| __all__ = ['deque', 'defaultdict', 'namedtuple', 'UserDict', 'UserList', | 
 |             'UserString', 'Counter', '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 | 
 | from keyword import iskeyword as _iskeyword | 
 | import sys as _sys | 
 | import heapq as _heapq | 
 | from weakref import proxy as _proxy | 
 | from itertools import repeat as _repeat, chain as _chain, starmap as _starmap | 
 |  | 
 | ################################################################################ | 
 | ### OrderedDict | 
 | ################################################################################ | 
 |  | 
 | class _Link(object): | 
 |     __slots__ = 'prev', 'next', 'key', '__weakref__' | 
 |  | 
 | class OrderedDict(dict, MutableMapping): | 
 |     '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 for regular dictionaries. | 
 |  | 
 |     # The internal self.__map dictionary 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). | 
 |     # The prev/next links are weakref proxies (to prevent circular references). | 
 |     # Individual links are kept alive by the hard reference in self.__map. | 
 |     # Those hard references disappear when a key is deleted from an OrderedDict. | 
 |  | 
 |     def __init__(self, *args, **kwds): | 
 |         '''Initialize an ordered dictionary.  Signature is the same as for | 
 |         regular dictionaries, but keyword arguments are not recommended | 
 |         because their insertion order is arbitrary. | 
 |  | 
 |         ''' | 
 |         if len(args) > 1: | 
 |             raise TypeError('expected at most 1 arguments, got %d' % len(args)) | 
 |         try: | 
 |             self.__root | 
 |         except AttributeError: | 
 |             self.__root = root = _Link()    # sentinel node for the doubly linked list | 
 |             root.prev = root.next = root | 
 |             self.__map = {} | 
 |         self.update(*args, **kwds) | 
 |  | 
 |     def clear(self): | 
 |         'od.clear() -> None.  Remove all items from od.' | 
 |         root = self.__root | 
 |         root.prev = root.next = root | 
 |         self.__map.clear() | 
 |         dict.clear(self) | 
 |  | 
 |     def __setitem__(self, key, value): | 
 |         'od.__setitem__(i, y) <==> od[i]=y' | 
 |         # Setting a new item creates a new link which goes at the end of the linked | 
 |         # list, and the inherited dictionary is updated with the new key/value pair. | 
 |         if key not in self: | 
 |             self.__map[key] = link = _Link() | 
 |             root = self.__root | 
 |             last = root.prev | 
 |             link.prev, link.next, link.key = last, root, key | 
 |             last.next = root.prev = _proxy(link) | 
 |         dict.__setitem__(self, key, value) | 
 |  | 
 |     def __delitem__(self, key): | 
 |         'od.__delitem__(y) <==> del od[y]' | 
 |         # Deleting an existing item uses self.__map to find the link which is | 
 |         # then removed by updating the links in the predecessor and successor nodes. | 
 |         dict.__delitem__(self, key) | 
 |         link = self.__map.pop(key) | 
 |         link.prev.next = link.next | 
 |         link.next.prev = link.prev | 
 |  | 
 |     def __iter__(self): | 
 |         'od.__iter__() <==> iter(od)' | 
 |         # Traverse the linked list in order. | 
 |         root = self.__root | 
 |         curr = root.next | 
 |         while curr is not root: | 
 |             yield curr.key | 
 |             curr = curr.next | 
 |  | 
 |     def __reversed__(self): | 
 |         'od.__reversed__() <==> reversed(od)' | 
 |         # Traverse the linked list in reverse order. | 
 |         root = self.__root | 
 |         curr = root.prev | 
 |         while curr is not root: | 
 |             yield curr.key | 
 |             curr = curr.prev | 
 |  | 
 |     def __reduce__(self): | 
 |         'Return state information for pickling' | 
 |         items = [[k, self[k]] for k in self] | 
 |         tmp = self.__map, self.__root | 
 |         del self.__map, self.__root | 
 |         inst_dict = vars(self).copy() | 
 |         self.__map, self.__root = tmp | 
 |         if inst_dict: | 
 |             return (self.__class__, (items,), inst_dict) | 
 |         return self.__class__, (items,) | 
 |  | 
 |     setdefault = MutableMapping.setdefault | 
 |     update = MutableMapping.update | 
 |     pop = MutableMapping.pop | 
 |     keys = MutableMapping.keys | 
 |     values = MutableMapping.values | 
 |     items = MutableMapping.items | 
 |  | 
 |     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): | 
 |         'od.__repr__() <==> repr(od)' | 
 |         if not self: | 
 |             return '%s()' % (self.__class__.__name__,) | 
 |         return '%s(%r)' % (self.__class__.__name__, list(self.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 | 
 |         and values equal to v (which defaults to None). | 
