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```import collections

class Counter(collections.Counter):

def __xor__(self, other):
''' Subtract count, but keep only abs results with non-zero counts.

>>> Counter('abbbc') ^ Counter('bccd')
Counter({'b': 2, 'a': 1, 'c': 1, 'd': 1})
>>> a, b = Counter('abbbc'), Counter('bccd')
>>> (a-b) + (b - a) == a ^ b
True

'''
if not isinstance(other, Counter):
return NotImplemented
result = Counter()
for elem in set(self) | set(other):
newcount = self[elem] - other[elem]
if newcount != 0:
result[elem] = newcount if newcount > 0 else -newcount
return result

def __mul__(self, other):
'''Multiply counts by an integer; or cartesioan product
of two counters.

>>> Counter('abbb') * 3
Counter({'b': 9, 'a': 3})
>>> Counter('12') * Counter('21')
Counter({('2', '1'): 1, ('1', '2'): 1, ('1', '1'): 1, ('2', '2'): 1})
>>> Counter('122') * Counter('211')
Counter({('2', '1'): 4, ('1', '1'): 2, ('2', '2'): 2, ('1', '2'): 1})
'''
if isinstance(other, int):
return Counter(**dict((k, v*other)
for k,v in self.items()))
elif isinstance(other, Counter):
return Counter( (x, y)
for x in self.elements()
for y in other.elements() )
else:
return NotImplemented

def __rmul__(self, other):
'''Multiply counts by an integer; or cartesioan product
of two counters.

>>> 3 * Counter('abbb')
Counter({'b': 9, 'a': 3, 'c': 3})
'''
return self.__mul__(other)
```

#### Diff to Previous Revision

```--- revision 2 2010-08-17 22:55:43
+++ revision 3 2010-08-18 21:02:41
@@ -1,5 +1,6 @@
-class Counter(dict):
-    # ... (all of Counter from file counter.py)
+import collections
+
+class Counter(collections.Counter):

def __xor__(self, other):
''' Subtract count, but keep only abs results with non-zero counts.
```