| '''This module implements specialized container datatypes providing | 
 | alternatives to Python's general purpose built-in containers, dict, | 
 | list, set, and tuple. | 
 |  | 
 | * namedtuple   factory function for creating tuple subclasses with named fields | 
 | * deque        list-like container with fast appends and pops on either end | 
 | * Counter      dict subclass for counting hashable objects | 
 | * OrderedDict  dict subclass that remembers the order entries were added | 
 | * defaultdict  dict subclass that calls a factory function to supply missing values | 
 |  | 
 | ''' | 
 |  | 
 | __all__ = ['Counter', 'deque', 'defaultdict', 'namedtuple', 'OrderedDict'] | 
 | # For bootstrapping reasons, the collection ABCs are defined in _abcoll.py. | 
 | # They should however be considered an integral part of collections.py. | 
 | from _abcoll import * | 
 | import _abcoll | 
 | __all__ += _abcoll.__all__ | 
 |  | 
 | from _collections import deque, defaultdict | 
 | from operator import itemgetter as _itemgetter, eq as _eq | 
 | from keyword import iskeyword as _iskeyword | 
 | import sys as _sys | 
 | import heapq as _heapq | 
 | from itertools import repeat as _repeat, chain as _chain, starmap as _starmap | 
 | from itertools import imap as _imap | 
 |  | 
 | try: | 
 |     from thread import get_ident as _get_ident | 
 | except ImportError: | 
 |     from dummy_thread import get_ident as _get_ident | 
 |  | 
 |  | 
 | ################################################################################ | 
 | ### OrderedDict | 
 | ################################################################################ | 
 |  | 
 | class OrderedDict(dict): | 
 |     'Dictionary that remembers insertion order' | 
 |     # An inherited dict maps keys to values. | 
 |     # The inherited dict provides __getitem__, __len__, __contains__, and get. | 
 |     # The remaining methods are order-aware. | 
 |     # Big-O running times for all methods are the same as regular dictionaries. | 
 |  | 
 |     # The internal self.__map dict maps keys to links in a doubly linked list. | 
 |     # The circular doubly linked list starts and ends with a sentinel element. | 
 |     # The sentinel element never gets deleted (this simplifies the algorithm). | 
 |     # Each link is stored as a list of length three:  [PREV, NEXT, KEY]. | 
 |  | 
 |     def __init__(*args, **kwds): | 
 |         '''Initialize an ordered dictionary.  The signature is the same as | 
 |         regular dictionaries, but keyword arguments are not recommended because | 
 |         their insertion order is arbitrary. | 
 |  | 
 |         ''' | 
 |         if not args: | 
 |             raise TypeError("descriptor '__init__' of 'OrderedDict' object " | 
 |                             "needs an argument") | 
 |         self = args[0] | 
 |         args = args[1:] | 
 |         if len(args) > 1: | 
 |             raise TypeError('expected at most 1 arguments, got %d' % len(args)) | 
 |         try: | 
 |             self.__root | 
 |         except AttributeError: | 
 |             self.__root = root = []                     # sentinel node | 
 |             root[:] = [root, root, None] | 
 |             self.__map = {} | 
 |         self.__update(*args, **kwds) | 
 |  | 
 |     def __setitem__(self, key, value, dict_setitem=dict.__setitem__): | 
 |         'od.__setitem__(i, y) <==> od[i]=y' | 
 |         # Setting a new item creates a new link at the end of the linked list, | 
 |         # and the inherited dictionary is updated with the new key/value pair. | 
 |         if key not in self: | 
 |             root = self.__root | 
 |             last = root[0] | 
 |             last[1] = root[0] = self.__map[key] = [last, root, key] | 
 |         return dict_setitem(self, key, value) | 
 |  | 
 |     def __delitem__(self, key, dict_delitem=dict.__delitem__): | 
 |         'od.__delitem__(y) <==> del od[y]' | 
 |         # Deleting an existing item uses self.__map to find the link which gets | 
 |         # removed by updating the links in the predecessor and successor nodes. | 
 |         dict_delitem(self, key) | 
