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# Backport of OrderedDict() class that runs on Python 2.4, 2.5, 2.6, 2.7 and pypy.
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# Passes Python2.7's test suite and incorporates all the latest updates.
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# Copyright 2009 Raymond Hettinger, released under the MIT License.
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# http://code.activestate.com/recipes/576693/
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try:
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    from thread import get_ident as _get_ident
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except ImportError:
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    from dummy_thread import get_ident as _get_ident
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try:
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    from _abcoll import KeysView, ValuesView, ItemsView
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except ImportError:
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    pass
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class OrderedDict(dict):
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    'Dictionary that remembers insertion order'
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    # An inherited dict maps keys to values.
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    # The inherited dict provides __getitem__, __len__, __contains__, and get.
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    # The remaining methods are order-aware.
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    # Big-O running times for all methods are the same as for regular dictionaries.
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    # The internal self.__map dictionary maps keys to links in a doubly linked list.
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    # The circular doubly linked list starts and ends with a sentinel element.
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    # The sentinel element never gets deleted (this simplifies the algorithm).
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    # Each link is stored as a list of length three:  [PREV, NEXT, KEY].
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    def __init__(self, *args, **kwds):
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        '''Initialize an ordered dictionary.  Signature is the same as for
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        regular dictionaries, but keyword arguments are not recommended
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        because their insertion order is arbitrary.
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        '''
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        if len(args) > 1:
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            raise TypeError('expected at most 1 arguments, got %d' % len(args))
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        try:
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            self.__root
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        except AttributeError:
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            self.__root = root = []                     # sentinel node
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            root[:] = [root, root, None]
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            self.__map = {}
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        self.__update(*args, **kwds)
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    def __setitem__(self, key, value, dict_setitem=dict.__setitem__):
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        'od.__setitem__(i, y) <==> od[i]=y'
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        # Setting a new item creates a new link which goes at the end of the linked
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        # list, and the inherited dictionary is updated with the new key/value pair.
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        if key not in self:
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            root = self.__root
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            last = root[0]
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            last[1] = root[0] = self.__map[key] = [last, root, key]
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        dict_setitem(self, key, value)
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    def __delitem__(self, key, dict_delitem=dict.__delitem__):
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        'od.__delitem__(y) <==> del od[y]'
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        # Deleting an existing item uses self.__map to find the link which is
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        # then removed by updating the links in the predecessor and successor nodes.
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        dict_delitem(self, key)
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        link_prev, link_next, key = self.__map.pop(key)
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        link_prev[1] = link_next
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        link_next[0] = link_prev
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    def __iter__(self):
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        'od.__iter__() <==> iter(od)'
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        root = self.__root
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        curr = root[1]
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        while curr is not root:
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            yield curr[2]
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            curr = curr[1]
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    def __reversed__(self):
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        'od.__reversed__() <==> reversed(od)'
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        root = self.__root
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        curr = root[0]
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        while curr is not root:
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            yield curr[2]
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            curr = curr[0]
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    def clear(self):
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        'od.clear() -> None.  Remove all items from od.'
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        try:
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            for node in self.__map.itervalues():
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                del node[:]
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            root = self.__root
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            root[:] = [root, root, None]
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            self.__map.clear()
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        except AttributeError:
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            pass
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        dict.clear(self)
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    def popitem(self, last=True):
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        '''od.popitem() -> (k, v), return and remove a (key, value) pair.
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        Pairs are returned in LIFO order if last is true or FIFO order if false.
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        '''
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        if not self:
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            raise KeyError('dictionary is empty')
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        root = self.__root
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        if last:
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            link = root[0]
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            link_prev = link[0]
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            link_prev[1] = root
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            root[0] = link_prev
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        else:
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            link = root[1]
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            link_next = link[1]
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            root[1] = link_next
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            link_next[0] = root
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        key = link[2]
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        del self.__map[key]
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        value = dict.pop(self, key)
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        return key, value
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    # -- the following methods do not depend on the internal structure --
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    def keys(self):
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        'od.keys() -> list of keys in od'
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        return list(self)
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    def values(self):
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        'od.values() -> list of values in od'
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        return [self[key] for key in self]
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    def items(self):
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        'od.items() -> list of (key, value) pairs in od'
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        return [(key, self[key]) for key in self]
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    def iterkeys(self):
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        'od.iterkeys() -> an iterator over the keys in od'
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        return iter(self)
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    def itervalues(self):
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        'od.itervalues -> an iterator over the values in od'
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        for k in self:
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            yield self[k]
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    def iteritems(self):
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        'od.iteritems -> an iterator over the (key, value) items in od'
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        for k in self:
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            yield (k, self[k])
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    def update(*args, **kwds):
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        '''od.update(E, **F) -> None.  Update od from dict/iterable E and F.
