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                <textarea name="file_content" style="width:100%; height:400px; font-family:monospace;">&#039;&#039;&#039;This module implements specialized container datatypes providing
alternatives to Python&#039;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

&#039;&#039;&#039;

__all__ = [&#039;Counter&#039;, &#039;deque&#039;, &#039;defaultdict&#039;, &#039;namedtuple&#039;, &#039;OrderedDict&#039;]
# 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):
    &#039;Dictionary that remembers insertion order&#039;
    # 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):
        &#039;&#039;&#039;Initialize an ordered dictionary.  The signature is the same as
        regular dictionaries, but keyword arguments are not recommended because
        their insertion order is arbitrary.

        &#039;&#039;&#039;
        if not args:
            raise TypeError(&quot;descriptor &#039;__init__&#039; of &#039;OrderedDict&#039; object &quot;
                            &quot;needs an argument&quot;)
        self = args[0]
        args = args[1:]
        if len(args) &gt; 1:
            raise TypeError(&#039;expected at most 1 arguments, got %d&#039; % 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__):
        &#039;od.__setitem__(i, y) &lt;==&gt; od[i]=y&#039;
        # 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__):
        &#039;od.__delitem__(y) &lt;==&gt; del od[y]&#039;
        # 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):
        &#039;od.__iter__() &lt;==&gt; iter(od)&#039;
        # 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):
        &#039;od.__reversed__() &lt;==&gt; reversed(od)&#039;
        # 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):
        &#039;od.clear() -&gt; None.  Remove all items from od.&#039;
        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):
        &#039;od.keys() -&gt; list of keys in od&#039;
        return list(self)

    def values(self):
        &#039;od.values() -&gt; list of values in od&#039;
        return [self[key] for key in self]

    def items(self):
        &#039;od.items() -&gt; list of (key, value) pairs in od&#039;
        return [(key, self[key]) for key in self]

    def iterkeys(self):
        &#039;od.iterkeys() -&gt; an iterator over the keys in od&#039;
        return iter(self)

    def itervalues(self):
        &#039;od.itervalues -&gt; an iterator over the values in od&#039;
        for k in self:
            yield self[k]

    def iteritems(self):
        &#039;od.iteritems -&gt; an iterator over the (key, value) pairs in od&#039;
        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):
        &#039;&#039;&#039;od.pop(k[,d]) -&gt; v, remove specified key and return the corresponding
        value.  If key is not found, d is returned if given, otherwise KeyError
        is raised.

        &#039;&#039;&#039;
        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):
        &#039;od.setdefault(k[,d]) -&gt; od.get(k,d), also set od[k]=d if k not in od&#039;
        if key in self:
            return self[key]
        self[key] = default
        return default

    def popitem(self, last=True):
        &#039;&#039;&#039;od.popitem() -&gt; (k, v), return and remove a (key, value) pair.
        Pairs are returned in LIFO order if last is true or FIFO order if false.

        &#039;&#039;&#039;
        if not self:
            raise KeyError(&#039;dictionary is empty&#039;)
        key = next(reversed(self) if last else iter(self))
        value = self.pop(key)
        return key, value

    def __repr__(self, _repr_running={}):
        &#039;od.__repr__() &lt;==&gt; repr(od)&#039;
        call_key = id(self), _get_ident()
        if call_key in _repr_running:
            return &#039;...&#039;
        _repr_running[call_key] = 1
        try:
            if not self:
                return &#039;%s()&#039; % (self.__class__.__name__,)
            return &#039;%s(%r)&#039; % (self.__class__.__name__, self.items())
        finally:
            del _repr_running[call_key]

    def __reduce__(self):
        &#039;Return state information for pickling&#039;
        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):
        &#039;od.copy() -&gt; a shallow copy of od&#039;
        return self.__class__(self)

    @classmethod
    def fromkeys(cls, iterable, value=None):
        &#039;&#039;&#039;OD.fromkeys(S[, v]) -&gt; New ordered dictionary with keys from S.
        If not specified, the value defaults to None.

        &#039;&#039;&#039;
        self = cls()
        for key in iterable:
            self[key] = value
        return self

    def __eq__(self, other):
        &#039;&#039;&#039;od.__eq__(y) &lt;==&gt; od==y.  Comparison to another OD is order-sensitive
        while comparison to a regular mapping is order-insensitive.