 |         link_prev, link_next, _ = self.__map.pop(key) | 
 |         link_prev[1] = link_next                        # update link_prev[NEXT] | 
 |         link_next[0] = link_prev                        # update link_next[PREV] | 
 |  | 
 |     def __iter__(self): | 
 |         'od.__iter__() <==> iter(od)' | 
 |         # Traverse the linked list in order. | 
 |         root = self.__root | 
 |         curr = root[1]                                  # start at the first node | 
 |         while curr is not root: | 
 |             yield curr[2]                               # yield the curr[KEY] | 
 |             curr = curr[1]                              # move to next node | 
 |  | 
 |     def __reversed__(self): | 
 |         'od.__reversed__() <==> reversed(od)' | 
 |         # Traverse the linked list in reverse order. | 
 |         root = self.__root | 
 |         curr = root[0]                                  # start at the last node | 
 |         while curr is not root: | 
 |             yield curr[2]                               # yield the curr[KEY] | 
 |             curr = curr[0]                              # move to previous node | 
 |  | 
 |     def clear(self): | 
 |         'od.clear() -> None.  Remove all items from od.' | 
 |         root = self.__root | 
 |         root[:] = [root, root, None] | 
 |         self.__map.clear() | 
 |         dict.clear(self) | 
 |  | 
 |     # -- the following methods do not depend on the internal structure -- | 
 |  | 
 |     def keys(self): | 
 |         'od.keys() -> list of keys in od' | 
 |         return list(self) | 
 |  | 
 |     def values(self): | 
 |         'od.values() -> list of values in od' | 
 |         return [self[key] for key in self] | 
 |  | 
 |     def items(self): | 
 |         'od.items() -> list of (key, value) pairs in od' | 
 |         return [(key, self[key]) for key in self] | 
 |  | 
 |     def iterkeys(self): | 
 |         'od.iterkeys() -> an iterator over the keys in od' | 
 |         return iter(self) | 
 |  | 
 |     def itervalues(self): | 
 |         'od.itervalues -> an iterator over the values in od' | 
 |         for k in self: | 
 |             yield self[k] | 
 |  | 
 |     def iteritems(self): | 
 |         'od.iteritems -> an iterator over the (key, value) pairs in od' | 
 |         for k in self: | 
 |             yield (k, self[k]) | 
 |  | 
 |     update = MutableMapping.update | 
 |  | 
 |     __update = update # let subclasses override update without breaking __init__ | 
 |  | 
 |     __marker = object() | 
 |  | 
 |     def pop(self, key, default=__marker): | 
 |         '''od.pop(k[,d]) -> v, remove specified key and return the corresponding | 
 |         value.  If key is not found, d is returned if given, otherwise KeyError | 
 |         is raised. | 
 |  | 
 |         ''' | 
 |         if key in self: | 
 |             result = self[key] | 
 |             del self[key] | 
 |             return result | 
 |         if default is self.__marker: | 
 |             raise KeyError(key) | 
 |         return default | 
 |  | 
 |     def setdefault(self, key, default=None): | 
 |         'od.setdefault(k[,d]) -> od.get(k,d), also set od[k]=d if k not in od' | 
 |         if key in self: | 
 |             return self[key] | 
 |         self[key] = default | 
 |         return default | 
 |  | 
 |     def popitem(self, last=True): | 
 |         '''od.popitem() -> (k, v), return and remove a (key, value) pair. | 
 |         Pairs are returned in LIFO order if last is true or FIFO order if false. | 
 |  | 
 |         ''' | 
 |         if not self: | 
 |             raise KeyError('dictionary is empty') | 
 |         key = next(reversed(self) if last else iter(self)) | 
 |         value = self.pop(key) | 
 |         return key, value | 
 |  | 
 |     def __repr__(self, _repr_running={}): | 
 |         'od.__repr__() <==> repr(od)' | 
 |         call_key = id(self), _get_ident() | 
 |         if call_key in _repr_running: | 
 |             return '...' | 
 |         _repr_running[call_key] = 1 | 
 |         try: | 
 |             if not self: | 
 |                 return '%s()' % (self.__class__.__name__,) | 