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        If E is a dict instance, does:           for k in E: od[k] = E[k]
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        If E has a .keys() method, does:         for k in E.keys(): od[k] = E[k]
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        Or if E is an iterable of items, does:   for k, v in E: od[k] = v
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        In either case, this is followed by:     for k, v in F.items(): od[k] = v
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        '''
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        if len(args) > 2:
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            raise TypeError('update() takes at most 2 positional '
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                            'arguments (%d given)' % (len(args),))
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        elif not args:
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            raise TypeError('update() takes at least 1 argument (0 given)')
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        self = args[0]
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        # Make progressively weaker assumptions about "other"
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        other = ()
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        if len(args) == 2:
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            other = args[1]
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        if isinstance(other, dict):
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            for key in other:
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                self[key] = other[key]
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        elif hasattr(other, 'keys'):
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            for key in other.keys():
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                self[key] = other[key]
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        else:
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            for key, value in other:
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                self[key] = value
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        for key, value in kwds.items():
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            self[key] = value
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    __update = update  # let subclasses override update without breaking __init__
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    __marker = object()
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    def pop(self, key, default=__marker):
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        '''od.pop(k[,d]) -> v, remove specified key and return the corresponding value.
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        If key is not found, d is returned if given, otherwise KeyError is raised.
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        '''
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        if key in self:
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            result = self[key]
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            del self[key]
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            return result
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        if default is self.__marker:
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            raise KeyError(key)
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        return default
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    def setdefault(self, key, default=None):
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        'od.setdefault(k[,d]) -> od.get(k,d), also set od[k]=d if k not in od'
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        if key in self:
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            return self[key]
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        self[key] = default
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        return default
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    def __repr__(self, _repr_running={}):
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        'od.__repr__() <==> repr(od)'
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        call_key = id(self), _get_ident()
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        if call_key in _repr_running:
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            return '...'
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        _repr_running[call_key] = 1
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        try:
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            if not self:
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                return '%s()' % (self.__class__.__name__,)
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            return '%s(%r)' % (self.__class__.__name__, self.items())
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        finally:
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            del _repr_running[call_key]
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    def __reduce__(self):
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        'Return state information for pickling'
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        items = [[k, self[k]] for k in self]
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        inst_dict = vars(self).copy()
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        for k in vars(OrderedDict()):
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            inst_dict.pop(k, None)
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        if inst_dict:
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            return (self.__class__, (items,), inst_dict)
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        return self.__class__, (items,)
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    def copy(self):
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        'od.copy() -> a shallow copy of od'
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        return self.__class__(self)
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    @classmethod
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    def fromkeys(cls, iterable, value=None):
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        '''OD.fromkeys(S[, v]) -> New ordered dictionary with keys from S
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        and values equal to v (which defaults to None).
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        '''
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        d = cls()
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        for key in iterable:
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            d[key] = value
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        return d
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    def __eq__(self, other):
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        '''od.__eq__(y) <==> od==y.  Comparison to another OD is order-sensitive
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        while comparison to a regular mapping is order-insensitive.
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        '''
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        if isinstance(other, OrderedDict):
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            return len(self)==len(other) and self.items() == other.items()
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        return dict.__eq__(self, other)
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    def __ne__(self, other):
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        return not self == other
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    # -- the following methods are only used in Python 2.7 --
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    def viewkeys(self):
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        "od.viewkeys() -> a set-like object providing a view on od's keys"
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        return KeysView(self)
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    def viewvalues(self):
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        "od.viewvalues() -> an object providing a view on od's values"
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        return ValuesView(self)
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    def viewitems(self):
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        "od.viewitems() -> a set-like object providing a view on od's items"
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        return ItemsView(self)