?%%%!%%?%!%!?%%!!!!!%?%%!%?%%%!!%%??%!!!!%!%%!?!%%?%!%!%%!?!?!!%%%!!%!!!%%%%!?!%!%!?%%%!%??!%??!!%!!%!!%!!!!%!!??%%%%!!?%%?%%!!%%%%!!??!!!%!%!!?!%%%%!%%!?%!!%%!%%!%%%%%!!!!%?!?%!!!??%%%!!%!!%!!%%%%%%!?!!%!!!%%%?%!?%?%?%!?%%%%%!!?%%%!%!%!?!%?%!?!%%%!%%%%!!%?%%?%!%!%%%%%%!!?%%!%%%%!!%?!%%%%!?%!!!%%!%!%%%%%%!!!??%!!%!!?????%!?%%%?!!%%%!%%?!!%!%!%!??%%!%!%!%%%%?!%?%%!%?%!!%?%?%!%%?%?%?!%%%!!!!%%%!?%%!??%!%%?%?%!%%%%?%%%!%!%!!??!!%!%%!%%!%%%%!?%!%%%%%%%?%%%%%%!!%%%?!%!%%%!%%!!%!%%!%%?!!?%?%?%!!%%!!!!!%%%%!%%%!?%!%!%%!?%%!%!?%%%?!%?!%?%!??!!%%!%!%%?!%%%%!%%!?!%%%!??%%!!%!%%%!%!!%?!%%%%%%%%%%!%%%%%!!?!%%%!?!%%%%%?!!?%!!%!%!%!!!!!%%?!!%!%!%%%%%!!?%?%!!!!%!!?%?%?!!%%%%%%%%?%%%%!!%%!%!!!%%%!?!?%%%!?!?%%!!!!%%%%!!!%%??%!!?%?%?!?!!%%!%?%%!%!!%!%%%%%%%%%%!!!%%?%%%%%%?!!%%?!%!!%!%?%?%%%%%%%%!?!%!!%?%!%%?%!%!!!?%??%!!%??%%%%%!?!!!%!%!%%%%!!%%%%%?%%%!!%!?%%%!!%%!?%!%!%!!!?%%%!?%!%!%?!%%%!!%!%%%!!!%%%%!!%%??%%%%?%%!%!?%%%!!?!%!%!!!%!??%!!%%!!!!??%!??%?%%!!!!!?!?!?%%?%%%%%!%%?!!%?%!!!%!%!%!!%