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```from operator import itemgetter
from heapq import nlargest
from itertools import repeat, ifilter

class Counter(dict):
'''Dict subclass for counting hashable objects.  Sometimes called a bag
or multiset.  Elements are stored as dictionary keys and their counts
are stored as dictionary values.

>>> Counter('zyzygy')
Counter({'y': 3, 'z': 2, 'g': 1})

'''

def __init__(self, iterable=None, **kwds):
'''Create a new, empty Counter object.  And if given, count elements
from an input iterable.  Or, initialize the count from another mapping
of elements to their counts.

>>> c = Counter()                           # a new, empty counter
>>> c = Counter('gallahad')                 # a new counter from an iterable
>>> c = Counter({'a': 4, 'b': 2})           # a new counter from a mapping
>>> c = Counter(a=4, b=2)                   # a new counter from keyword args

'''
self.update(iterable, **kwds)

def __missing__(self, key):
return 0

def most_common(self, n=None):
'''List the n most common elements and their counts from the most
common to the least.  If n is None, then list all element counts.

[('a', 5), ('r', 2), ('b', 2)]

'''
if n is None:
return sorted(self.iteritems(), key=itemgetter(1), reverse=True)
return nlargest(n, self.iteritems(), key=itemgetter(1))

def elements(self):
'''Iterator over elements repeating each as many times as its count.

>>> c = Counter('ABCABC')
>>> sorted(c.elements())
['A', 'A', 'B', 'B', 'C', 'C']

If an element's count has been set to zero or is a negative number,
elements() will ignore it.

'''
for elem, count in self.iteritems():
for _ in repeat(None, count):
yield elem

# Override dict methods where the meaning changes for Counter objects.

@classmethod
def fromkeys(cls, iterable, v=None):
raise NotImplementedError(
'Counter.fromkeys() is undefined.  Use Counter(iterable) instead.')

def update(self, iterable=None, **kwds):

Source can be an iterable, a dictionary, or another Counter instance.

>>> c = Counter('which')
>>> c.update('witch')           # add elements from another iterable
>>> d = Counter('watch')
>>> c.update(d)                 # add elements from another counter
>>> c['h']                      # four 'h' in which, witch, and watch
4

'''
if iterable is not None:
if hasattr(iterable, 'iteritems'):
if self:
self_get = self.get
for elem, count in iterable.iteritems():
self[elem] = self_get(elem, 0) + count
else:
dict.update(self, iterable) # fast path when counter is empty
else:
self_get = self.get
for elem in iterable:
self[elem] = self_get(elem, 0) + 1
if kwds:
self.update(kwds)

def copy(self):
'Like dict.copy() but returns a Counter instance instead of a dict.'
return Counter(self)

def __delitem__(self, elem):
'Like dict.__delitem__() but does not raise KeyError for missing values.'
if elem in self:
dict.__delitem__(self, elem)

def __repr__(self):
if not self:
return '%s()' % self.__class__.__name__
items = ', '.join(map('%r: %r'.__mod__, self.most_common()))
return '%s({%s})' % (self.__class__.__name__, items)

# Multiset-style mathematical operations discussed in:
#       Knuth TAOCP Volume II section 4.6.3 exercise 19
#       and at http://en.wikipedia.org/wiki/Multiset
#
# Outputs guaranteed to only include positive counts.
#
# To strip negative and zero counts, add-in an empty counter:
#       c += Counter()

>>> Counter('abbb') + Counter('bcc')
Counter({'b': 4, 'c': 2, 'a': 1})

'''
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
return result

def __sub__(self, other):
''' Subtract count, but keep only results with positive counts.

>>> Counter('abbbc') - Counter('bccd')
Counter({'b': 2, 'a': 1})

'''
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
return result

def __or__(self, other):
'''Union is the maximum of value in either of the input counters.

>>> Counter('abbb') | Counter('bcc')
Counter({'b': 3, 'c': 2, 'a': 1})

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

def __and__(self, other):
''' Intersection is the minimum of corresponding counts.

>>> Counter('abbb') & Counter('bcc')
Counter({'b': 1})

'''
if not isinstance(other, Counter):
return NotImplemented
_min = min
result = Counter()
if len(self) < len(other):
self, other = other, self
for elem in ifilter(self.__contains__, other):
newcount = _min(self[elem], other[elem])
if newcount > 0:
result[elem] = newcount
return result

if __name__ == '__main__':
import doctest
print doctest.testmod()
```