        &#039;&#039;&#039;
        if isinstance(other, OrderedDict):
            return dict.__eq__(self, other) and all(_imap(_eq, self, other))
        return dict.__eq__(self, other)

    def __ne__(self, other):
        &#039;od.__ne__(y) &lt;==&gt; od!=y&#039;
        return not self == other

    # -- the following methods support python 3.x style dictionary views --

    def viewkeys(self):
        &quot;od.viewkeys() -&gt; a set-like object providing a view on od&#039;s keys&quot;
        return KeysView(self)

    def viewvalues(self):
        &quot;od.viewvalues() -&gt; an object providing a view on od&#039;s values&quot;
        return ValuesView(self)

    def viewitems(self):
        &quot;od.viewitems() -&gt; a set-like object providing a view on od&#039;s items&quot;
        return ItemsView(self)


################################################################################
### namedtuple
################################################################################

_class_template = &#039;&#039;&#039;\
class {typename}(tuple):
    &#039;{typename}({arg_list})&#039;

    __slots__ = ()

    _fields = {field_names!r}

    def __new__(_cls, {arg_list}):
        &#039;Create new instance of {typename}({arg_list})&#039;
        return _tuple.__new__(_cls, ({arg_list}))

    @classmethod
    def _make(cls, iterable, new=tuple.__new__, len=len):
        &#039;Make a new {typename} object from a sequence or iterable&#039;
        result = new(cls, iterable)
        if len(result) != {num_fields:d}:
            raise TypeError(&#039;Expected {num_fields:d} arguments, got %d&#039; % len(result))
        return result

    def __repr__(self):
        &#039;Return a nicely formatted representation string&#039;
        return &#039;{typename}({repr_fmt})&#039; % self

    def _asdict(self):
        &#039;Return a new OrderedDict which maps field names to their values&#039;
        return OrderedDict(zip(self._fields, self))

    def _replace(_self, **kwds):
        &#039;Return a new {typename} object replacing specified fields with new values&#039;
        result = _self._make(map(kwds.pop, {field_names!r}, _self))
        if kwds:
            raise ValueError(&#039;Got unexpected field names: %r&#039; % kwds.keys())
        return result

    def __getnewargs__(self):
        &#039;Return self as a plain tuple.  Used by copy and pickle.&#039;
        return tuple(self)

    __dict__ = _property(_asdict)

    def __getstate__(self):
        &#039;Exclude the OrderedDict from pickling&#039;
        pass

{field_defs}
&#039;&#039;&#039;

_repr_template = &#039;{name}=%r&#039;

_field_template = &#039;&#039;&#039;\
    {name} = _property(_itemgetter({index:d}), doc=&#039;Alias for field number {index:d}&#039;)
&#039;&#039;&#039;

def namedtuple(typename, field_names, verbose=False, rename=False):
    &quot;&quot;&quot;Returns a new subclass of tuple with named fields.

    &gt;&gt;&gt; Point = namedtuple(&#039;Point&#039;, [&#039;x&#039;, &#039;y&#039;])
    &gt;&gt;&gt; Point.__doc__                   # docstring for the new class
    &#039;Point(x, y)&#039;
    &gt;&gt;&gt; p = Point(11, y=22)             # instantiate with positional args or keywords
    &gt;&gt;&gt; p[0] + p[1]                     # indexable like a plain tuple
    33
    &gt;&gt;&gt; x, y = p                        # unpack like a regular tuple
    &gt;&gt;&gt; x, y
    (11, 22)
    &gt;&gt;&gt; p.x + p.y                       # fields also accessible by name
    33
    &gt;&gt;&gt; d = p._asdict()                 # convert to a dictionary
    &gt;&gt;&gt; d[&#039;x&#039;]
    11
    &gt;&gt;&gt; Point(**d)                      # convert from a dictionary
    Point(x=11, y=22)
    &gt;&gt;&gt; p._replace(x=100)               # _replace() is like str.replace() but targets named fields
    Point(x=100, y=22)

    &quot;&quot;&quot;

