bpo-44605: Teach @total_ordering() to work with metaclasses (GH-27633) (GH-27640)

diff --git a/Lib/functools.py b/Lib/functools.py
index 357c1df..77ec852 100644
--- a/Lib/functools.py
+++ b/Lib/functools.py
@@ -88,84 +88,84 @@ def wraps(wrapped,
 
 def _gt_from_lt(self, other, NotImplemented=NotImplemented):
     'Return a > b.  Computed by @total_ordering from (not a < b) and (a != b).'
-    op_result = self.__lt__(other)
+    op_result = type(self).__lt__(self, other)
     if op_result is NotImplemented:
         return op_result
     return not op_result and self != other
 
 def _le_from_lt(self, other, NotImplemented=NotImplemented):
     'Return a <= b.  Computed by @total_ordering from (a < b) or (a == b).'
-    op_result = self.__lt__(other)
+    op_result = type(self).__lt__(self, other)
     if op_result is NotImplemented:
         return op_result
     return op_result or self == other
 
 def _ge_from_lt(self, other, NotImplemented=NotImplemented):
     'Return a >= b.  Computed by @total_ordering from (not a < b).'
-    op_result = self.__lt__(other)
+    op_result = type(self).__lt__(self, other)
     if op_result is NotImplemented:
         return op_result
     return not op_result
 
 def _ge_from_le(self, other, NotImplemented=NotImplemented):
     'Return a >= b.  Computed by @total_ordering from (not a <= b) or (a == b).'
-    op_result = self.__le__(other)
+    op_result = type(self).__le__(self, other)
     if op_result is NotImplemented:
         return op_result
     return not op_result or self == other
 
 def _lt_from_le(self, other, NotImplemented=NotImplemented):
     'Return a < b.  Computed by @total_ordering from (a <= b) and (a != b).'
-    op_result = self.__le__(other)
+    op_result = type(self).__le__(self, other)
     if op_result is NotImplemented:
         return op_result
     return op_result and self != other
 
 def _gt_from_le(self, other, NotImplemented=NotImplemented):
     'Return a > b.  Computed by @total_ordering from (not a <= b).'
-    op_result = self.__le__(other)
+    op_result = type(self).__le__(self, other)
     if op_result is NotImplemented:
         return op_result
     return not op_result
 
 def _lt_from_gt(self, other, NotImplemented=NotImplemented):
     'Return a < b.  Computed by @total_ordering from (not a > b) and (a != b).'
-    op_result = self.__gt__(other)
+    op_result = type(self).__gt__(self, other)
     if op_result is NotImplemented:
         return op_result
     return not op_result and self != other
 
 def _ge_from_gt(self, other, NotImplemented=NotImplemented):
     'Return a >= b.  Computed by @total_ordering from (a > b) or (a == b).'
-    op_result = self.__gt__(other)
+    op_result = type(self).__gt__(self, other)
     if op_result is NotImplemented:
         return op_result
     return op_result or self == other
 
 def _le_from_gt(self, other, NotImplemented=NotImplemented):
     'Return a <= b.  Computed by @total_ordering from (not a > b).'
-    op_result = self.__gt__(other)
+    op_result = type(self).__gt__(self, other)
     if op_result is NotImplemented:
         return op_result
     return not op_result
 
 def _le_from_ge(self, other, NotImplemented=NotImplemented):
     'Return a <= b.  Computed by @total_ordering from (not a >= b) or (a == b).'
-    op_result = self.__ge__(other)
+    op_result = type(self).__ge__(self, other)
     if op_result is NotImplemented:
         return op_result
     return not op_result or self == other
 
 def _gt_from_ge(self, other, NotImplemented=NotImplemented):
     'Return a > b.  Computed by @total_ordering from (a >= b) and (a != b).'
-    op_result = self.__ge__(other)
+    op_result = type(self).__ge__(self, other)
     if op_result is NotImplemented:
         return op_result
     return op_result and self != other
 
 def _lt_from_ge(self, other, NotImplemented=NotImplemented):
     'Return a < b.  Computed by @total_ordering from (not a >= b).'
-    op_result = self.__ge__(other)
+    op_result = type(self).__ge__(self, other)
     if op_result is NotImplemented:
         return op_result
     return not op_result
diff --git a/Lib/test/test_functools.py b/Lib/test/test_functools.py
index 78a8a5f..fbf5578 100644
--- a/Lib/test/test_functools.py
+++ b/Lib/test/test_functools.py
@@ -1163,6 +1163,34 @@ def test_pickle(self):
                     method_copy = pickle.loads(pickle.dumps(method, proto))
                     self.assertIs(method_copy, method)
 
+
+    def test_total_ordering_for_metaclasses_issue_44605(self):
+
+        @functools.total_ordering
+        class SortableMeta(type):
+            def __new__(cls, name, bases, ns):
+                return super().__new__(cls, name, bases, ns)
+
+            def __lt__(self, other):
+                if not isinstance(other, SortableMeta):
+                    pass
+                return self.__name__ < other.__name__
+
+            def __eq__(self, other):
+                if not isinstance(other, SortableMeta):
+                    pass
+                return self.__name__ == other.__name__
+
+        class B(metaclass=SortableMeta):
+            pass
+
+        class A(metaclass=SortableMeta):
+            pass
+
+        self.assertTrue(A < B)
+        self.assertFalse(A > B)
+
+
 @functools.total_ordering
 class Orderable_LT:
     def __init__(self, value):