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1'''This module implements specialized container datatypes providing
2alternatives to Python's general purpose built-in containers, dict,
3list, set, and tuple.
4
5* namedtuple   factory function for creating tuple subclasses with named fields
6* deque        list-like container with fast appends and pops on either end
7* ChainMap     dict-like class for creating a single view of multiple mappings
8* Counter      dict subclass for counting hashable objects
9* OrderedDict  dict subclass that remembers the order entries were added
10* defaultdict  dict subclass that calls a factory function to supply missing values
11* UserDict     wrapper around dictionary objects for easier dict subclassing
12* UserList     wrapper around list objects for easier list subclassing
13* UserString   wrapper around string objects for easier string subclassing
14
15'''
16
17__all__ = [
18    'ChainMap',
19    'Counter',
20    'OrderedDict',
21    'UserDict',
22    'UserList',
23    'UserString',
24    'defaultdict',
25    'deque',
26    'namedtuple',
27]
28
29import _collections_abc
30import heapq as _heapq
31import sys as _sys
32
33from itertools import chain as _chain
34from itertools import repeat as _repeat
35from itertools import starmap as _starmap
36from keyword import iskeyword as _iskeyword
37from operator import eq as _eq
38from operator import itemgetter as _itemgetter
39from reprlib import recursive_repr as _recursive_repr
40from _weakref import proxy as _proxy
41
42try:
43    from _collections import deque
44except ImportError:
45    pass
46else:
47    _collections_abc.MutableSequence.register(deque)
48
49try:
50    from _collections import defaultdict
51except ImportError:
52    pass
53
54
55def __getattr__(name):
56    # For backwards compatibility, continue to make the collections ABCs
57    # through Python 3.6 available through the collections module.
58    # Note, no new collections ABCs were added in Python 3.7
59    if name in _collections_abc.__all__:
60        obj = getattr(_collections_abc, name)
61        import warnings
62        warnings.warn("Using or importing the ABCs from 'collections' instead "
63                      "of from 'collections.abc' is deprecated since Python 3.3, "
64                      "and in 3.10 it will stop working",
65                      DeprecationWarning, stacklevel=2)
66        globals()[name] = obj
67        return obj
68    raise AttributeError(f'module {__name__!r} has no attribute {name!r}')
69
70
71################################################################################
72### OrderedDict
73################################################################################
74
75class _OrderedDictKeysView(_collections_abc.KeysView):
76
77    def __reversed__(self):
78        yield from reversed(self._mapping)
79
80class _OrderedDictItemsView(_collections_abc.ItemsView):
81
82    def __reversed__(self):
83        for key in reversed(self._mapping):
84            yield (key, self._mapping[key])
85
86class _OrderedDictValuesView(_collections_abc.ValuesView):
87
88    def __reversed__(self):
89        for key in reversed(self._mapping):
90            yield self._mapping[key]
91
92class _Link(object):
93    __slots__ = 'prev', 'next', 'key', '__weakref__'
94
95class OrderedDict(dict):
96    'Dictionary that remembers insertion order'
97    # An inherited dict maps keys to values.
98    # The inherited dict provides __getitem__, __len__, __contains__, and get.
99    # The remaining methods are order-aware.
100    # Big-O running times for all methods are the same as regular dictionaries.
101
102    # The internal self.__map dict maps keys to links in a doubly linked list.
103    # The circular doubly linked list starts and ends with a sentinel element.
104    # The sentinel element never gets deleted (this simplifies the algorithm).
105    # The sentinel is in self.__hardroot with a weakref proxy in self.__root.
106    # The prev links are weakref proxies (to prevent circular references).
107    # Individual links are kept alive by the hard reference in self.__map.
108    # Those hard references disappear when a key is deleted from an OrderedDict.
109
110    def __init__(self, other=(), /, **kwds):
111        '''Initialize an ordered dictionary.  The signature is the same as
112        regular dictionaries.  Keyword argument order is preserved.
113        '''
114        try:
115            self.__root
116        except AttributeError:
117            self.__hardroot = _Link()
118            self.__root = root = _proxy(self.__hardroot)
119            root.prev = root.next = root
120            self.__map = {}
121        self.__update(other, **kwds)
122
123    def __setitem__(self, key, value,
124                    dict_setitem=dict.__setitem__, proxy=_proxy, Link=_Link):
125        'od.__setitem__(i, y) <==> od[i]=y'
126        # Setting a new item creates a new link at the end of the linked list,
127        # and the inherited dictionary is updated with the new key/value pair.
128        if key not in self:
129            self.__map[key] = link = Link()
130            root = self.__root
131            last = root.prev
132            link.prev, link.next, link.key = last, root, key
133            last.next = link
134            root.prev = proxy(link)
135        dict_setitem(self, key, value)
136
137    def __delitem__(self, key, dict_delitem=dict.__delitem__):
138        'od.__delitem__(y) <==> del od[y]'
139        # Deleting an existing item uses self.__map to find the link which gets
140        # removed by updating the links in the predecessor and successor nodes.
141        dict_delitem(self, key)
142        link = self.__map.pop(key)
143        link_prev = link.prev
144        link_next = link.next
145        link_prev.next = link_next
146        link_next.prev = link_prev
147        link.prev = None
148        link.next = None
149
150    def __iter__(self):
151        'od.__iter__() <==> iter(od)'
152        # Traverse the linked list in order.
153        root = self.__root
154        curr = root.next
155        while curr is not root:
156            yield curr.key
157            curr = curr.next
158
159    def __reversed__(self):
160        'od.__reversed__() <==> reversed(od)'
161        # Traverse the linked list in reverse order.
162        root = self.__root
163        curr = root.prev
164        while curr is not root:
165            yield curr.key
166            curr = curr.prev
167
168    def clear(self):
169        'od.clear() -> None.  Remove all items from od.'
170        root = self.__root
171        root.prev = root.next = root
172        self.__map.clear()
173        dict.clear(self)
174
175    def popitem(self, last=True):
176        '''Remove and return a (key, value) pair from the dictionary.