 |  | 
 |         ''' | 
 |         d = cls() | 
 |         for key in iterable: | 
 |             d[key] = value | 
 |         return d | 
 |  | 
 |     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 len(self)==len(other) and \ | 
 |                    all(p==q for p, q in zip(self.items(), other.items())) | 
 |         return dict.__eq__(self, other) | 
 |  | 
 |     def __ne__(self, other): | 
 |         '''od.__ne__(y) <==> od!=y.  Comparison to another OD is order-sensitive | 
 |         while comparison to a regular mapping is order-insensitive. | 
 |  | 
 |         ''' | 
 |         return not self == other | 
 |  | 
 |  | 
 |  | 
 | ################################################################################ | 
 | ### namedtuple | 
 | ################################################################################ | 
 |  | 
 | 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) | 
 |  | 
 |     """ | 
 |  | 
 |     # Parse and validate the field names.  Validation serves two purposes, | 
 |     # generating informative error messages and preventing template injection attacks. | 
 |     if isinstance(field_names, str): | 
 |         field_names = field_names.replace(',', ' ').split() # names separated by whitespace and/or commas | 
 |     field_names = tuple(map(str, field_names)) | 
 |     if rename: | 
 |         names = list(field_names) | 
 |         seen = set() | 
 |         for i, name in enumerate(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): | 
 |                 names[i] = '_%d' % i | 
 |             seen.add(name) | 
 |         field_names = tuple(names) | 
 |     for name in (typename,) + field_names: | 
 |         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_names = 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_names: | 
 |             raise ValueError('Encountered duplicate field name: %r' % name) | 
 |         seen_names.add(name) | 
 |  | 
 |     # Create and fill-in the class template | 
 |     numfields = len(field_names) | 
 |     argtxt = repr(field_names).replace("'", "")[1:-1]   # tuple repr without parens or quotes | 
 |     reprtxt = ', '.join('%s=%%r' % name for name in field_names) | 
 |     template = '''class %(typename)s(tuple): | 
 |         '%(typename)s(%(argtxt)s)' \n | 
 |         __slots__ = () \n | 
 |         _fields = %(field_names)r \n | 
 |         def __new__(_cls, %(argtxt)s): | 
 |             return _tuple.__new__(_cls, (%(argtxt)s)) \n | 
 |         @classmethod | 
 |         def _make(cls, iterable, new=tuple.__new__, len=len): | 
 |             'Make a new %(typename)s object from a sequence or iterable' | 
 |             result = new(cls, iterable) | 
 |             if len(result) != %(numfields)d: | 
 |                 raise TypeError('Expected %(numfields)d arguments, got %%d' %% len(result)) | 
 |             return result \n | 
 |         def __repr__(self): | 
 |             return '%(typename)s(%(reprtxt)s)' %% self \n | 
 |         def _asdict(self): | 
 |             'Return a new OrderedDict which maps field names to their values' | 
 |             return OrderedDict(zip(self._fields, self)) \n | 
 |         def _replace(_self, **kwds): | 
 |             'Return a new %(typename)s 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 \n | 
 |         def __getnewargs__(self): | 
 |             return tuple(self) \n\n''' % locals() | 
 |     for i, name in enumerate(field_names): | 
 |         template += '        %s = _property(_itemgetter(%d))\n' % (name, i) | 
 |     if verbose: | 
 |         print(template) | 
 |  | 
 |     # 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(template, namespace) | 
 |     except SyntaxError as e: | 
 |         raise SyntaxError(e.msg + ':\n' + template) from e | 
 |     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 enviroments 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('abracadabra')      # count elements from a string | 
 |  | 
 |     >>> c.most_common(3)                # three most common elements | 
 |     [('a', 5), ('r', 2), ('b', 2)] | 
 |     >>> sorted(c)                       # list all unique elements | 
 |     ['a', 'b', 'c', 'd', 'r'] | 
 |     >>> ''.join(sorted(c.elements()))   # list elements with repetitions | 
 |     'aaaaabbcdrr' | 
 |     >>> sum(c.values())                 # total of all counts | 
 |     11 | 
 |  | 
 |     >>> 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['r']                      # remove all 'r' | 
 |     >>> c['r']                          # now there are zero 'r' | 
 |     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__(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): | 
 |         '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('abracadabra').most_common(3) | 
 |         [('a', 5), ('r', 2), ('b', 2)] | 
 |  | 
 |         ''' | 
