'ChainMap',

'Counter',

'OrderedDict',

'UserDict',

'UserList',

'UserString',

'defaultdict',

'deque',

'namedtuple',

def __reversed__(self):

for key in reversed(self._mapping):

def __reversed__(self):

for key in reversed(self._mapping):

'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).

# The sentinel is in self.__hardroot with a weakref proxy in self.__root.

# The prev 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, other=(), /, **kwds):

'''Initialize an ordered dictionary. The signature is the same as

regular dictionaries. Keyword argument order is preserved.

'''

try:

self.__root

except AttributeError:

self.__hardroot = _Link()

self.__root = root = _proxy(self.__hardroot)

root.prev = root.next = root

self.__map = {}

self.__update(other, **kwds)

def __setitem__(self, key, value,

dict_setitem=dict.__setitem__, proxy=_proxy, Link=_Link):

'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:

self.__map[key] = link = Link()

root = self.__root

last = root.prev

link.prev, link.next, link.key = last, root, key

last.next = link

root.prev = proxy(link)

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 = self.__map.pop(key)

link_prev = link.prev

link_next = link.next

link_prev.next = link_next

link_next.prev = link_prev

link.prev = None

link.next = None

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 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 popitem(self, last=True):

'''Remove and return a (key, value) pair from the dictionary.

Pairs are returned in LIFO order if last is true or FIFO order if false.

'''

if not self:

raise KeyError('dictionary is empty')

root = self.__root

if last:

link = root.prev

link_prev = link.prev

link_prev.next = root

root.prev = link_prev

else:

link = root.next

link_next = link.next

root.next = link_next

link_next.prev = root

key = link.key

del self.__map[key]

value = dict.pop(self, key)

return key, value

def move_to_end(self, key, last=True):

'''Move an existing element to the end (or beginning if last is false).

Raise KeyError if the element does not exist.

'''

link = self.__map[key]

link_prev = link.prev

link_next = link.next

soft_link = link_next.prev

link_prev.next = link_next

link_next.prev = link_prev

root = self.__root

if last:

last = root.prev

link.prev = last

link.next = root

root.prev = soft_link

last.next = link

else:

first = root.next

link.prev = root

link.next = first

first.prev = soft_link

root.next = link

def __sizeof__(self):

sizeof = _sys.getsizeof

n = len(self) + 1 # number of links including root

size = sizeof(self.__dict__) # instance dictionary

size += sizeof(self.__map) * 2 # internal dict and inherited dict

size += sizeof(self.__hardroot) * n # link objects

size += sizeof(self.__root) * n # proxy objects

return size

update = __update = _collections_abc.MutableMapping.update

def keys(self):

"D.keys() -> a set-like object providing a view on D's keys"

return _OrderedDictKeysView(self)

def items(self):

"D.items() -> a set-like object providing a view on D's items"

return _OrderedDictItemsView(self)

def values(self):

"D.values() -> an object providing a view on D's values"

return _OrderedDictValuesView(self)

__ne__ = _collections_abc.MutableMapping.__ne__

__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):

'''Insert key with a value of default if key is not in the dictionary.

Return the value for key if key is in the dictionary, else default.

'''

if key in self:

return self[key]

self[key] = default

return default

@_recursive_repr()

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 __reduce__(self):

'Return state information for pickling'

inst_dict = vars(self).copy()

for k in vars(OrderedDict()):

inst_dict.pop(k, None)

return self.__class__, (), inst_dict or None, None, iter(self.items())

def copy(self):

'od.copy() -> a shallow copy of od'

return self.__class__(self)

@classmethod

def fromkeys(cls, iterable, value=None):

'''Create a new ordered dictionary with keys from iterable and values set to value.

'''

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(map(_eq, self, other))

return dict.__eq__(self, other)

def __ior__(self, other):

self.update(other)

return self

def __or__(self, other):

if not isinstance(other, dict):

return NotImplemented

new = self.__class__(self)

new.update(other)

return new

def __ror__(self, other):

if not isinstance(other, dict):

return NotImplemented

new = self.__class__(other)

new.update(self)

"""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 accessible 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, str):

field_names = field_names.replace(',', ' ').split()

field_names = list(map(str, field_names))

typename = _sys.intern(str(typename))

if rename:

seen = set()

for index, name in enumerate(field_names):

if (not name.isidentifier()

or _iskeyword(name)

or name.startswith('_')

or name in seen):

field_names[index] = f'_{index}'

seen.add(name)

for name in [typename] + field_names:

if type(name) is not str:

raise TypeError('Type names and field names must be strings')

if not name.isidentifier():

raise ValueError('Type names and field names must be valid '

f'identifiers: {name!r}')

if _iskeyword(name):

raise ValueError('Type names and field names cannot be a '

f'keyword: {name!r}')

seen = set()

for name in field_names:

if name.startswith('_') and not rename:

raise ValueError('Field names cannot start with an underscore: '

f'{name!r}')

if name in seen:

raise ValueError(f'Encountered duplicate field name: {name!r}')

seen.add(name)

field_defaults = {}

if defaults is not None:

defaults = tuple(defaults)

if len(defaults) > len(field_names):

raise TypeError('Got more default values than field names')

field_defaults = dict(reversed(list(zip(reversed(field_names),

reversed(defaults)))))

