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

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):