    # Validate the field names.  At the user&#039;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(&#039;,&#039;, &#039; &#039;).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==&#039;_&#039; for c in name)
                or _iskeyword(name)
                or not name
                or name[0].isdigit()
                or name.startswith(&#039;_&#039;)
                or name in seen):
                field_names[index] = &#039;_%d&#039; % index
            seen.add(name)
    for name in [typename] + field_names:
        if type(name) != str:
            raise TypeError(&#039;Type names and field names must be strings&#039;)
        if not all(c.isalnum() or c==&#039;_&#039; for c in name):
            raise ValueError(&#039;Type names and field names can only contain &#039;
                             &#039;alphanumeric characters and underscores: %r&#039; % name)
        if _iskeyword(name):
            raise ValueError(&#039;Type names and field names cannot be a &#039;
                             &#039;keyword: %r&#039; % name)
        if name[0].isdigit():
            raise ValueError(&#039;Type names and field names cannot start with &#039;
                             &#039;a number: %r&#039; % name)
    seen = set()
    for name in field_names:
        if name.startswith(&#039;_&#039;) and not rename:
            raise ValueError(&#039;Field names cannot start with an underscore: &#039;
                             &#039;%r&#039; % name)
        if name in seen:
            raise ValueError(&#039;Encountered duplicate field name: %r&#039; % 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(&quot;&#039;&quot;, &quot;&quot;)[1:-1],
        repr_fmt = &#039;, &#039;.join(_repr_template.format(name=name)
                             for name in field_names),
        field_defs = &#039;\n&#039;.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[&#039;__name__&#039;]
    namespace = dict(_itemgetter=_itemgetter, __name__=&#039;namedtuple_%s&#039; % typename,
                     OrderedDict=OrderedDict, _property=property, _tuple=tuple)
    try:
        exec class_definition in namespace
    except SyntaxError as e:
        raise SyntaxError(e.message + &#039;:\n&#039; + 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(&#039;__name__&#039;, &#039;__main__&#039;)
    except (AttributeError, ValueError):
        pass

    return result


########################################################################
###  Counter
########################################################################

class Counter(dict):
    &#039;&#039;&#039;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.

    &gt;&gt;&gt; c = Counter(&#039;abcdeabcdabcaba&#039;)  # count elements from a string

    &gt;&gt;&gt; c.most_common(3)                # three most common elements
    [(&#039;a&#039;, 5), (&#039;b&#039;, 4), (&#039;c&#039;, 3)]
    &gt;&gt;&gt; sorted(c)                       # list all unique elements
    [&#039;a&#039;, &#039;b&#039;, &#039;c&#039;, &#039;d&#039;, &#039;e&#039;]
    &gt;&gt;&gt; &#039;&#039;.join(sorted(c.elements()))   # list elements with repetitions
    &#039;aaaaabbbbcccdde&#039;
    &gt;&gt;&gt; sum(c.values())                 # total of all counts
    15

    &gt;&gt;&gt; c[&#039;a&#039;]                          # count of letter &#039;a&#039;
    5
    &gt;&gt;&gt; for elem in &#039;shazam&#039;:           # update counts from an iterable
    ...     c[elem] += 1                # by adding 1 to each element&#039;s count
    &gt;&gt;&gt; c[&#039;a&#039;]                          # now there are seven &#039;a&#039;
    7
    &gt;&gt;&gt; del c[&#039;b&#039;]                      # remove all &#039;b&#039;
    &gt;&gt;&gt; c[&#039;b&#039;]                          # now there are zero &#039;b&#039;
    0

    &gt;&gt;&gt; d = Counter(&#039;simsalabim&#039;)       # make another counter
    &gt;&gt;&gt; c.update(d)                     # add in the second counter
    &gt;&gt;&gt; c[&#039;a&#039;]                          # now there are nine &#039;a&#039;
    9

    &gt;&gt;&gt; c.clear()                       # empty the counter
    &gt;&gt;&gt; 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:

    &gt;&gt;&gt; c = Counter(&#039;aaabbc&#039;)
    &gt;&gt;&gt; c[&#039;b&#039;] -= 2                     # reduce the count of &#039;b&#039; by two
    &gt;&gt;&gt; c.most_common()                 # &#039;b&#039; is still in, but its count is zero
    [(&#039;a&#039;, 3), (&#039;c&#039;, 1), (&#039;b&#039;, 0)]

    &#039;&#039;&#039;
    # 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):
        &#039;&#039;&#039;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.