 |         # Emulate Bag.sortedByCount from Smalltalk | 
 |         if n is None: | 
 |             return sorted(self.items(), key=_itemgetter(1), reverse=True) | 
 |         return _heapq.nlargest(n, self.items(), 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.items())) | 
 |  | 
 |     # 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(self, iterable=None, **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 iterable is not None: | 
 |             if isinstance(iterable, Mapping): | 
 |                 if self: | 
 |                     self_get = self.get | 
 |                     for elem, count in iterable.items(): | 
 |                         self[elem] = count + self_get(elem, 0) | 
 |                 else: | 
 |                     dict.update(self, iterable) # fast path when counter is empty | 
 |             else: | 
 |                 self_get = self.get | 
 |                 for elem in iterable: | 
 |                     self[elem] = 1 + self_get(elem, 0) | 
 |         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() | 
 |  | 
 |     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 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 | 
 |         result = Counter() | 
 |         for elem in set(self) | set(other): | 
 |             p, q = self[elem], other[elem] | 
 |             newcount = q if p < q else p | 
 |             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 | 
 |         result = Counter() | 
 |         if len(self) < len(other): | 
 |             self, other = other, self | 
 |         for elem in filter(self.__contains__, other): | 
 |             p, q = self[elem], other[elem] | 
 |             newcount = p if p < q else q | 
 |             if newcount > 0: | 
 |                 result[elem] = newcount | 
 |         return result | 
 |  | 
 |  | 
 | ################################################################################ | 
 | ### UserDict | 
 | ################################################################################ | 
 |  | 
 | class UserDict(MutableMapping): | 
 |  | 
 |     # Start by filling-out the abstract methods | 
 |     def __init__(self, dict=None, **kwargs): | 
 |         self.data = {} | 
 |         if dict is not None: | 
 |             self.update(dict) | 
 |         if len(kwargs): | 
 |             self.update(kwargs) | 
 |     def __len__(self): return len(self.data) | 
 |     def __getitem__(self, key): | 
 |         if key in self.data: | 
 |             return self.data[key] | 
 |         if hasattr(self.__class__, "__missing__"): | 
 |             return self.__class__.__missing__(self, key) | 
 |         raise KeyError(key) | 
 |     def __setitem__(self, key, item): self.data[key] = item | 
 |     def __delitem__(self, key): del self.data[key] | 
 |     def __iter__(self): | 
 |         return iter(self.data) | 
 |  | 
 |     # Modify __contains__ to work correctly when __missing__ is present | 
 |     def __contains__(self, key): | 
 |         return key in self.data | 
 |  | 
 |     # Now, add the methods in dicts but not in MutableMapping | 
 |     def __repr__(self): return repr(self.data) | 
 |     def copy(self): | 
 |         if self.__class__ is UserDict: | 
 |             return UserDict(self.data.copy()) | 
 |         import copy | 
 |         data = self.data | 
 |         try: | 
 |             self.data = {} | 
 |             c = copy.copy(self) | 
 |         finally: | 
 |             self.data = data | 
 |         c.update(self) | 
 |         return c | 
 |     @classmethod | 
 |     def fromkeys(cls, iterable, value=None): | 
 |         d = cls() | 
 |         for key in iterable: | 
 |             d[key] = value | 
 |         return d | 
 |  | 
 |  | 
 |  | 
 | ################################################################################ | 
 | ### UserList | 
 | ################################################################################ | 
 |  | 
 | class UserList(MutableSequence): | 
 |     """A more or less complete user-defined wrapper around list objects.""" | 
 |     def __init__(self, initlist=None): | 
 |         self.data = [] | 
 |         if initlist is not None: | 
 |             # XXX should this accept an arbitrary sequence? | 
 |             if type(initlist) == type(self.data): | 
 |                 self.data[:] = initlist | 
 |             elif isinstance(initlist, UserList): | 
 |                 self.data[:] = initlist.data[:] | 
 |             else: | 
 |                 self.data = list(initlist) | 
 |     def __repr__(self): return repr(self.data) | 
 |     def __lt__(self, other): return self.data <  self.__cast(other) | 
 |     def __le__(self, other): return self.data <= self.__cast(other) | 
 |     def __eq__(self, other): return self.data == self.__cast(other) | 
 |     def __ne__(self, other): return self.data != self.__cast(other) | 
 |     def __gt__(self, other): return self.data >  self.__cast(other) | 