177
178        Pairs are returned in LIFO order if last is true or FIFO order if false.
179        '''
180        if not self:
181            raise KeyError('dictionary is empty')
182        root = self.__root
183        if last:
184            link = root.prev
185            link_prev = link.prev
186            link_prev.next = root
187            root.prev = link_prev
188        else:
189            link = root.next
190            link_next = link.next
191            root.next = link_next
192            link_next.prev = root
193        key = link.key
194        del self.__map[key]
195        value = dict.pop(self, key)
196        return key, value
197
198    def move_to_end(self, key, last=True):
199        '''Move an existing element to the end (or beginning if last is false).
200
201        Raise KeyError if the element does not exist.
202        '''
203        link = self.__map[key]
204        link_prev = link.prev
205        link_next = link.next
206        soft_link = link_next.prev
207        link_prev.next = link_next
208        link_next.prev = link_prev
209        root = self.__root
210        if last:
211            last = root.prev
212            link.prev = last
213            link.next = root
214            root.prev = soft_link
215            last.next = link
216        else:
217            first = root.next
218            link.prev = root
219            link.next = first
220            first.prev = soft_link
221            root.next = link
222
223    def __sizeof__(self):
224        sizeof = _sys.getsizeof
225        n = len(self) + 1                       # number of links including root
226        size = sizeof(self.__dict__)            # instance dictionary
227        size += sizeof(self.__map) * 2          # internal dict and inherited dict
228        size += sizeof(self.__hardroot) * n     # link objects
229        size += sizeof(self.__root) * n         # proxy objects
230        return size
231
232    update = __update = _collections_abc.MutableMapping.update
233
234    def keys(self):
235        "D.keys() -> a set-like object providing a view on D's keys"
236        return _OrderedDictKeysView(self)
237
238    def items(self):
239        "D.items() -> a set-like object providing a view on D's items"
240        return _OrderedDictItemsView(self)
241
242    def values(self):
243        "D.values() -> an object providing a view on D's values"
244        return _OrderedDictValuesView(self)
245
246    __ne__ = _collections_abc.MutableMapping.__ne__
247
248    __marker = object()
249
250    def pop(self, key, default=__marker):
251        '''od.pop(k[,d]) -> v, remove specified key and return the corresponding
252        value.  If key is not found, d is returned if given, otherwise KeyError
253        is raised.
254
255        '''
256        if key in self:
257            result = self[key]
258            del self[key]
259            return result
260        if default is self.__marker:
261            raise KeyError(key)
262        return default
263
264    def setdefault(self, key, default=None):
265        '''Insert key with a value of default if key is not in the dictionary.
266
267        Return the value for key if key is in the dictionary, else default.
268        '''
269        if key in self:
270            return self[key]
271        self[key] = default
272        return default
273
274    @_recursive_repr()
275    def __repr__(self):
276        'od.__repr__() <==> repr(od)'
277        if not self:
278            return '%s()' % (self.__class__.__name__,)
279        return '%s(%r)' % (self.__class__.__name__, list(self.items()))
280
281    def __reduce__(self):
282        'Return state information for pickling'
283        inst_dict = vars(self).copy()
284        for k in vars(OrderedDict()):
285            inst_dict.pop(k, None)
286        return self.__class__, (), inst_dict or None, None, iter(self.items())
287
288    def copy(self):
289        'od.copy() -> a shallow copy of od'
290        return self.__class__(self)
291
292    @classmethod
293    def fromkeys(cls, iterable, value=None):
294        '''Create a new ordered dictionary with keys from iterable and values set to value.
295        '''
296        self = cls()
297        for key in iterable:
298            self[key] = value
299        return self
300
301    def __eq__(self, other):
302        '''od.__eq__(y) <==> od==y.  Comparison to another OD is order-sensitive
303        while comparison to a regular mapping is order-insensitive.
304
305        '''
306        if isinstance(other, OrderedDict):
307            return dict.__eq__(self, other) and all(map(_eq, self, other))
308        return dict.__eq__(self, other)
309
310    def __ior__(self, other):
311        self.update(other)
312        return self
313
314    def __or__(self, other):
315        if not isinstance(other, dict):
316            return NotImplemented
317        new = self.__class__(self)
318        new.update(other)
319        return new
320
321    def __ror__(self, other):
322        if not isinstance(other, dict):
323            return NotImplemented
324        new = self.__class__(other)
325        new.update(self)
326        return new
327
328
329try:
330    from _collections import OrderedDict
331except ImportError:
332    # Leave the pure Python version in place.
333    pass
334
335
336################################################################################
337### namedtuple
338################################################################################
339
340try:
341    from _collections import _tuplegetter
342except ImportError:
343    _tuplegetter = lambda index, doc: property(_itemgetter(index), doc=doc)
344
345def namedtuple(typename, field_names, *, rename=False, defaults=None, module=None):
346    """Returns a new subclass of tuple with named fields.
347
348    >>> Point = namedtuple('Point', ['x', 'y'])
349    >>> Point.__doc__                   # docstring for the new class
350    'Point(x, y)'
351    >>> p = Point(11, y=22)             # instantiate with positional args or keywords
352    >>> p[0] + p[1]                     # indexable like a plain tuple
353    33
354    >>> x, y = p                        # unpack like a regular tuple
355    >>> x, y
356    (11, 22)
357    >>> p.x + p.y                       # fields also accessible by name
358    33
359    >>> d = p._asdict()                 # convert to a dictionary
360    >>> d['x']
361    11
362    >>> Point(**d)                      # convert from a dictionary
363    Point(x=11, y=22)
364    >>> p._replace(x=100)               # _replace() is like str.replace() but targets named fields
365    Point(x=100, y=22)
366
367    """
368
369    # Validate the field names.  At the user's option, either generate an error
370    # message or automatically replace the field name with a valid name.
