text: """functools.py - Tools for working with functions and callable objects
  """
  # Python module wrapper for _functools C module
  # to allow utilities written in Python to be added
  # to the functools module.
  # Written by Nick Coghlan <ncoghlan at gmail.com>,
  # Raymond Hettinger <python at rcn.com>,
  # and Łukasz Langa <lukasz at langa.pl>.
  #   Copyright (C) 2006-2013 Python Software Foundation.
  # See C source code for _functools credits/copyright
  
  __all__ = ['update_wrapper', 'wraps', 'WRAPPER_ASSIGNMENTS', 'WRAPPER_UPDATES',
             'total_ordering', 'cmp_to_key', 'lru_cache', 'reduce', 'partial',
             'partialmethod', 'singledispatch', 'singledispatchmethod']
  
  from abc import get_cache_token
  from collections import namedtuple
  # import types, weakref  # Deferred to single_dispatch()
  from reprlib import recursive_repr
  from _thread import RLock
  
  
  ################################################################################
  ### update_wrapper() and wraps() decorator
  ################################################################################
  
  # update_wrapper() and wraps() are tools to help write
  # wrapper functions that can handle naive introspection
  
  WRAPPER_ASSIGNMENTS = ('__module__', '__name__', '__qualname__', '__doc__',
                         '__annotations__')
  WRAPPER_UPDATES = ('__dict__',)
  def update_wrapper(wrapper,
                     wrapped,
                     assigned = WRAPPER_ASSIGNMENTS,
                     updated = WRAPPER_UPDATES):
      """Update a wrapper function to look like the wrapped function
  
         wrapper is the function to be updated
         wrapped is the original function
         assigned is a tuple naming the attributes assigned directly
         from the wrapped function to the wrapper function (defaults to
         functools.WRAPPER_ASSIGNMENTS)
         updated is a tuple naming the attributes of the wrapper that
         are updated with the corresponding attribute from the wrapped
         function (defaults to functools.WRAPPER_UPDATES)
      """
      for attr in assigned:
          try:
              value = getattr(wrapped, attr)
          except AttributeError:
              pass
          else:
              setattr(wrapper, attr, value)
      for attr in updated:
          getattr(wrapper, attr).update(getattr(wrapped, attr, {}))
      # Issue #17482: set __wrapped__ last so we don't inadvertently copy it
      # from the wrapped function when updating __dict__
      wrapper.__wrapped__ = wrapped
      # Return the wrapper so this can be used as a decorator via partial()
      return wrapper
  
  def wraps(wrapped,
            assigned = WRAPPER_ASSIGNMENTS,
            updated = WRAPPER_UPDATES):
      """Decorator factory to apply update_wrapper() to a wrapper function
  
         Returns a decorator that invokes update_wrapper() with the decorated
         function as the wrapper argument and the arguments to wraps() as the
         remaining arguments. Default arguments are as for update_wrapper().
         This is a convenience function to simplify applying partial() to
         update_wrapper().
      """
      return partial(update_wrapper, wrapped=wrapped,
                     assigned=assigned, updated=updated)
  
  
  ################################################################################
  ### total_ordering class decorator
  ################################################################################
  
  # The total ordering functions all invoke the root magic method directly
  # rather than using the corresponding operator.  This avoids possible
  # infinite recursion that could occur when the operator dispatch logic
  # detects a NotImplemented result and then calls a reflected method.
  
  def _gt_from_lt(self, other, NotImplemented=NotImplemented):
      'Return a > b.  Computed by @total_ordering from (not a < b) and (a != b).'
      op_result = self.__lt__(other)
      if op_result is NotImplemented:
          return op_result
      return not op_result and self != other
  
  def _le_from_lt(self, other, NotImplemented=NotImplemented):
      'Return a <= b.  Computed by @total_ordering from (a < b) or (a == b).'
      op_result = self.__lt__(other)
      return op_result or self == other
  
  def _ge_from_lt(self, other, NotImplemented=NotImplemented):
      'Return a >= b.  Computed by @total_ordering from (not a < b).'
      op_result = self.__lt__(other)
      if op_result is NotImplemented:
          return op_result
      return not op_result
  
  def _ge_from_le(self, other, NotImplemented=NotImplemented):
      'Return a >= b.  Computed by @total_ordering from (not a <= b) or (a == b).'
      op_result = self.__le__(other)
      if op_result is NotImplemented:
          return op_result
      return not op_result or self == other
  
  def _lt_from_le(self, other, NotImplemented=NotImplemented):
      'Return a < b.  Computed by @total_ordering from (a <= b) and (a != b).'
      op_result = self.__le__(other)
      if op_result is NotImplemented:
          return op_result
      return op_result and self != other
  
  def _gt_from_le(self, other, NotImplemented=NotImplemented):
      'Return a > b.  Computed by @total_ordering from (not a <= b).'
      op_result = self.__le__(other)
      if op_result is NotImplemented:
          return op_result
      return not op_result
  