 |             return '%s(%r)' % (self.__class__.__name__, self.items()) | 
 |         finally: | 
 |             del _repr_running[call_key] | 
 |  | 
 |     def __reduce__(self): | 
 |         'Return state information for pickling' | 
 |         items = [[k, self[k]] for k in self] | 
 |         inst_dict = vars(self).copy() | 
 |         for k in vars(OrderedDict()): | 
 |             inst_dict.pop(k, None) | 
 |         if inst_dict: | 
 |             return (self.__class__, (items,), inst_dict) | 
 |         return self.__class__, (items,) | 
 |  | 
 |     def copy(self): | 
 |         'od.copy() -> a shallow copy of od' | 
 |         return self.__class__(self) | 
 |  | 
 |     @classmethod | 
 |     def fromkeys(cls, iterable, value=None): | 
 |         '''OD.fromkeys(S[, v]) -> New ordered dictionary with keys from S. | 
 |         If not specified, the value defaults to None. | 
 |  | 
 |         ''' | 
 |         self = cls() | 
 |         for key in iterable: | 
 |             self[key] = value | 
 |         return self | 
 |  | 
 |     def __eq__(self, other): | 
 |         '''od.__eq__(y) <==> od==y.  Comparison to another OD is order-sensitive | 
 |         while comparison to a regular mapping is order-insensitive. | 
 |  | 
 |         ''' | 
 |         if isinstance(other, OrderedDict): | 
 |             return dict.__eq__(self, other) and all(_imap(_eq, self, other)) | 
 |         return dict.__eq__(self, other) | 
 |  | 
 |     def __ne__(self, other): | 
 |         'od.__ne__(y) <==> od!=y' | 
 |         return not self == other | 
 |  | 
 |     # -- the following methods support python 3.x style dictionary views -- | 
 |  | 
 |     def viewkeys(self): | 
 |         "od.viewkeys() -> a set-like object providing a view on od's keys" | 
 |         return KeysView(self) | 
 |  | 
 |     def viewvalues(self): | 
 |         "od.viewvalues() -> an object providing a view on od's values" | 
 |         return ValuesView(self) | 
 |  | 
 |     def viewitems(self): | 
 |         "od.viewitems() -> a set-like object providing a view on od's items" | 
 |         return ItemsView(self) | 
 |  | 
 |  | 
 | ################################################################################ | 
 | ### namedtuple | 
 | ################################################################################ | 
 |  | 
 | _class_template = '''\ | 
 | class {typename}(tuple): | 
 |     '{typename}({arg_list})' | 
 |  | 
 |     __slots__ = () | 
 |  | 
 |     _fields = {field_names!r} | 
 |  | 
 |     def __new__(_cls, {arg_list}): | 
 |         'Create new instance of {typename}({arg_list})' | 
 |         return _tuple.__new__(_cls, ({arg_list})) | 
 |  | 
 |     @classmethod | 
 |     def _make(cls, iterable, new=tuple.__new__, len=len): | 
 |         'Make a new {typename} object from a sequence or iterable' | 
 |         result = new(cls, iterable) | 
 |         if len(result) != {num_fields:d}: | 
 |             raise TypeError('Expected {num_fields:d} arguments, got %d' % len(result)) | 
 |         return result | 
 |  | 
 |     def __repr__(self): | 
 |         'Return a nicely formatted representation string' | 
 |         return '{typename}({repr_fmt})' % self | 
 |  | 
 |     def _asdict(self): | 
 |         'Return a new OrderedDict which maps field names to their values' | 
 |         return OrderedDict(zip(self._fields, self)) | 
 |  | 
 |     def _replace(_self, **kwds): | 
 |         'Return a new {typename} object replacing specified fields with new values' | 
 |         result = _self._make(map(kwds.pop, {field_names!r}, _self)) | 
 |         if kwds: | 
 |             raise ValueError('Got unexpected field names: %r' % kwds.keys()) | 
 |         return result | 
 |  | 
 |     def __getnewargs__(self): | 
 |         'Return self as a plain tuple.  Used by copy and pickle.' | 
 |         return tuple(self) | 
 |  | 
 |     __dict__ = _property(_asdict) | 
 |  | 
 |     def __getstate__(self): | 
 |         'Exclude the OrderedDict from pickling' | 
 |         pass | 
 |  | 
 | {field_defs} | 
 | ''' | 
 |  | 
 | _repr_template = '{name}=%r' | 
 |  | 
 | _field_template = '''\ | 