371    if isinstance(field_names, str):
372        field_names = field_names.replace(',', ' ').split()
373    field_names = list(map(str, field_names))
374    typename = _sys.intern(str(typename))
375
376    if rename:
377        seen = set()
378        for index, name in enumerate(field_names):
379            if (not name.isidentifier()
380                or _iskeyword(name)
381                or name.startswith('_')
382                or name in seen):
383                field_names[index] = f'_{index}'
384            seen.add(name)
385
386    for name in [typename] + field_names:
387        if type(name) is not str:
388            raise TypeError('Type names and field names must be strings')
389        if not name.isidentifier():
390            raise ValueError('Type names and field names must be valid '
391                             f'identifiers: {name!r}')
392        if _iskeyword(name):
393            raise ValueError('Type names and field names cannot be a '
394                             f'keyword: {name!r}')
395
396    seen = set()
397    for name in field_names:
398        if name.startswith('_') and not rename:
399            raise ValueError('Field names cannot start with an underscore: '
400                             f'{name!r}')
401        if name in seen:
402            raise ValueError(f'Encountered duplicate field name: {name!r}')
403        seen.add(name)
404
405    field_defaults = {}
406    if defaults is not None:
407        defaults = tuple(defaults)
408        if len(defaults) > len(field_names):
409            raise TypeError('Got more default values than field names')
410        field_defaults = dict(reversed(list(zip(reversed(field_names),
411                                                reversed(defaults)))))
412
413    # Variables used in the methods and docstrings
414    field_names = tuple(map(_sys.intern, field_names))
415    num_fields = len(field_names)
416    arg_list = ', '.join(field_names)
417    if num_fields == 1:
418        arg_list += ','
419    repr_fmt = '(' + ', '.join(f'{name}=%r' for name in field_names) + ')'
420    tuple_new = tuple.__new__
421    _dict, _tuple, _len, _map, _zip = dict, tuple, len, map, zip
422
423    # Create all the named tuple methods to be added to the class namespace
424
425    namespace = {
426        '_tuple_new': tuple_new,
427        '__builtins__': None,
428        '__name__': f'namedtuple_{typename}',
429    }
430    code = f'lambda _cls, {arg_list}: _tuple_new(_cls, ({arg_list}))'
431    __new__ = eval(code, namespace)
432    __new__.__name__ = '__new__'
433    __new__.__doc__ = f'Create new instance of {typename}({arg_list})'
434    if defaults is not None:
435        __new__.__defaults__ = defaults
436
437    @classmethod
438    def _make(cls, iterable):
439        result = tuple_new(cls, iterable)
440        if _len(result) != num_fields:
441            raise TypeError(f'Expected {num_fields} arguments, got {len(result)}')
442        return result
443
444    _make.__func__.__doc__ = (f'Make a new {typename} object from a sequence '
445                              'or iterable')
446
447    def _replace(self, /, **kwds):
448        result = self._make(_map(kwds.pop, field_names, self))
449        if kwds:
450            raise ValueError(f'Got unexpected field names: {list(kwds)!r}')
451        return result
452
453    _replace.__doc__ = (f'Return a new {typename} object replacing specified '
454                        'fields with new values')
455
456    def __repr__(self):
457        'Return a nicely formatted representation string'
458        return self.__class__.__name__ + repr_fmt % self
459
460    def _asdict(self):
461        'Return a new dict which maps field names to their values.'
462        return _dict(_zip(self._fields, self))
463
464    def __getnewargs__(self):
465        'Return self as a plain tuple.  Used by copy and pickle.'
466        return _tuple(self)
467
468    # Modify function metadata to help with introspection and debugging
469    for method in (
470        __new__,
471        _make.__func__,
472        _replace,
473        __repr__,
474        _asdict,
475        __getnewargs__,
476    ):
477        method.__qualname__ = f'{typename}.{method.__name__}'
478
479    # Build-up the class namespace dictionary
480    # and use type() to build the result class
481    class_namespace = {
482        '__doc__': f'{typename}({arg_list})',
483        '__slots__': (),
484        '_fields': field_names,
485        '_field_defaults': field_defaults,
486        '__new__': __new__,
487        '_make': _make,
488        '_replace': _replace,
489        '__repr__': __repr__,
490        '_asdict': _asdict,
491        '__getnewargs__': __getnewargs__,
492    }
493    for index, name in enumerate(field_names):
494        doc = _sys.intern(f'Alias for field number {index}')
495        class_namespace[name] = _tuplegetter(index, doc)
496
497    result = type(typename, (tuple,), class_namespace)
498
499    # For pickling to work, the __module__ variable needs to be set to the frame
500    # where the named tuple is created.  Bypass this step in environments where
501    # sys._getframe is not defined (Jython for example) or sys._getframe is not
502    # defined for arguments greater than 0 (IronPython), or where the user has
503    # specified a particular module.
504    if module is None:
505        try:
506            module = _sys._getframe(1).f_globals.get('__name__', '__main__')
507        except (AttributeError, ValueError):
508            pass
509    if module is not None:
510        result.__module__ = module
511
512    return result
513
514
515########################################################################
516###  Counter
517########################################################################
518
519def _count_elements(mapping, iterable):
520    'Tally elements from the iterable.'
521    mapping_get = mapping.get
522    for elem in iterable:
523        mapping[elem] = mapping_get(elem, 0) + 1
524
525try:                                    # Load C helper function if available
526    from _collections import _count_elements
527except ImportError:
528    pass
529
530class Counter(dict):
531    '''Dict subclass for counting hashable items.  Sometimes called a bag
532    or multiset.  Elements are stored as dictionary keys and their counts
533    are stored as dictionary values.