  def _lt_from_gt(self, other, NotImplemented=NotImplemented):
      'Return a < b.  Computed by @total_ordering from (not a > b) and (a != b).'
      op_result = self.__gt__(other)
      if op_result is NotImplemented:
          return op_result
      return not op_result and self != other
  
  def _ge_from_gt(self, other, NotImplemented=NotImplemented):
      'Return a >= b.  Computed by @total_ordering from (a > b) or (a == b).'
      op_result = self.__gt__(other)
      return op_result or self == other
  
  def _le_from_gt(self, other, NotImplemented=NotImplemented):
      'Return a <= b.  Computed by @total_ordering from (not a > b).'
      op_result = self.__gt__(other)
      if op_result is NotImplemented:
          return op_result
      return not op_result
  
  def _le_from_ge(self, other, NotImplemented=NotImplemented):
      'Return a <= b.  Computed by @total_ordering from (not a >= b) or (a == b).'
      op_result = self.__ge__(other)
      if op_result is NotImplemented:
          return op_result
      return not op_result or self == other
  
  def _gt_from_ge(self, other, NotImplemented=NotImplemented):
      'Return a > b.  Computed by @total_ordering from (a >= b) and (a != b).'
      op_result = self.__ge__(other)
      if op_result is NotImplemented:
          return op_result
      return op_result and self != other
  
  def _lt_from_ge(self, other, NotImplemented=NotImplemented):
      'Return a < b.  Computed by @total_ordering from (not a >= b).'
      op_result = self.__ge__(other)
      if op_result is NotImplemented:
          return op_result
      return not op_result
  
  _convert = {
      '__lt__': [('__gt__', _gt_from_lt),
                 ('__le__', _le_from_lt),
                 ('__ge__', _ge_from_lt)],
      '__le__': [('__ge__', _ge_from_le),
                 ('__lt__', _lt_from_le),
                 ('__gt__', _gt_from_le)],
      '__gt__': [('__lt__', _lt_from_gt),
                 ('__ge__', _ge_from_gt),
                 ('__le__', _le_from_gt)],
      '__ge__': [('__le__', _le_from_ge),
                 ('__gt__', _gt_from_ge),
                 ('__lt__', _lt_from_ge)]
  }
  
  def total_ordering(cls):
      """Class decorator that fills in missing ordering methods"""
      # Find user-defined comparisons (not those inherited from object).
      roots = {op for op in _convert if getattr(cls, op, None) is not getattr(object, op, None)}
      if not roots:
          raise ValueError('must define at least one ordering operation: < > <= >=')
      root = max(roots)       # prefer __lt__ to __le__ to __gt__ to __ge__
      for opname, opfunc in _convert[root]:
          if opname not in roots:
              opfunc.__name__ = opname
              setattr(cls, opname, opfunc)
      return cls
  
  
  ################################################################################
  ### cmp_to_key() function converter
  ################################################################################
  
  def cmp_to_key(mycmp):
      """Convert a cmp= function into a key= function"""
      class K(object):
          __slots__ = ['obj']
          def __init__(self, obj):
              self.obj = obj
          def __lt__(self, other):
              return mycmp(self.obj, other.obj) < 0
          def __gt__(self, other):
              return mycmp(self.obj, other.obj) > 0
          def __eq__(self, other):
              return mycmp(self.obj, other.obj) == 0
          def __le__(self, other):
              return mycmp(self.obj, other.obj) <= 0
          def __ge__(self, other):
              return mycmp(self.obj, other.obj) >= 0
          __hash__ = None
      return K
  
  try:
      from _functools import cmp_to_key
  except ImportError:
      pass
  
  
  ################################################################################
  ### reduce() sequence to a single item
  ################################################################################
  
  _initial_missing = object()
  
  def reduce(function, sequence, initial=_initial_missing):
      """
      reduce(function, sequence[, initial]) -> value
  
      Apply a function of two arguments cumulatively to the items of a sequence,
      from left to right, so as to reduce the sequence to a single value.
      For example, reduce(lambda x, y: x+y, [1, 2, 3, 4, 5]) calculates
      ((((1+2)+3)+4)+5).  If initial is present, it is placed before the items
      of the sequence in the calculation, and serves as a default when the
      sequence is empty.
      """
  
      it = iter(sequence)
  
      if initial is _initial_missing:
          try:
              value = next(it)
          except StopIteration:
              raise TypeError("reduce() of empty sequence with no initial value") from None
      else:
          value = initial
  
      for element in it:
          value = function(value, element)
  
      return value
  
  try:
      from _functools import reduce
  except ImportError:
      pass
  
  
  ################################################################################
  ### partial() argument application
  ################################################################################
  
  # Purely functional, no descriptor behaviour
  class partial:
      """New function with partial application of the given arguments
      and keywords.
      """
  