 |     {name} = _property(_itemgetter({index:d}), doc='Alias for field number {index:d}') | 
 | ''' | 
 |  | 
 | def namedtuple(typename, field_names, verbose=False, rename=False): | 
 |     """Returns a new subclass of tuple with named fields. | 
 |  | 
 |     >>> Point = namedtuple('Point', ['x', 'y']) | 
 |     >>> Point.__doc__                   # docstring for the new class | 
 |     'Point(x, y)' | 
 |     >>> p = Point(11, y=22)             # instantiate with positional args or keywords | 
 |     >>> p[0] + p[1]                     # indexable like a plain tuple | 
 |     33 | 
 |     >>> x, y = p                        # unpack like a regular tuple | 
 |     >>> x, y | 
 |     (11, 22) | 
 |     >>> p.x + p.y                       # fields also accessable by name | 
 |     33 | 
 |     >>> d = p._asdict()                 # convert to a dictionary | 
 |     >>> d['x'] | 
 |     11 | 
 |     >>> Point(**d)                      # convert from a dictionary | 
 |     Point(x=11, y=22) | 
 |     >>> p._replace(x=100)               # _replace() is like str.replace() but targets named fields | 
 |     Point(x=100, y=22) | 
 |  | 
 |     """ | 
 |  | 
 |     # Validate the field names.  At the user's option, either generate an error | 
 |     # message or automatically replace the field name with a valid name. | 
 |     if isinstance(field_names, basestring): | 
 |         field_names = field_names.replace(',', ' ').split() | 
 |     field_names = map(str, field_names) | 
 |     typename = str(typename) | 
 |     if rename: | 
 |         seen = set() | 
 |         for index, name in enumerate(field_names): | 
 |             if (not all(c.isalnum() or c=='_' for c in name) | 
 |                 or _iskeyword(name) | 
 |                 or not name | 
 |                 or name[0].isdigit() | 
 |                 or name.startswith('_') | 
 |                 or name in seen): | 
 |                 field_names[index] = '_%d' % index | 
 |             seen.add(name) | 
 |     for name in [typename] + field_names: | 
 |         if type(name) != str: | 
 |             raise TypeError('Type names and field names must be strings') | 
 |         if not all(c.isalnum() or c=='_' for c in name): | 
 |             raise ValueError('Type names and field names can only contain ' | 
 |                              'alphanumeric characters and underscores: %r' % name) | 
 |         if _iskeyword(name): | 
 |             raise ValueError('Type names and field names cannot be a ' | 
 |                              'keyword: %r' % name) | 
 |         if name[0].isdigit(): | 
 |             raise ValueError('Type names and field names cannot start with ' | 
 |                              'a number: %r' % name) | 
 |     seen = set() | 
 |     for name in field_names: | 
 |         if name.startswith('_') and not rename: | 
 |             raise ValueError('Field names cannot start with an underscore: ' | 
 |                              '%r' % name) | 
 |         if name in seen: | 
 |             raise ValueError('Encountered duplicate field name: %r' % name) | 
 |         seen.add(name) | 
 |  | 
 |     # Fill-in the class template | 
 |     class_definition = _class_template.format( | 
 |         typename = typename, | 
 |         field_names = tuple(field_names), | 
 |         num_fields = len(field_names), | 
 |         arg_list = repr(tuple(field_names)).replace("'", "")[1:-1], | 
 |         repr_fmt = ', '.join(_repr_template.format(name=name) | 
 |                              for name in field_names), | 
 |         field_defs = '\n'.join(_field_template.format(index=index, name=name) | 
 |                                for index, name in enumerate(field_names)) | 
 |     ) | 
 |     if verbose: | 
 |         print class_definition | 
 |  | 
 |     # Execute the template string in a temporary namespace and support | 
 |     # tracing utilities by setting a value for frame.f_globals['__name__'] | 
 |     namespace = dict(_itemgetter=_itemgetter, __name__='namedtuple_%s' % typename, | 
 |                      OrderedDict=OrderedDict, _property=property, _tuple=tuple) | 
 |     try: | 
 |         exec class_definition in namespace | 