534
535    >>> c = Counter('abcdeabcdabcaba')  # count elements from a string
536
537    >>> c.most_common(3)                # three most common elements
538    [('a', 5), ('b', 4), ('c', 3)]
539    >>> sorted(c)                       # list all unique elements
540    ['a', 'b', 'c', 'd', 'e']
541    >>> ''.join(sorted(c.elements()))   # list elements with repetitions
542    'aaaaabbbbcccdde'
543    >>> sum(c.values())                 # total of all counts
544    15
545
546    >>> c['a']                          # count of letter 'a'
547    5
548    >>> for elem in 'shazam':           # update counts from an iterable
549    ...     c[elem] += 1                # by adding 1 to each element's count
550    >>> c['a']                          # now there are seven 'a'
551    7
552    >>> del c['b']                      # remove all 'b'
553    >>> c['b']                          # now there are zero 'b'
554    0
555
556    >>> d = Counter('simsalabim')       # make another counter
557    >>> c.update(d)                     # add in the second counter
558    >>> c['a']                          # now there are nine 'a'
559    9
560
561    >>> c.clear()                       # empty the counter
562    >>> c
563    Counter()
564
565    Note:  If a count is set to zero or reduced to zero, it will remain
566    in the counter until the entry is deleted or the counter is cleared:
567
568    >>> c = Counter('aaabbc')
569    >>> c['b'] -= 2                     # reduce the count of 'b' by two
570    >>> c.most_common()                 # 'b' is still in, but its count is zero
571    [('a', 3), ('c', 1), ('b', 0)]
572
573    '''
574    # References:
575    #   http://en.wikipedia.org/wiki/Multiset
576    #   http://www.gnu.org/software/smalltalk/manual-base/html_node/Bag.html
577    #   http://www.demo2s.com/Tutorial/Cpp/0380__set-multiset/Catalog0380__set-multiset.htm
578    #   http://code.activestate.com/recipes/259174/
579    #   Knuth, TAOCP Vol. II section 4.6.3
580
581    def __init__(self, iterable=None, /, **kwds):
582        '''Create a new, empty Counter object.  And if given, count elements
583        from an input iterable.  Or, initialize the count from another mapping
584        of elements to their counts.
585
586        >>> c = Counter()                           # a new, empty counter
587        >>> c = Counter('gallahad')                 # a new counter from an iterable
588        >>> c = Counter({'a': 4, 'b': 2})           # a new counter from a mapping
589        >>> c = Counter(a=4, b=2)                   # a new counter from keyword args
590
591        '''
592        super().__init__()
593        self.update(iterable, **kwds)
594
595    def __missing__(self, key):
596        'The count of elements not in the Counter is zero.'
597        # Needed so that self[missing_item] does not raise KeyError
598        return 0
599
600    def most_common(self, n=None):
601        '''List the n most common elements and their counts from the most
602        common to the least.  If n is None, then list all element counts.
603
604        >>> Counter('abracadabra').most_common(3)
605        [('a', 5), ('b', 2), ('r', 2)]
606
607        '''
608        # Emulate Bag.sortedByCount from Smalltalk
609        if n is None:
610            return sorted(self.items(), key=_itemgetter(1), reverse=True)
611        return _heapq.nlargest(n, self.items(), key=_itemgetter(1))
612
613    def elements(self):
614        '''Iterator over elements repeating each as many times as its count.
615
616        >>> c = Counter('ABCABC')
617        >>> sorted(c.elements())
618        ['A', 'A', 'B', 'B', 'C', 'C']
619
620        # Knuth's example for prime factors of 1836:  2**2 * 3**3 * 17**1
621        >>> prime_factors = Counter({2: 2, 3: 3, 17: 1})
622        >>> product = 1
623        >>> for factor in prime_factors.elements():     # loop over factors
624        ...     product *= factor                       # and multiply them
625        >>> product
626        1836
627
628        Note, if an element's count has been set to zero or is a negative
629        number, elements() will ignore it.
630
631        '''
632        # Emulate Bag.do from Smalltalk and Multiset.begin from C++.
633        return _chain.from_iterable(_starmap(_repeat, self.items()))
634
635    # Override dict methods where necessary
636
637    @classmethod
638    def fromkeys(cls, iterable, v=None):
639        # There is no equivalent method for counters because the semantics
640        # would be ambiguous in cases such as Counter.fromkeys('aaabbc', v=2).
641        # Initializing counters to zero values isn't necessary because zero
642        # is already the default value for counter lookups.  Initializing
643        # to one is easily accomplished with Counter(set(iterable)).  For
644        # more exotic cases, create a dictionary first using a dictionary
645        # comprehension or dict.fromkeys().
646        raise NotImplementedError(
647            'Counter.fromkeys() is undefined.  Use Counter(iterable) instead.')
648
649    def update(self, iterable=None, /, **kwds):
650        '''Like dict.update() but add counts instead of replacing them.
651
652        Source can be an iterable, a dictionary, or another Counter instance.
653
654        >>> c = Counter('which')
655        >>> c.update('witch')           # add elements from another iterable
656        >>> d = Counter('watch')
657        >>> c.update(d)                 # add elements from another counter
658        >>> c['h']                      # four 'h' in which, witch, and watch
659        4
660
661        '''
662        # The regular dict.update() operation makes no sense here because the
663        # replace behavior results in the some of original untouched counts
664        # being mixed-in with all of the other counts for a mismash that
665        # doesn't have a straight-forward interpretation in most counting
666        # contexts.  Instead, we implement straight-addition.  Both the inputs
667        # and outputs are allowed to contain zero and negative counts.
668
669        if iterable is not None:
670            if isinstance(iterable, _collections_abc.Mapping):
671                if self:
672                    self_get = self.get
673                    for elem, count in iterable.items():
674                        self[elem] = count + self_get(elem, 0)
675                else:
676                    # fast path when counter is empty
677                    super().update(iterable)
678            else:
679                _count_elements(self, iterable)
680        if kwds:
681            self.update(kwds)
682
683    def subtract(self, iterable=None, /, **kwds):
684        '''Like dict.update() but subtracts counts instead of replacing them.
685        Counts can be reduced below zero.  Both the inputs and outputs are
686        allowed to contain zero and negative counts.
687
688        Source can be an iterable, a dictionary, or another Counter instance.
689
690        >>> c = Counter('which')
691        >>> c.subtract('witch')             # subtract elements from another iterable
692        >>> c.subtract(Counter('watch'))    # subtract elements from another counter
693        >>> c['h']                          # 2 in which, minus 1 in witch, minus 1 in watch
694        0
695        >>> c['w']                          # 1 in which, minus 1 in witch, minus 1 in watch
696        -1
697
698        '''
699        if iterable is not None:
700            self_get = self.get
701            if isinstance(iterable, _collections_abc.Mapping):
702                for elem, count in iterable.items():
703                    self[elem] = self_get(elem, 0) - count
704            else:
705                for elem in iterable:
706                    self[elem] = self_get(elem, 0) - 1
707        if kwds:
708            self.subtract(kwds)
709
710    def copy(self):
711        'Return a shallow copy.'