# Variables used in the methods and docstrings

field_names = tuple(map(_sys.intern, field_names))

num_fields = len(field_names)

arg_list = ', '.join(field_names)

if num_fields == 1:

arg_list += ','

repr_fmt = '(' + ', '.join(f'{name}=%r' for name in field_names) + ')'

tuple_new = tuple.__new__

_dict, _tuple, _len, _map, _zip = dict, tuple, len, map, zip

# Create all the named tuple methods to be added to the class namespace

namespace = {

'_tuple_new': tuple_new,

'__builtins__': {},

'__name__': f'namedtuple_{typename}',

}

code = f'lambda _cls, {arg_list}: _tuple_new(_cls, ({arg_list}))'

__new__ = eval(code, namespace)

__new__.__name__ = '__new__'

__new__.__doc__ = f'Create new instance of {typename}({arg_list})'

if defaults is not None:

__new__.__defaults__ = defaults

@classmethod

def _make(cls, iterable):

result = tuple_new(cls, iterable)

if _len(result) != num_fields:

raise TypeError(f'Expected {num_fields} arguments, got {len(result)}')

return result

_make.__func__.__doc__ = (f'Make a new {typename} object from a sequence '

'or iterable')

def _replace(self, /, **kwds):

result = self._make(_map(kwds.pop, field_names, self))

if kwds:

raise ValueError(f'Got unexpected field names: {list(kwds)!r}')

return result

_replace.__doc__ = (f'Return a new {typename} object replacing specified '

'fields with new values')

def __repr__(self):

'Return a nicely formatted representation string'

return self.__class__.__name__ + repr_fmt % self

def _asdict(self):

'Return a new dict which maps field names to their values.'

return _dict(_zip(self._fields, self))

def __getnewargs__(self):

'Return self as a plain tuple. Used by copy and pickle.'

return _tuple(self)

# Modify function metadata to help with introspection and debugging

for method in (

__new__,

_make.__func__,

_replace,

__repr__,

_asdict,

__getnewargs__,

):

method.__qualname__ = f'{typename}.{method.__name__}'

# Build-up the class namespace dictionary

# and use type() to build the result class

class_namespace = {

'__doc__': f'{typename}({arg_list})',

'__slots__': (),

'_fields': field_names,

'_field_defaults': field_defaults,

'__new__': __new__,

'_make': _make,

'_replace': _replace,

'__repr__': __repr__,

'_asdict': _asdict,

'__getnewargs__': __getnewargs__,

'__match_args__': field_names,

}

for index, name in enumerate(field_names):

doc = _sys.intern(f'Alias for field number {index}')

class_namespace[name] = _tuplegetter(index, doc)

result = type(typename, (tuple,), class_namespace)

# 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), or where the user has

# specified a particular module.

if module is None:

try:

module = _sys._getframe(1).f_globals.get('__name__', '__main__')

except (AttributeError, ValueError):

pass

if module is not None:

result.__module__ = module

'Tally elements from the iterable.'

mapping_get = mapping.get

for elem in iterable:

'''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__(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

'''

super().__init__()

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 total(self):

'Sum of the counts'

return sum(self.values())

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), ('b', 2), ('r', 2)]

'''

# Emulate Bag.sortedByCount from Smalltalk

if n is None:

return sorted(self.items(), key=_itemgetter(1), reverse=True)

# Lazy import to speedup Python startup time

import heapq

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 the semantics

# would be ambiguous in cases such as Counter.fromkeys('aaabbc', v=2).

# Initializing counters to zero values isn't necessary because zero

# is already the default value for counter lookups. Initializing

# to one is easily accomplished with Counter(set(iterable)). For

# more exotic cases, create a dictionary first using a dictionary

# comprehension or dict.fromkeys().

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, _collections_abc.Mapping):

if self:

self_get = self.get

for elem, count in iterable.items():

self[elem] = count + self_get(elem, 0)

else:

# fast path when counter is empty

super().update(iterable)

else:

_count_elements(self, iterable)

if kwds:

self.update(kwds)

def subtract(self, iterable=None, /, **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 iterable is not None:

self_get = self.get

if isinstance(iterable, _collections_abc.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().__delitem__(elem)

def __eq__(self, other):

'True if all counts agree. Missing counts are treated as zero.'

if not isinstance(other, Counter):

return NotImplemented

return all(self[e] == other[e] for c in (self, other) for e in c)

def __ne__(self, other):

'True if any counts disagree. Missing counts are treated as zero.'

if not isinstance(other, Counter):

return NotImplemented

return not self == other

def __le__(self, other):