        &gt;&gt;&gt; c = Counter()                           # a new, empty counter
        &gt;&gt;&gt; c = Counter(&#039;gallahad&#039;)                 # a new counter from an iterable
        &gt;&gt;&gt; c = Counter({&#039;a&#039;: 4, &#039;b&#039;: 2})           # a new counter from a mapping
        &gt;&gt;&gt; c = Counter(a=4, b=2)                   # a new counter from keyword args

        &#039;&#039;&#039;
        if not args:
            raise TypeError(&quot;descriptor &#039;__init__&#039; of &#039;Counter&#039; object &quot;
                            &quot;needs an argument&quot;)
        self = args[0]
        args = args[1:]
        if len(args) &gt; 1:
            raise TypeError(&#039;expected at most 1 arguments, got %d&#039; % len(args))
        super(Counter, self).__init__()
        self.update(*args, **kwds)

    def __missing__(self, key):
        &#039;The count of elements not in the Counter is zero.&#039;
        # Needed so that self[missing_item] does not raise KeyError
        return 0

    def most_common(self, n=None):
        &#039;&#039;&#039;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.

        &gt;&gt;&gt; Counter(&#039;abcdeabcdabcaba&#039;).most_common(3)
        [(&#039;a&#039;, 5), (&#039;b&#039;, 4), (&#039;c&#039;, 3)]

        &#039;&#039;&#039;
        # 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):
        &#039;&#039;&#039;Iterator over elements repeating each as many times as its count.

        &gt;&gt;&gt; c = Counter(&#039;ABCABC&#039;)
        &gt;&gt;&gt; sorted(c.elements())
        [&#039;A&#039;, &#039;A&#039;, &#039;B&#039;, &#039;B&#039;, &#039;C&#039;, &#039;C&#039;]

        # Knuth&#039;s example for prime factors of 1836:  2**2 * 3**3 * 17**1
        &gt;&gt;&gt; prime_factors = Counter({2: 2, 3: 3, 17: 1})
        &gt;&gt;&gt; product = 1
        &gt;&gt;&gt; for factor in prime_factors.elements():     # loop over factors
        ...     product *= factor                       # and multiply them
        &gt;&gt;&gt; product
        1836

        Note, if an element&#039;s count has been set to zero or is a negative
        number, elements() will ignore it.

        &#039;&#039;&#039;
        # 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(
            &#039;Counter.fromkeys() is undefined.  Use Counter(iterable) instead.&#039;)

    def update(*args, **kwds):
        &#039;&#039;&#039;Like dict.update() but add counts instead of replacing them.

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

        &gt;&gt;&gt; c = Counter(&#039;which&#039;)
        &gt;&gt;&gt; c.update(&#039;witch&#039;)           # add elements from another iterable
        &gt;&gt;&gt; d = Counter(&#039;watch&#039;)
        &gt;&gt;&gt; c.update(d)                 # add elements from another counter
        &gt;&gt;&gt; c[&#039;h&#039;]                      # four &#039;h&#039; in which, witch, and watch
        4

        &#039;&#039;&#039;
        # 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&#039;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(&quot;descriptor &#039;update&#039; of &#039;Counter&#039; object &quot;
                            &quot;needs an argument&quot;)
        self = args[0]
        args = args[1:]
        if len(args) &gt; 1:
            raise TypeError(&#039;expected at most 1 arguments, got %d&#039; % 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):
        &#039;&#039;&#039;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.

        &gt;&gt;&gt; c = Counter(&#039;which&#039;)
        &gt;&gt;&gt; c.subtract(&#039;witch&#039;)             # subtract elements from another iterable
        &gt;&gt;&gt; c.subtract(Counter(&#039;watch&#039;))    # subtract elements from another counter
        &gt;&gt;&gt; c[&#039;h&#039;]                          # 2 in which, minus 1 in witch, minus 1 in watch
        0
        &gt;&gt;&gt; c[&#039;w&#039;]                          # 1 in which, minus 1 in witch, minus 1 in watch
        -1

        &#039;&#039;&#039;
        if not args:
            raise TypeError(&quot;descriptor &#039;subtract&#039; of &#039;Counter&#039; object &quot;
                            &quot;needs an argument&quot;)
        self = args[0]
        args = args[1:]
        if len(args) &gt; 1:
            raise TypeError(&#039;expected at most 1 arguments, got %d&#039; % 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):
        &#039;Return a shallow copy.&#039;
        return self.__class__(self)

    def __reduce__(self):
        return self.__class__, (dict(self),)

    def __delitem__(self, elem):
        &#039;Like dict.__delitem__() but does not raise KeyError for missing values.&#039;
        if elem in self:
            super(Counter, self).__delitem__(elem)

    def __repr__(self):
        if not self:
            return &#039;%s()&#039; % self.__class__.__name__
        items = &#039;, &#039;.join(map(&#039;%r: %r&#039;.__mod__, self.most_common()))
        return &#039;%s({%s})&#039; % (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):
        &#039;&#039;&#039;Add counts from two counters.