 |     def __ge__(self, other): return self.data >= self.__cast(other) | 
 |     def __cast(self, other): | 
 |         return other.data if isinstance(other, UserList) else other | 
 |     def __contains__(self, item): return item in self.data | 
 |     def __len__(self): return len(self.data) | 
 |     def __getitem__(self, i): return self.data[i] | 
 |     def __setitem__(self, i, item): self.data[i] = item | 
 |     def __delitem__(self, i): del self.data[i] | 
 |     def __add__(self, other): | 
 |         if isinstance(other, UserList): | 
 |             return self.__class__(self.data + other.data) | 
 |         elif isinstance(other, type(self.data)): | 
 |             return self.__class__(self.data + other) | 
 |         return self.__class__(self.data + list(other)) | 
 |     def __radd__(self, other): | 
 |         if isinstance(other, UserList): | 
 |             return self.__class__(other.data + self.data) | 
 |         elif isinstance(other, type(self.data)): | 
 |             return self.__class__(other + self.data) | 
 |         return self.__class__(list(other) + self.data) | 
 |     def __iadd__(self, other): | 
 |         if isinstance(other, UserList): | 
 |             self.data += other.data | 
 |         elif isinstance(other, type(self.data)): | 
 |             self.data += other | 
 |         else: | 
 |             self.data += list(other) | 
 |         return self | 
 |     def __mul__(self, n): | 
 |         return self.__class__(self.data*n) | 
 |     __rmul__ = __mul__ | 
 |     def __imul__(self, n): | 
 |         self.data *= n | 
 |         return self | 
 |     def append(self, item): self.data.append(item) | 
 |     def insert(self, i, item): self.data.insert(i, item) | 
 |     def pop(self, i=-1): return self.data.pop(i) | 
 |     def remove(self, item): self.data.remove(item) | 
 |     def count(self, item): return self.data.count(item) | 
 |     def index(self, item, *args): return self.data.index(item, *args) | 
 |     def reverse(self): self.data.reverse() | 
 |     def sort(self, *args, **kwds): self.data.sort(*args, **kwds) | 
 |     def extend(self, other): | 
 |         if isinstance(other, UserList): | 
 |             self.data.extend(other.data) | 
 |         else: | 
 |             self.data.extend(other) | 
 |  | 
 |  | 
 |  | 
 | ################################################################################ | 
 | ### UserString | 
 | ################################################################################ | 
 |  | 
 | class UserString(Sequence): | 
 |     def __init__(self, seq): | 
 |         if isinstance(seq, str): | 
 |             self.data = seq | 
 |         elif isinstance(seq, UserString): | 
 |             self.data = seq.data[:] | 
 |         else: | 
 |             self.data = str(seq) | 
 |     def __str__(self): return str(self.data) | 
 |     def __repr__(self): return repr(self.data) | 
 |     def __int__(self): return int(self.data) | 
 |     def __float__(self): return float(self.data) | 
 |     def __complex__(self): return complex(self.data) | 
 |     def __hash__(self): return hash(self.data) | 
 |  | 
 |     def __eq__(self, string): | 
 |         if isinstance(string, UserString): | 
 |             return self.data == string.data | 
 |         return self.data == string | 
 |     def __ne__(self, string): | 
 |         if isinstance(string, UserString): | 
 |             return self.data != string.data | 
 |         return self.data != string | 
 |     def __lt__(self, string): | 
 |         if isinstance(string, UserString): | 
 |             return self.data < string.data | 
 |         return self.data < string | 
 |     def __le__(self, string): | 
 |         if isinstance(string, UserString): | 
 |             return self.data <= string.data | 
 |         return self.data <= string | 
 |     def __gt__(self, string): | 
 |         if isinstance(string, UserString): | 
 |             return self.data > string.data | 
 |         return self.data > string | 
 |     def __ge__(self, string): | 
 |         if isinstance(string, UserString): | 
 |             return self.data >= string.data | 
 |         return self.data >= string | 
 |  | 
 |     def __contains__(self, char): | 
 |         if isinstance(char, UserString): | 
 |             char = char.data | 
 |         return char in self.data | 
 |  | 
 |     def __len__(self): return len(self.data) | 
 |     def __getitem__(self, index): return self.__class__(self.data[index]) | 
 |     def __add__(self, other): | 
 |         if isinstance(other, UserString): | 
 |             return self.__class__(self.data + other.data) | 
 |         elif isinstance(other, str): | 
 |             return self.__class__(self.data + other) | 
 |         return self.__class__(self.data + str(other)) | 
 |     def __radd__(self, other): | 
 |         if isinstance(other, str): | 