'True if all counts in self are a subset of those in other.'

if not isinstance(other, Counter):

return NotImplemented

return all(self[e] <= other[e] for c in (self, other) for e in c)

def __lt__(self, other):

'True if all counts in self are a proper subset of those in other.'

if not isinstance(other, Counter):

return NotImplemented

return self <= other and self != other

def __ge__(self, other):

'True if all counts in self are a superset of those in other.'

if not isinstance(other, Counter):

return NotImplemented

return all(self[e] >= other[e] for c in (self, other) for e in c)

def __gt__(self, other):

'True if all counts in self are a proper superset of those in other.'

if not isinstance(other, Counter):

return NotImplemented

return self >= other and self != other

def __repr__(self):

if not self:

return f'{self.__class__.__name__}()'

try:

# dict() preserves the ordering returned by most_common()

d = dict(self.most_common())

except TypeError:

# handle case where values are not orderable

d = dict(self)

return f'{self.__class__.__name__}({d!r})'

# 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()

#

# When the multiplicities are all zero or one, multiset operations

# are guaranteed to be equivalent to the corresponding operations

# for regular sets.

# Given counter multisets such as:

# cp = Counter(a=1, b=0, c=1)

# cq = Counter(c=1, d=0, e=1)

# The corresponding regular sets would be:

# sp = {'a', 'c'}

# sq = {'c', 'e'}

# All of the following relations would hold:

# set(cp + cq) == sp | sq

# set(cp - cq) == sp - sq

# set(cp | cq) == sp | sq

# set(cp & cq) == sp & sq

# (cp == cq) == (sp == sq)

# (cp != cq) == (sp != sq)

# (cp <= cq) == (sp <= sq)

# (cp < cq) == (sp < sq)

# (cp >= cq) == (sp >= sq)

# (cp > cq) == (sp > sq)

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

def __pos__(self):

'Adds an empty counter, effectively stripping negative and zero counts'

result = Counter()

for elem, count in self.items():

if count > 0:

result[elem] = count

return result

def __neg__(self):

'''Subtracts from an empty counter. Strips positive and zero counts,

and flips the sign on negative counts.

'''

result = Counter()

for elem, count in self.items():

if count < 0:

result[elem] = 0 - count

return result

def _keep_positive(self):

'''Internal method to strip elements with a negative or zero count'''

nonpositive = [elem for elem, count in self.items() if not count > 0]

for elem in nonpositive:

del self[elem]

return self

def __iadd__(self, other):

'''Inplace add from another counter, keeping only positive counts.

>>> c = Counter('abbb')

>>> c += Counter('bcc')

>>> c

Counter({'b': 4, 'c': 2, 'a': 1})

'''

for elem, count in other.items():

self[elem] += count

return self._keep_positive()

def __isub__(self, other):

'''Inplace subtract counter, but keep only results with positive counts.

>>> c = Counter('abbbc')

>>> c -= Counter('bccd')

>>> c

Counter({'b': 2, 'a': 1})

'''

for elem, count in other.items():

self[elem] -= count

return self._keep_positive()

def __ior__(self, other):

'''Inplace union is the maximum of value from either counter.

>>> c = Counter('abbb')

>>> c |= Counter('bcc')

>>> c

Counter({'b': 3, 'c': 2, 'a': 1})

'''

for elem, other_count in other.items():

count = self[elem]

if other_count > count:

self[elem] = other_count

return self._keep_positive()

def __iand__(self, other):

'''Inplace intersection is the minimum of corresponding counts.

>>> c = Counter('abbb')

>>> c &= Counter('bcc')

>>> c

Counter({'b': 1})

'''

for elem, count in self.items():

other_count = other[elem]

if other_count < count:

self[elem] = other_count

''' A ChainMap groups multiple dicts (or other mappings) together

to create a single, updateable view.

The underlying mappings are stored in a list. That list is public and can

be accessed or updated using the *maps* attribute. There is no other

state.

Lookups search the underlying mappings successively until a key is found.

In contrast, writes, updates, and deletions only operate on the first

mapping.

'''

def __init__(self, *maps):

'''Initialize a ChainMap by setting *maps* to the given mappings.

If no mappings are provided, a single empty dictionary is used.

'''

self.maps = list(maps) or [{}] # always at least one map

def __missing__(self, key):

raise KeyError(key)

def __getitem__(self, key):

for mapping in self.maps:

try:

return mapping[key] # can't use 'key in mapping' with defaultdict

except KeyError:

pass

return self.__missing__(key) # support subclasses that define __missing__

def get(self, key, default=None):

return self[key] if key in self else default

def __len__(self):

return len(set().union(*self.maps)) # reuses stored hash values if possible

def __iter__(self):

d = {}

for mapping in reversed(self.maps):

d.update(dict.fromkeys(mapping)) # reuses stored hash values if possible

return iter(d)

def __contains__(self, key):

return any(key in m for m in self.maps)

def __bool__(self):

return any(self.maps)