712        return self.__class__(self)
713
714    def __reduce__(self):
715        return self.__class__, (dict(self),)
716
717    def __delitem__(self, elem):
718        'Like dict.__delitem__() but does not raise KeyError for missing values.'
719        if elem in self:
720            super().__delitem__(elem)
721
722    def __repr__(self):
723        if not self:
724            return f'{self.__class__.__name__}()'
725        try:
726            # dict() preserves the ordering returned by most_common()
727            d = dict(self.most_common())
728        except TypeError:
729            # handle case where values are not orderable
730            d = dict(self)
731        return f'{self.__class__.__name__}({d!r})'
732
733    # Multiset-style mathematical operations discussed in:
734    #       Knuth TAOCP Volume II section 4.6.3 exercise 19
735    #       and at http://en.wikipedia.org/wiki/Multiset
736    #
737    # Outputs guaranteed to only include positive counts.
738    #
739    # To strip negative and zero counts, add-in an empty counter:
740    #       c += Counter()
741    #
742    # Rich comparison operators for multiset subset and superset tests
743    # are deliberately omitted due to semantic conflicts with the
744    # existing inherited dict equality method.  Subset and superset
745    # semantics ignore zero counts and require that p≤q ∧ p≥q → p=q;
746    # however, that would not be the case for p=Counter(a=1, b=0)
747    # and q=Counter(a=1) where the dictionaries are not equal.
748
749    def __add__(self, other):
750        '''Add counts from two counters.
751
752        >>> Counter('abbb') + Counter('bcc')
753        Counter({'b': 4, 'c': 2, 'a': 1})
754
755        '''
756        if not isinstance(other, Counter):
757            return NotImplemented
758        result = Counter()
759        for elem, count in self.items():
760            newcount = count + other[elem]
761            if newcount > 0:
762                result[elem] = newcount
763        for elem, count in other.items():
764            if elem not in self and count > 0:
765                result[elem] = count
766        return result
767
768    def __sub__(self, other):
769        ''' Subtract count, but keep only results with positive counts.
770
771        >>> Counter('abbbc') - Counter('bccd')
772        Counter({'b': 2, 'a': 1})
773
774        '''
775        if not isinstance(other, Counter):
776            return NotImplemented
777        result = Counter()
778        for elem, count in self.items():
779            newcount = count - other[elem]
780            if newcount > 0:
781                result[elem] = newcount
782        for elem, count in other.items():
783            if elem not in self and count < 0:
784                result[elem] = 0 - count
785        return result
786
787    def __or__(self, other):
788        '''Union is the maximum of value in either of the input counters.
789
790        >>> Counter('abbb') | Counter('bcc')
791        Counter({'b': 3, 'c': 2, 'a': 1})
792
793        '''
794        if not isinstance(other, Counter):
795            return NotImplemented
796        result = Counter()
797        for elem, count in self.items():
798            other_count = other[elem]
799            newcount = other_count if count < other_count else count
800            if newcount > 0:
801                result[elem] = newcount
802        for elem, count in other.items():
803            if elem not in self and count > 0:
804                result[elem] = count
805        return result
806
807    def __and__(self, other):
808        ''' Intersection is the minimum of corresponding counts.
809
810        >>> Counter('abbb') & Counter('bcc')
811        Counter({'b': 1})
812
813        '''
814        if not isinstance(other, Counter):
815            return NotImplemented
816        result = Counter()
817        for elem, count in self.items():
818            other_count = other[elem]
819            newcount = count if count < other_count else other_count
820            if newcount > 0:
821                result[elem] = newcount
822        return result
823
824    def __pos__(self):
825        'Adds an empty counter, effectively stripping negative and zero counts'
826        result = Counter()
827        for elem, count in self.items():
828            if count > 0:
829                result[elem] = count
830        return result
831
832    def __neg__(self):
833        '''Subtracts from an empty counter.  Strips positive and zero counts,
834        and flips the sign on negative counts.
835
836        '''
837        result = Counter()
838        for elem, count in self.items():
839            if count < 0:
840                result[elem] = 0 - count
841        return result
842
843    def _keep_positive(self):
844        '''Internal method to strip elements with a negative or zero count'''
845        nonpositive = [elem for elem, count in self.items() if not count > 0]
846        for elem in nonpositive:
847            del self[elem]
848        return self
849
850    def __iadd__(self, other):
851        '''Inplace add from another counter, keeping only positive counts.
852
853        >>> c = Counter('abbb')
854        >>> c += Counter('bcc')
855        >>> c
856        Counter({'b': 4, 'c': 2, 'a': 1})
857
858        '''
859        for elem, count in other.items():
860            self[elem] += count
861        return self._keep_positive()
862
863    def __isub__(self, other):
864        '''Inplace subtract counter, but keep only results with positive counts.
865
866        >>> c = Counter('abbbc')
867        >>> c -= Counter('bccd')
868        >>> c
869        Counter({'b': 2, 'a': 1})
870
871        '''
872        for elem, count in other.items():
873            self[elem] -= count
874        return self._keep_positive()
875
876    def __ior__(self, other):
877        '''Inplace union is the maximum of value from either counter.
878
879        >>> c = Counter('abbb')
880        >>> c |= Counter('bcc')
881        >>> c
882        Counter({'b': 3, 'c': 2, 'a': 1})
883
884        '''
885        for elem, other_count in other.items():
886            count = self[elem]
887            if other_count > count:
888                self[elem] = other_count
889        return self._keep_positive()
890
891    def __iand__(self, other):
892        '''Inplace intersection is the minimum of corresponding counts.