 |     except SyntaxError as e: | 
 |         raise SyntaxError(e.message + ':\n' + class_definition) | 
 |     result = namespace[typename] | 
 |  | 
 |     # For pickling to work, the __module__ variable needs to be set to the frame | 
 |     # where the named tuple is created.  Bypass this step in environments where | 
 |     # sys._getframe is not defined (Jython for example) or sys._getframe is not | 
 |     # defined for arguments greater than 0 (IronPython). | 
 |     try: | 
 |         result.__module__ = _sys._getframe(1).f_globals.get('__name__', '__main__') | 
 |     except (AttributeError, ValueError): | 
 |         pass | 
 |  | 
 |     return result | 
 |  | 
 |  | 
 | ######################################################################## | 
 | ###  Counter | 
 | ######################################################################## | 
 |  | 
 | class Counter(dict): | 
 |     '''Dict subclass for counting hashable items.  Sometimes called a bag | 
 |     or multiset.  Elements are stored as dictionary keys and their counts | 
 |     are stored as dictionary values. | 
 |  | 
 |     >>> c = Counter('abcdeabcdabcaba')  # count elements from a string | 
 |  | 
 |     >>> c.most_common(3)                # three most common elements | 
 |     [('a', 5), ('b', 4), ('c', 3)] | 
 |     >>> sorted(c)                       # list all unique elements | 
 |     ['a', 'b', 'c', 'd', 'e'] | 
 |     >>> ''.join(sorted(c.elements()))   # list elements with repetitions | 
 |     'aaaaabbbbcccdde' | 
 |     >>> sum(c.values())                 # total of all counts | 
 |     15 | 
 |  | 
 |     >>> c['a']                          # count of letter 'a' | 
 |     5 | 
 |     >>> for elem in 'shazam':           # update counts from an iterable | 
 |     ...     c[elem] += 1                # by adding 1 to each element's count | 
 |     >>> c['a']                          # now there are seven 'a' | 
 |     7 | 
 |     >>> del c['b']                      # remove all 'b' | 
 |     >>> c['b']                          # now there are zero 'b' | 
 |     0 | 
 |  | 
 |     >>> d = Counter('simsalabim')       # make another counter | 
 |     >>> c.update(d)                     # add in the second counter | 
 |     >>> c['a']                          # now there are nine 'a' | 
 |     9 | 
 |  | 
 |     >>> c.clear()                       # empty the counter | 
 |     >>> c | 
 |     Counter() | 
 |  | 
 |     Note:  If a count is set to zero or reduced to zero, it will remain | 
 |     in the counter until the entry is deleted or the counter is cleared: | 
 |  | 
 |     >>> c = Counter('aaabbc') | 
 |     >>> c['b'] -= 2                     # reduce the count of 'b' by two | 
 |     >>> c.most_common()                 # 'b' is still in, but its count is zero | 
 |     [('a', 3), ('c', 1), ('b', 0)] | 
 |  | 
 |     ''' | 
 |     # References: | 
 |     #   http://en.wikipedia.org/wiki/Multiset | 
 |     #   http://www.gnu.org/software/smalltalk/manual-base/html_node/Bag.html | 
 |     #   http://www.demo2s.com/Tutorial/Cpp/0380__set-multiset/Catalog0380__set-multiset.htm | 
 |     #   http://code.activestate.com/recipes/259174/ | 
 |     #   Knuth, TAOCP Vol. II section 4.6.3 | 
 |  | 
 |     def __init__(*args, **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 | 
 |  | 
 |         ''' | 
 |         if not args: | 
 |             raise TypeError("descriptor '__init__' of 'Counter' object " | 
 |                             "needs an argument") | 
 |         self = args[0] | 
 |         args = args[1:] | 
 |         if len(args) > 1: | 
 |             raise TypeError('expected at most 1 arguments, got %d' % len(args)) | 
 |         super(Counter, self).__init__() | 
 |         self.update(*args, **kwds) | 
 |  | 
 |     def __missing__(self, key): | 
 |         'The count of elements not in the Counter is zero.' | 
 |         # Needed so that self[missing_item] does not raise KeyError | 
 |         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. | 
 |  | 
 |         >>> Counter('abcdeabcdabcaba').most_common(3) | 
 |         [('a', 5), ('b', 4), ('c', 3)] | 
 |  | 
 |         ''' | 
