diff --git a/src/PIL/PpmImagePlugin.py b/src/PIL/PpmImagePlugin.py
index d43e21e14..9d37dcde0 100644
--- a/src/PIL/PpmImagePlugin.py
+++ b/src/PIL/PpmImagePlugin.py
@@ -100,6 +100,7 @@ class PpmImageFile(ImageFile.ImageFile):
         except KeyError:
             msg = "not a PPM file"
             raise SyntaxError(msg)
+        self._mode = mode
 
         if magic_number in (b"P1", b"P4"):
             self.custom_mimetype = "image/x-portable-bitmap"
@@ -108,49 +109,40 @@ class PpmImageFile(ImageFile.ImageFile):
         elif magic_number in (b"P3", b"P6"):
             self.custom_mimetype = "image/x-portable-pixmap"
 
-        maxval = None
+        self._size = int(self._read_token()), int(self._read_token())
+
         decoder_name = "raw"
         if magic_number in (b"P1", b"P2", b"P3"):
             decoder_name = "ppm_plain"
-        for ix in range(3):
-            if mode == "F" and ix == 2:
-                scale = float(self._read_token())
-                if scale == 0.0 or not math.isfinite(scale):
-                    msg = "scale must be finite and non-zero"
-                    raise ValueError(msg)
-                rawmode = "F;32F" if scale < 0 else "F;32BF"
-                self.info["scale"] = abs(scale)
-                continue
-            token = int(self._read_token())
-            if ix == 0:  # token is the x size
-                xsize = token
-            elif ix == 1:  # token is the y size
-                ysize = token
-                if mode == "1":
-                    self._mode = "1"
-                    rawmode = "1;I"
-                    break
-                else:
-                    self._mode = rawmode = mode
-            elif ix == 2:  # token is maxval
-                maxval = token
-                if not 0 < maxval < 65536:
-                    msg = "maxval must be greater than 0 and less than 65536"
-                    raise ValueError(msg)
-                if maxval > 255 and mode == "L":
-                    self._mode = "I"
+        if mode == "1":
+            args = "1;I"
+        elif mode == "F":
+            scale = float(self._read_token())
+            if scale == 0.0 or not math.isfinite(scale):
+                msg = "scale must be finite and non-zero"
+                raise ValueError(msg)
+            self.info["scale"] = abs(scale)
 
-                if decoder_name != "ppm_plain":
-                    # If maxval matches a bit depth, use the raw decoder directly
-                    if maxval == 65535 and mode == "L":
-                        rawmode = "I;16B"
-                    elif maxval != 255:
-                        decoder_name = "ppm"
+            rawmode = "F;32F" if scale < 0 else "F;32BF"
+            args = (rawmode, 0, -1)
+        else:
+            maxval = int(self._read_token())
+            if not 0 < maxval < 65536:
+                msg = "maxval must be greater than 0 and less than 65536"
+                raise ValueError(msg)
+            if maxval > 255 and mode == "L":
+                self._mode = "I"
 
-        row_order = -1 if mode == "F" else 1
-        args = (rawmode, 0, row_order) if decoder_name == "raw" else (rawmode, maxval)
-        self._size = xsize, ysize
-        self.tile = [(decoder_name, (0, 0, xsize, ysize), self.fp.tell(), args)]
+            rawmode = mode
+            if decoder_name != "ppm_plain":
+                # If maxval matches a bit depth, use the raw decoder directly
+                if maxval == 65535 and mode == "L":
+                    rawmode = "I;16B"
+                elif maxval != 255:
+                    decoder_name = "ppm"
+
+            args = rawmode if decoder_name == "raw" else (rawmode, maxval)
+        self.tile = [(decoder_name, (0, 0) + self.size, self.fp.tell(), args)]
 
 
 #
@@ -319,7 +311,6 @@ class PpmDecoder(ImageFile.PyDecoder):
 
 
 def _save(im, fp, filename):
-    row_order = 1
     if im.mode == "1":
         rawmode, head = "1;I", b"P4"
     elif im.mode == "L":
@@ -330,7 +321,6 @@ def _save(im, fp, filename):
         rawmode, head = "RGB", b"P6"
     elif im.mode == "F":
         rawmode, head = "F;32F", b"Pf"
-        row_order = -1
     else:
         msg = f"cannot write mode {im.mode} as PPM"
         raise OSError(msg)
@@ -344,6 +334,7 @@ def _save(im, fp, filename):
             fp.write(b"65535\n")
     elif head == b"Pf":
         fp.write(b"-1.0\n")
+    row_order = -1 if im.mode == "F" else 1
     ImageFile._save(im, fp, [("raw", (0, 0) + im.size, 0, (rawmode, 0, row_order))])