893
894        >>> c = Counter('abbb')
895        >>> c &= Counter('bcc')
896        >>> c
897        Counter({'b': 1})
898
899        '''
900        for elem, count in self.items():
901            other_count = other[elem]
902            if other_count < count:
903                self[elem] = other_count
904        return self._keep_positive()
905
906
907########################################################################
908###  ChainMap
909########################################################################
910
911class ChainMap(_collections_abc.MutableMapping):
912    ''' A ChainMap groups multiple dicts (or other mappings) together
913    to create a single, updateable view.
914
915    The underlying mappings are stored in a list.  That list is public and can
916    be accessed or updated using the *maps* attribute.  There is no other
917    state.
918
919    Lookups search the underlying mappings successively until a key is found.
920    In contrast, writes, updates, and deletions only operate on the first
921    mapping.
922
923    '''
924
925    def __init__(self, *maps):
926        '''Initialize a ChainMap by setting *maps* to the given mappings.
927        If no mappings are provided, a single empty dictionary is used.
928
929        '''
930        self.maps = list(maps) or [{}]          # always at least one map
931
932    def __missing__(self, key):
933        raise KeyError(key)
934
935    def __getitem__(self, key):
936        for mapping in self.maps:
937            try:
938                return mapping[key]             # can't use 'key in mapping' with defaultdict
939            except KeyError:
940                pass
941        return self.__missing__(key)            # support subclasses that define __missing__
942
943    def get(self, key, default=None):
944        return self[key] if key in self else default
945
946    def __len__(self):
947        return len(set().union(*self.maps))     # reuses stored hash values if possible
948
949    def __iter__(self):
950        d = {}
951        for mapping in reversed(self.maps):
952            d.update(dict.fromkeys(mapping))    # reuses stored hash values if possible
953        return iter(d)
954
955    def __contains__(self, key):
956        return any(key in m for m in self.maps)
957
958    def __bool__(self):
959        return any(self.maps)
960
961    @_recursive_repr()
962    def __repr__(self):
963        return f'{self.__class__.__name__}({", ".join(map(repr, self.maps))})'
964
965    @classmethod
966    def fromkeys(cls, iterable, *args):
967        'Create a ChainMap with a single dict created from the iterable.'
968        return cls(dict.fromkeys(iterable, *args))
969
970    def copy(self):
971        'New ChainMap or subclass with a new copy of maps[0] and refs to maps[1:]'
972        return self.__class__(self.maps[0].copy(), *self.maps[1:])
973
974    __copy__ = copy
975
976    def new_child(self, m=None):                # like Django's Context.push()
977        '''New ChainMap with a new map followed by all previous maps.
978        If no map is provided, an empty dict is used.
979        '''
980        if m is None:
981            m = {}
982        return self.__class__(m, *self.maps)
983
984    @property
985    def parents(self):                          # like Django's Context.pop()
986        'New ChainMap from maps[1:].'
987        return self.__class__(*self.maps[1:])
988
989    def __setitem__(self, key, value):
990        self.maps[0][key] = value
991
992    def __delitem__(self, key):
993        try:
994            del self.maps[0][key]
995        except KeyError:
996            raise KeyError(f'Key not found in the first mapping: {key!r}')
997
998    def popitem(self):
999        'Remove and return an item pair from maps[0]. Raise KeyError is maps[0] is empty.'
1000        try:
1001            return self.maps[0].popitem()
1002        except KeyError:
1003            raise KeyError('No keys found in the first mapping.')
1004
1005    def pop(self, key, *args):
1006        'Remove *key* from maps[0] and return its value. Raise KeyError if *key* not in maps[0].'
1007        try:
1008            return self.maps[0].pop(key, *args)
1009        except KeyError:
1010            raise KeyError(f'Key not found in the first mapping: {key!r}')
1011
1012    def clear(self):
1013        'Clear maps[0], leaving maps[1:] intact.'
1014        self.maps[0].clear()
1015
1016    def __ior__(self, other):
1017        self.maps[0].update(other)
1018        return self
1019
1020    def __or__(self, other):
1021        if not isinstance(other, _collections_abc.Mapping):
1022            return NotImplemented
1023        m = self.copy()
1024        m.maps[0].update(other)
1025        return m
1026
1027    def __ror__(self, other):
1028        if not isinstance(other, _collections_abc.Mapping):
1029            return NotImplemented
1030        m = dict(other)
1031        for child in reversed(self.maps):
1032            m.update(child)
1033        return self.__class__(m)
1034
1035
1036################################################################################
1037### UserDict
1038################################################################################
1039
1040class UserDict(_collections_abc.MutableMapping):
1041
1042    # Start by filling-out the abstract methods
1043    def __init__(self, dict=None, /, **kwargs):
1044        self.data = {}
1045        if dict is not None:
1046            self.update(dict)
1047        if kwargs:
1048            self.update(kwargs)
1049
1050    def __len__(self):
1051        return len(self.data)
1052
1053    def __getitem__(self, key):
1054        if key in self.data:
1055            return self.data[key]
1056        if hasattr(self.__class__, "__missing__"):
1057            return self.__class__.__missing__(self, key)
1058        raise KeyError(key)
1059
1060    def __setitem__(self, key, item):
1061        self.data[key] = item
1062
1063    def __delitem__(self, key):
1064        del self.data[key]
1065
1066    def __iter__(self):
1067        return iter(self.data)
1068
1069    # Modify __contains__ to work correctly when __missing__ is present
1070    def __contains__(self, key):
1071        return key in self.data
1072
1073    # Now, add the methods in dicts but not in MutableMapping
1074    def __repr__(self):
1075        return repr(self.data)
1076
1077    def __or__(self, other):
1078        if isinstance(other, UserDict):
1079            return self.__class__(self.data | other.data)
1080        if isinstance(other, dict):
1081            return self.__class__(self.data | other)
1082        return NotImplemented
1083
1084    def __ror__(self, other):
1085        if isinstance(other, UserDict):
1086            return self.__class__(other.data | self.data)
1087        if isinstance(other, dict):
1088            return self.__class__(other | self.data)
1089        return NotImplemented
1090
1091    def __ior__(self, other):
1092        if isinstance(other, UserDict):
1093            self.data |= other.data
1094        else:
1095            self.data |= other
1096        return self
1097
1098    def __copy__(self):
1099        inst = self.__class__.__new__(self.__class__)
1100        inst.__dict__.update(self.__dict__)
1101        # Create a copy and avoid triggering descriptors
1102        inst.__dict__["data"] = self.__dict__["data"].copy()
1103        return inst
1104
1105    def copy(self):
1106        if self.__class__ is UserDict:
1107            return UserDict(self.data.copy())
1108        import copy
1109        data = self.data
1110        try:
1111            self.data = {}
1112            c = copy.copy(self)
1113        finally:
1114            self.data = data
1115        c.update(self)
1116        return c
1117
1118    @classmethod
1119    def fromkeys(cls, iterable, value=None):
1120        d = cls()
1121        for key in iterable:
1122            d[key] = value
1123        return d
1124
1125
1126################################################################################
1127### UserList
1128################################################################################
1129
1130class UserList(_collections_abc.MutableSequence):
1131    """A more or less complete user-defined wrapper around list objects."""