 |         # Emulate Bag.sortedByCount from Smalltalk | 
 |         if n is None: | 
 |             return sorted(self.iteritems(), key=_itemgetter(1), reverse=True) | 
 |         return _heapq.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'] | 
 |  | 
 |         # Knuth's example for prime factors of 1836:  2**2 * 3**3 * 17**1 | 
 |         >>> prime_factors = Counter({2: 2, 3: 3, 17: 1}) | 
 |         >>> product = 1 | 
 |         >>> for factor in prime_factors.elements():     # loop over factors | 
 |         ...     product *= factor                       # and multiply them | 
 |         >>> product | 
 |         1836 | 
 |  | 
 |         Note, if an element's count has been set to zero or is a negative | 
 |         number, elements() will ignore it. | 
 |  | 
 |         ''' | 
 |         # Emulate Bag.do from Smalltalk and Multiset.begin from C++. | 
 |         return _chain.from_iterable(_starmap(_repeat, self.iteritems())) | 
 |  | 
 |     # Override dict methods where necessary | 
 |  | 
 |     @classmethod | 
 |     def fromkeys(cls, iterable, v=None): | 
 |         # There is no equivalent method for counters because setting v=1 | 
 |         # means that no element can have a count greater than one. | 
 |         raise NotImplementedError( | 
 |             'Counter.fromkeys() is undefined.  Use Counter(iterable) instead.') | 
 |  | 
 |     def update(*args, **kwds): | 
 |         '''Like dict.update() but add counts instead of replacing them. | 
 |  | 
 |         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 | 
 |  | 
 |         ''' | 
 |         # The regular dict.update() operation makes no sense here because the | 
 |         # replace behavior results in the some of original untouched counts | 
 |         # being mixed-in with all of the other counts for a mismash that | 
 |         # doesn't have a straight-forward interpretation in most counting | 
 |         # contexts.  Instead, we implement straight-addition.  Both the inputs | 
 |         # and outputs are allowed to contain zero and negative counts. | 
 |  | 
 |         if not args: | 
 |             raise TypeError("descriptor 'update' of 'Counter' object " | 
 |                             "needs an argument") | 
 |         self = args[0] | 
 |         args = args[1:] | 
 |         if len(args) > 1: | 
 |             raise TypeError('expected at most 1 arguments, got %d' % len(args)) | 
 |         iterable = args[0] if args else None | 
 |         if iterable is not None: | 
 |             if isinstance(iterable, Mapping): | 
 |                 if self: | 
 |                     self_get = self.get | 
 |                     for elem, count in iterable.iteritems(): | 
 |                         self[elem] = self_get(elem, 0) + count | 
 |                 else: | 
 |                     super(Counter, self).update(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 subtract(*args, **kwds): | 
 |         '''Like dict.update() but subtracts counts instead of replacing them. | 
 |         Counts can be reduced below zero.  Both the inputs and outputs are | 
 |         allowed to contain zero and negative counts. | 
 |  | 
 |         Source can be an iterable, a dictionary, or another Counter instance. | 
 |  | 
 |         >>> c = Counter('which') | 
 |         >>> c.subtract('witch')             # subtract elements from another iterable | 
 |         >>> c.subtract(Counter('watch'))    # subtract elements from another counter | 
 |         >>> c['h']                          # 2 in which, minus 1 in witch, minus 1 in watch | 
 |         0 | 
 |         >>> c['w']                          # 1 in which, minus 1 in witch, minus 1 in watch | 
 |         -1 | 
 |  | 
 |         ''' | 
 |         if not args: | 
 |             raise TypeError("descriptor 'subtract' of 'Counter' object " | 
 |                             "needs an argument") | 
 |         self = args[0] | 
 |         args = args[1:] | 
 |         if len(args) > 1: | 
 |             raise TypeError('expected at most 1 arguments, got %d' % len(args)) | 
 |         iterable = args[0] if args else None | 
 |         if iterable is not None: | 