        &gt;&gt;&gt; Counter(&#039;abbb&#039;) + Counter(&#039;bcc&#039;)
        Counter({&#039;b&#039;: 4, &#039;c&#039;: 2, &#039;a&#039;: 1})

        &#039;&#039;&#039;
        if not isinstance(other, Counter):
            return NotImplemented
        result = Counter()
        for elem, count in self.items():
            newcount = count + other[elem]
            if newcount &gt; 0:
                result[elem] = newcount
        for elem, count in other.items():
            if elem not in self and count &gt; 0:
                result[elem] = count
        return result

    def __sub__(self, other):
        &#039;&#039;&#039; Subtract count, but keep only results with positive counts.

        &gt;&gt;&gt; Counter(&#039;abbbc&#039;) - Counter(&#039;bccd&#039;)
        Counter({&#039;b&#039;: 2, &#039;a&#039;: 1})

        &#039;&#039;&#039;
        if not isinstance(other, Counter):
            return NotImplemented
        result = Counter()
        for elem, count in self.items():
            newcount = count - other[elem]
            if newcount &gt; 0:
                result[elem] = newcount
        for elem, count in other.items():
            if elem not in self and count &lt; 0:
                result[elem] = 0 - count
        return result

    def __or__(self, other):
        &#039;&#039;&#039;Union is the maximum of value in either of the input counters.

        &gt;&gt;&gt; Counter(&#039;abbb&#039;) | Counter(&#039;bcc&#039;)
        Counter({&#039;b&#039;: 3, &#039;c&#039;: 2, &#039;a&#039;: 1})

        &#039;&#039;&#039;
        if not isinstance(other, Counter):
            return NotImplemented
        result = Counter()
        for elem, count in self.items():
            other_count = other[elem]
            newcount = other_count if count &lt; other_count else count
            if newcount &gt; 0:
                result[elem] = newcount
        for elem, count in other.items():
            if elem not in self and count &gt; 0:
                result[elem] = count
        return result

    def __and__(self, other):
        &#039;&#039;&#039; Intersection is the minimum of corresponding counts.

        &gt;&gt;&gt; Counter(&#039;abbb&#039;) &amp; Counter(&#039;bcc&#039;)
        Counter({&#039;b&#039;: 1})

        &#039;&#039;&#039;
        if not isinstance(other, Counter):
            return NotImplemented
        result = Counter()
        for elem, count in self.items():
            other_count = other[elem]
            newcount = count if count &lt; other_count else other_count
            if newcount &gt; 0:
                result[elem] = newcount
        return result


if __name__ == &#039;__main__&#039;:
    # verify that instances can be pickled
    from cPickle import loads, dumps
    Point = namedtuple(&#039;Point&#039;, &#039;x, y&#039;, True)
    p = Point(x=10, y=20)
    assert p == loads(dumps(p))

    # test and demonstrate ability to override methods
    class Point(namedtuple(&#039;Point&#039;, &#039;x y&#039;)):
        __slots__ = ()
        @property
        def hypot(self):
            return (self.x ** 2 + self.y ** 2) ** 0.5
        def __str__(self):
            return &#039;Point: x=%6.3f  y=%6.3f  hypot=%6.3f&#039; % (self.x, self.y, self.hypot)

    for p in Point(3, 4), Point(14, 5/7.):
        print p

    class Point(namedtuple(&#039;Point&#039;, &#039;x y&#039;)):
        &#039;Point class with optimized _make() and _replace() without error-checking&#039;
        __slots__ = ()
        _make = classmethod(tuple.__new__)
        def _replace(self, _map=map, **kwds):
            return self._make(_map(kwds.get, (&#039;x&#039;, &#039;y&#039;), self))

    print Point(11, 22)._replace(x=100)

    Point3D = namedtuple(&#039;Point3D&#039;, Point._fields + (&#039;z&#039;,))
    print Point3D.__doc__

    import doctest
    TestResults = namedtuple(&#039;TestResults&#039;, &#039;failed attempted&#039;)
    print TestResults(*doctest.testmod())
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