1132
1133    def __init__(self, initlist=None):
1134        self.data = []
1135        if initlist is not None:
1136            # XXX should this accept an arbitrary sequence?
1137            if type(initlist) == type(self.data):
1138                self.data[:] = initlist
1139            elif isinstance(initlist, UserList):
1140                self.data[:] = initlist.data[:]
1141            else:
1142                self.data = list(initlist)
1143
1144    def __repr__(self):
1145        return repr(self.data)
1146
1147    def __lt__(self, other):
1148        return self.data < self.__cast(other)
1149
1150    def __le__(self, other):
1151        return self.data <= self.__cast(other)
1152
1153    def __eq__(self, other):
1154        return self.data == self.__cast(other)
1155
1156    def __gt__(self, other):
1157        return self.data > self.__cast(other)
1158
1159    def __ge__(self, other):
1160        return self.data >= self.__cast(other)
1161
1162    def __cast(self, other):
1163        return other.data if isinstance(other, UserList) else other
1164
1165    def __contains__(self, item):
1166        return item in self.data
1167
1168    def __len__(self):
1169        return len(self.data)
1170
1171    def __getitem__(self, i):
1172        if isinstance(i, slice):
1173            return self.__class__(self.data[i])
1174        else:
1175            return self.data[i]
1176
1177    def __setitem__(self, i, item):
1178        self.data[i] = item
1179
1180    def __delitem__(self, i):
1181        del self.data[i]
1182
1183    def __add__(self, other):
1184        if isinstance(other, UserList):
1185            return self.__class__(self.data + other.data)
1186        elif isinstance(other, type(self.data)):
1187            return self.__class__(self.data + other)
1188        return self.__class__(self.data + list(other))
1189
1190    def __radd__(self, other):
1191        if isinstance(other, UserList):
1192            return self.__class__(other.data + self.data)
1193        elif isinstance(other, type(self.data)):
1194            return self.__class__(other + self.data)
1195        return self.__class__(list(other) + self.data)
1196
1197    def __iadd__(self, other):
1198        if isinstance(other, UserList):
1199            self.data += other.data
1200        elif isinstance(other, type(self.data)):
1201            self.data += other
1202        else:
1203            self.data += list(other)
1204        return self
1205
1206    def __mul__(self, n):
1207        return self.__class__(self.data * n)
1208
1209    __rmul__ = __mul__
1210
1211    def __imul__(self, n):
1212        self.data *= n
1213        return self
1214
1215    def __copy__(self):
1216        inst = self.__class__.__new__(self.__class__)
1217        inst.__dict__.update(self.__dict__)
1218        # Create a copy and avoid triggering descriptors
1219        inst.__dict__["data"] = self.__dict__["data"][:]
1220        return inst
1221
1222    def append(self, item):
1223        self.data.append(item)
1224
1225    def insert(self, i, item):
1226        self.data.insert(i, item)
1227
1228    def pop(self, i=-1):
1229        return self.data.pop(i)
1230
1231    def remove(self, item):
1232        self.data.remove(item)
1233
1234    def clear(self):
1235        self.data.clear()
1236
1237    def copy(self):
1238        return self.__class__(self)
1239
1240    def count(self, item):
1241        return self.data.count(item)
1242
1243    def index(self, item, *args):
1244        return self.data.index(item, *args)
1245
1246    def reverse(self):
1247        self.data.reverse()
1248
1249    def sort(self, /, *args, **kwds):
1250        self.data.sort(*args, **kwds)
1251
1252    def extend(self, other):
1253        if isinstance(other, UserList):
1254            self.data.extend(other.data)
1255        else:
1256            self.data.extend(other)
1257
1258
1259################################################################################
1260### UserString
1261################################################################################
1262
1263class UserString(_collections_abc.Sequence):
1264
1265    def __init__(self, seq):
1266        if isinstance(seq, str):
1267            self.data = seq
1268        elif isinstance(seq, UserString):
1269            self.data = seq.data[:]
1270        else:
1271            self.data = str(seq)
1272
1273    def __str__(self):
1274        return str(self.data)
1275
1276    def __repr__(self):
1277        return repr(self.data)
1278
1279    def __int__(self):
1280        return int(self.data)
1281
1282    def __float__(self):
1283        return float(self.data)
1284
1285    def __complex__(self):
1286        return complex(self.data)
1287
1288    def __hash__(self):
1289        return hash(self.data)
1290
1291    def __getnewargs__(self):
1292        return (self.data[:],)
1293
1294    def __eq__(self, string):
1295        if isinstance(string, UserString):
1296            return self.data == string.data
1297        return self.data == string
1298
1299    def __lt__(self, string):
1300        if isinstance(string, UserString):
1301            return self.data < string.data
1302        return self.data < string
1303
1304    def __le__(self, string):
1305        if isinstance(string, UserString):
1306            return self.data <= string.data
1307        return self.data <= string
1308
1309    def __gt__(self, string):
1310        if isinstance(string, UserString):
1311            return self.data > string.data
1312        return self.data > string
1313
1314    def __ge__(self, string):
1315        if isinstance(string, UserString):
1316            return self.data >= string.data
1317        return self.data >= string
1318
1319    def __contains__(self, char):
1320        if isinstance(char, UserString):
1321            char = char.data
1322        return char in self.data
1323
1324    def __len__(self):
1325        return len(self.data)
1326
1327    def __getitem__(self, index):