 |             return self.__class__(other + self.data) | 
 |         return self.__class__(str(other) + self.data) | 
 |     def __mul__(self, n): | 
 |         return self.__class__(self.data*n) | 
 |     __rmul__ = __mul__ | 
 |     def __mod__(self, args): | 
 |         return self.__class__(self.data % args) | 
 |  | 
 |     # the following methods are defined in alphabetical order: | 
 |     def capitalize(self): return self.__class__(self.data.capitalize()) | 
 |     def center(self, width, *args): | 
 |         return self.__class__(self.data.center(width, *args)) | 
 |     def count(self, sub, start=0, end=_sys.maxsize): | 
 |         if isinstance(sub, UserString): | 
 |             sub = sub.data | 
 |         return self.data.count(sub, start, end) | 
 |     def encode(self, encoding=None, errors=None): # XXX improve this? | 
 |         if encoding: | 
 |             if errors: | 
 |                 return self.__class__(self.data.encode(encoding, errors)) | 
 |             return self.__class__(self.data.encode(encoding)) | 
 |         return self.__class__(self.data.encode()) | 
 |     def endswith(self, suffix, start=0, end=_sys.maxsize): | 
 |         return self.data.endswith(suffix, start, end) | 
 |     def expandtabs(self, tabsize=8): | 
 |         return self.__class__(self.data.expandtabs(tabsize)) | 
 |     def find(self, sub, start=0, end=_sys.maxsize): | 
 |         if isinstance(sub, UserString): | 
 |             sub = sub.data | 
 |         return self.data.find(sub, start, end) | 
 |     def format(self, *args, **kwds): | 
 |         return self.data.format(*args, **kwds) | 
 |     def index(self, sub, start=0, end=_sys.maxsize): | 
 |         return self.data.index(sub, start, end) | 
 |     def isalpha(self): return self.data.isalpha() | 
 |     def isalnum(self): return self.data.isalnum() | 
 |     def isdecimal(self): return self.data.isdecimal() | 
 |     def isdigit(self): return self.data.isdigit() | 
 |     def isidentifier(self): return self.data.isidentifier() | 
 |     def islower(self): return self.data.islower() | 
 |     def isnumeric(self): return self.data.isnumeric() | 
 |     def isspace(self): return self.data.isspace() | 
 |     def istitle(self): return self.data.istitle() | 
 |     def isupper(self): return self.data.isupper() | 
 |     def join(self, seq): return self.data.join(seq) | 
 |     def ljust(self, width, *args): | 
 |         return self.__class__(self.data.ljust(width, *args)) | 
 |     def lower(self): return self.__class__(self.data.lower()) | 
 |     def lstrip(self, chars=None): return self.__class__(self.data.lstrip(chars)) | 
 |     def partition(self, sep): | 
 |         return self.data.partition(sep) | 
 |     def replace(self, old, new, maxsplit=-1): | 
 |         if isinstance(old, UserString): | 
 |             old = old.data | 
 |         if isinstance(new, UserString): | 
 |             new = new.data | 
 |         return self.__class__(self.data.replace(old, new, maxsplit)) | 
 |     def rfind(self, sub, start=0, end=_sys.maxsize): | 
 |         if isinstance(sub, UserString): | 
 |             sub = sub.data | 
 |         return self.data.rfind(sub, start, end) | 
 |     def rindex(self, sub, start=0, end=_sys.maxsize): | 
 |         return self.data.rindex(sub, start, end) | 
 |     def rjust(self, width, *args): | 
 |         return self.__class__(self.data.rjust(width, *args)) | 
 |     def rpartition(self, sep): | 
 |         return self.data.rpartition(sep) | 
 |     def rstrip(self, chars=None): | 
 |         return self.__class__(self.data.rstrip(chars)) | 
 |     def split(self, sep=None, maxsplit=-1): | 
 |         return self.data.split(sep, maxsplit) | 
 |     def rsplit(self, sep=None, maxsplit=-1): | 
 |         return self.data.rsplit(sep, maxsplit) | 
 |     def splitlines(self, keepends=0): return self.data.splitlines(keepends) | 
 |     def startswith(self, prefix, start=0, end=_sys.maxsize): | 
 |         return self.data.startswith(prefix, start, end) | 
 |     def strip(self, chars=None): return self.__class__(self.data.strip(chars)) | 
 |     def swapcase(self): return self.__class__(self.data.swapcase()) | 
 |     def title(self): return self.__class__(self.data.title()) | 
 |     def translate(self, *args): | 
 |         return self.__class__(self.data.translate(*args)) | 
 |     def upper(self): return self.__class__(self.data.upper()) | 
 |     def zfill(self, width): return self.__class__(self.data.zfill(width)) | 
 |  | 
 |  | 
 |  | 
 | ################################################################################ | 
 | ### Simple tests | 
 | ################################################################################ | 
 |  | 
 | if __name__ == '__main__': | 
 |     # verify that instances can be pickled | 
 |     from pickle 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())) |