 |             self_get = self.get | 
 |             if isinstance(iterable, Mapping): | 
 |                 for elem, count in iterable.items(): | 
 |                     self[elem] = self_get(elem, 0) - count | 
 |             else: | 
 |                 for elem in iterable: | 
 |                     self[elem] = self_get(elem, 0) - 1 | 
 |         if kwds: | 
 |             self.subtract(kwds) | 
 |  | 
 |     def copy(self): | 
 |         'Return a shallow copy.' | 
 |         return self.__class__(self) | 
 |  | 
 |     def __reduce__(self): | 
 |         return self.__class__, (dict(self),) | 
 |  | 
 |     def __delitem__(self, elem): | 
 |         'Like dict.__delitem__() but does not raise KeyError for missing values.' | 
 |         if elem in self: | 
 |             super(Counter, self).__delitem__(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() | 
 |  | 
 |     def __add__(self, other): | 
 |         '''Add counts from two counters. | 
 |  | 
 |         >>> Counter('abbb') + Counter('bcc') | 
 |         Counter({'b': 4, 'c': 2, 'a': 1}) | 
 |  | 
 |         ''' | 
 |         if not isinstance(other, Counter): | 
 |             return NotImplemented | 
 |         result = Counter() | 
 |         for elem, count in self.items(): | 
 |             newcount = count + other[elem] | 
 |             if newcount > 0: | 
 |                 result[elem] = newcount | 
 |         for elem, count in other.items(): | 
 |             if elem not in self and count > 0: | 
 |                 result[elem] = count | 
 |         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, count in self.items(): | 
 |             newcount = count - other[elem] | 
 |             if newcount > 0: | 
 |                 result[elem] = newcount | 
 |         for elem, count in other.items(): | 
 |             if elem not in self and count < 0: | 
 |                 result[elem] = 0 - count | 
 |         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 | 
 |         result = Counter() | 
 |         for elem, count in self.items(): | 
 |             other_count = other[elem] | 
 |             newcount = other_count if count < other_count else count | 
 |             if newcount > 0: | 
 |                 result[elem] = newcount | 
 |         for elem, count in other.items(): | 
 |             if elem not in self and count > 0: | 
 |                 result[elem] = count | 
 |         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 | 
 |         result = Counter() | 
 |         for elem, count in self.items(): | 
 |             other_count = other[elem] | 
 |             newcount = count if count < other_count else other_count | 
 |             if newcount > 0: | 
 |                 result[elem] = newcount | 
 |         return result | 
 |  | 
 |  | 
 | if __name__ == '__main__': | 
 |     # verify that instances can be pickled | 
 |     from cPickle import loads, dumps | 
 |     Point = namedtuple('Point', 'x, y', True) | 
 |     p = Point(x=10, y=20) | 
 |     assert p == loads(dumps(p)) | 
 |  | 
 |     # test and demonstrate ability to override methods | 
 |     class Point(namedtuple('Point', 'x y')): | 
 |         __slots__ = () | 
 |         @property | 
 |         def hypot(self): | 
 |             return (self.x ** 2 + self.y ** 2) ** 0.5 | 
 |         def __str__(self): | 
 |             return 'Point: x=%6.3f  y=%6.3f  hypot=%6.3f' % (self.x, self.y, self.hypot) | 
 |  | 
 |     for p in Point(3, 4), Point(14, 5/7.): | 
 |         print p | 
 |  | 
 |     class Point(namedtuple('Point', 'x y')): | 
 |         'Point class with optimized _make() and _replace() without error-checking' | 
 |         __slots__ = () | 
 |         _make = classmethod(tuple.__new__) | 
 |         def _replace(self, _map=map, **kwds): | 
 |             return self._make(_map(kwds.get, ('x', 'y'), self)) | 
 |  | 
 |     print Point(11, 22)._replace(x=100) | 
 |  | 
 |     Point3D = namedtuple('Point3D', Point._fields + ('z',)) | 
 |     print Point3D.__doc__ | 
 |  | 
 |     import doctest | 
 |     TestResults = namedtuple('TestResults', 'failed attempted') | 
 |     print TestResults(*doctest.testmod()) |