1328        return self.__class__(self.data[index])
1329
1330    def __add__(self, other):
1331        if isinstance(other, UserString):
1332            return self.__class__(self.data + other.data)
1333        elif isinstance(other, str):
1334            return self.__class__(self.data + other)
1335        return self.__class__(self.data + str(other))
1336
1337    def __radd__(self, other):
1338        if isinstance(other, str):
1339            return self.__class__(other + self.data)
1340        return self.__class__(str(other) + self.data)
1341
1342    def __mul__(self, n):
1343        return self.__class__(self.data * n)
1344
1345    __rmul__ = __mul__
1346
1347    def __mod__(self, args):
1348        return self.__class__(self.data % args)
1349
1350    def __rmod__(self, template):
1351        return self.__class__(str(template) % self)
1352
1353    # the following methods are defined in alphabetical order:
1354    def capitalize(self):
1355        return self.__class__(self.data.capitalize())
1356
1357    def casefold(self):
1358        return self.__class__(self.data.casefold())
1359
1360    def center(self, width, *args):
1361        return self.__class__(self.data.center(width, *args))
1362
1363    def count(self, sub, start=0, end=_sys.maxsize):
1364        if isinstance(sub, UserString):
1365            sub = sub.data
1366        return self.data.count(sub, start, end)
1367
1368    def removeprefix(self, prefix, /):
1369        if isinstance(prefix, UserString):
1370            prefix = prefix.data
1371        return self.__class__(self.data.removeprefix(prefix))
1372
1373    def removesuffix(self, suffix, /):
1374        if isinstance(suffix, UserString):
1375            suffix = suffix.data
1376        return self.__class__(self.data.removesuffix(suffix))
1377
1378    def encode(self, encoding='utf-8', errors='strict'):
1379        encoding = 'utf-8' if encoding is None else encoding
1380        errors = 'strict' if errors is None else errors
1381        return self.data.encode(encoding, errors)
1382
1383    def endswith(self, suffix, start=0, end=_sys.maxsize):
1384        return self.data.endswith(suffix, start, end)
1385
1386    def expandtabs(self, tabsize=8):
1387        return self.__class__(self.data.expandtabs(tabsize))
1388
1389    def find(self, sub, start=0, end=_sys.maxsize):
1390        if isinstance(sub, UserString):
1391            sub = sub.data
1392        return self.data.find(sub, start, end)
1393
1394    def format(self, /, *args, **kwds):
1395        return self.data.format(*args, **kwds)
1396
1397    def format_map(self, mapping):
1398        return self.data.format_map(mapping)
1399
1400    def index(self, sub, start=0, end=_sys.maxsize):
1401        return self.data.index(sub, start, end)
1402
1403    def isalpha(self):
1404        return self.data.isalpha()
1405
1406    def isalnum(self):
1407        return self.data.isalnum()
1408
1409    def isascii(self):
1410        return self.data.isascii()
1411
1412    def isdecimal(self):
1413        return self.data.isdecimal()
1414
1415    def isdigit(self):
1416        return self.data.isdigit()
1417
1418    def isidentifier(self):
1419        return self.data.isidentifier()
1420
1421    def islower(self):
1422        return self.data.islower()
1423
1424    def isnumeric(self):
1425        return self.data.isnumeric()
1426
1427    def isprintable(self):
1428        return self.data.isprintable()
1429
1430    def isspace(self):
1431        return self.data.isspace()
1432
1433    def istitle(self):
1434        return self.data.istitle()
1435
1436    def isupper(self):
1437        return self.data.isupper()
1438
1439    def join(self, seq):
1440        return self.data.join(seq)
1441
1442    def ljust(self, width, *args):
1443        return self.__class__(self.data.ljust(width, *args))
1444
1445    def lower(self):
1446        return self.__class__(self.data.lower())
1447
1448    def lstrip(self, chars=None):
1449        return self.__class__(self.data.lstrip(chars))
1450
1451    maketrans = str.maketrans
1452
1453    def partition(self, sep):
1454        return self.data.partition(sep)
1455
1456    def replace(self, old, new, maxsplit=-1):
1457        if isinstance(old, UserString):
1458            old = old.data
1459        if isinstance(new, UserString):
1460            new = new.data
1461        return self.__class__(self.data.replace(old, new, maxsplit))
1462
1463    def rfind(self, sub, start=0, end=_sys.maxsize):
1464        if isinstance(sub, UserString):
1465            sub = sub.data
1466        return self.data.rfind(sub, start, end)
1467
1468    def rindex(self, sub, start=0, end=_sys.maxsize):
1469        return self.data.rindex(sub, start, end)
1470
1471    def rjust(self, width, *args):
1472        return self.__class__(self.data.rjust(width, *args))
1473
1474    def rpartition(self, sep):
1475        return self.data.rpartition(sep)
1476
1477    def rstrip(self, chars=None):
1478        return self.__class__(self.data.rstrip(chars))
1479
1480    def split(self, sep=None, maxsplit=-1):
1481        return self.data.split(sep, maxsplit)
1482
1483    def rsplit(self, sep=None, maxsplit=-1):
1484        return self.data.rsplit(sep, maxsplit)
1485
1486    def splitlines(self, keepends=False):
1487        return self.data.splitlines(keepends)
1488
1489    def startswith(self, prefix, start=0, end=_sys.maxsize):
1490        return self.data.startswith(prefix, start, end)
1491
1492    def strip(self, chars=None):
1493        return self.__class__(self.data.strip(chars))
1494
1495    def swapcase(self):
1496        return self.__class__(self.data.swapcase())
1497
1498    def title(self):
1499        return self.__class__(self.data.title())
1500
1501    def translate(self, *args):
1502        return self.__class__(self.data.translate(*args))
1503
1504    def upper(self):
1505        return self.__class__(self.data.upper())
1506
1507    def zfill(self, width):
1508        return self.__class__(self.data.zfill(width))
1509