      __slots__ = "func", "args", "keywords", "__dict__", "__weakref__"
  
      def __new__(cls, func, /, *args, **keywords):
          if not callable(func):
              raise TypeError("the first argument must be callable")
  
          if hasattr(func, "func"):
              args = func.args + args
              keywords = {**func.keywords, **keywords}
              func = func.func
  
          self = super(partial, cls).__new__(cls)
  
          self.func = func
          self.args = args
          self.keywords = keywords
          return self
  
      def __call__(self, /, *args, **keywords):
          keywords = {**self.keywords, **keywords}
          return self.func(*self.args, *args, **keywords)
  
      @recursive_repr()
      def __repr__(self):
          qualname = type(self).__qualname__
          args = [repr(self.func)]
          args.extend(repr(x) for x in self.args)
          args.extend(f"{k}={v!r}" for (k, v) in self.keywords.items())
          if type(self).__module__ == "functools":
              return f"functools.{qualname}({', '.join(args)})"
          return f"{qualname}({', '.join(args)})"
  
      def __reduce__(self):
          return type(self), (self.func,), (self.func, self.args,
                 self.keywords or None, self.__dict__ or None)
  
      def __setstate__(self, state):
          if not isinstance(state, tuple):
              raise TypeError("argument to __setstate__ must be a tuple")
          if len(state) != 4:
              raise TypeError(f"expected 4 items in state, got {len(state)}")
          func, args, kwds, namespace = state
          if (not callable(func) or not isinstance(args, tuple) or
             (kwds is not None and not isinstance(kwds, dict)) or
             (namespace is not None and not isinstance(namespace, dict))):
              raise TypeError("invalid partial state")
  
          args = tuple(args) # just in case it's a subclass
          if kwds is None:
              kwds = {}
          elif type(kwds) is not dict: # XXX does it need to be *exactly* dict?
              kwds = dict(kwds)
          if namespace is None:
              namespace = {}
  
          self.__dict__ = namespace
          self.func = func
          self.args = args
          self.keywords = kwds
  
  try:
      from _functools import partial
  except ImportError:
      pass
  
  # Descriptor version
  class partialmethod(object):
      """Method descriptor with partial application of the given arguments
      and keywords.
  
      Supports wrapping existing descriptors and handles non-descriptor
      callables as instance methods.
      """
  
      def __init__(self, func, /, *args, **keywords):
          if not callable(func) and not hasattr(func, "__get__"):
              raise TypeError("{!r} is not callable or a descriptor"
                                   .format(func))
  
          # func could be a descriptor like classmethod which isn't callable,
          # so we can't inherit from partial (it verifies func is callable)
          if isinstance(func, partialmethod):
              # flattening is mandatory in order to place cls/self before all
              # other arguments
              # it's also more efficient since only one function will be called
              self.func = func.func
              self.args = func.args + args
              self.keywords = {**func.keywords, **keywords}
          else:
              self.func = func
              self.args = args
              self.keywords = keywords
  
      def __repr__(self):
          args = ", ".join(map(repr, self.args))
          keywords = ", ".join("{}={!r}".format(k, v)
                                   for k, v in self.keywords.items())
          format_string = "{module}.{cls}({func}, {args}, {keywords})"
          return format_string.format(module=self.__class__.__module__,
                                      cls=self.__class__.__qualname__,
                                      func=self.func,
                                      args=args,
                                      keywords=keywords)
  
      def _make_unbound_method(self):
          def _method(cls_or_self, /, *args, **keywords):
              keywords = {**self.keywords, **keywords}
              return self.func(cls_or_self, *self.args, *args, **keywords)
          _method.__isabstractmethod__ = self.__isabstractmethod__
          _method._partialmethod = self
          return _method
  
      def __get__(self, obj, cls=None):
          get = getattr(self.func, "__get__", None)
          result = None
          if get is not None:
              new_func = get(obj, cls)
              if new_func is not self.func:
                  # Assume __get__ returning something new indicates the
                  # creation of an appropriate callable
                  result = partial(new_func, *self.args, **self.keywords)
                  try:
                      result.__self__ = new_func.__self__
                  except AttributeError:
                      pass
          if result is None:
              # If the underlying descriptor didn't do anything, treat this
              # like an instance method
              result = self._make_unbound_method().__get__(obj, cls)
          return result
  
      @property
      def __isabstractmethod__(self):
          return getattr(self.func, "__isabstractmethod__", False)
  
  # Helper functions
  
  def _unwrap_partial(func):
      while isinstance(func, partial):
          func = func.func
      return func
  
  ################################################################################
  ### LRU Cache function decorator
  ################################################################################
  
  _CacheInfo = namedtuple("CacheInfo", ["hits", "misses", "maxsize", "currsize"])
  
  class _HashedSeq(list):
      """ This class guarantees that hash() will be called no more than once
          per element.  This is important because the lru_cache() will hash
          the key multiple times on a cache miss.
  
      """
  
      __slots__ = 'hashvalue'
  
      def __init__(self, tup, hash=hash):
          self[:] = tup
          self.hashvalue = hash(tup)
  
      def __hash__(self):
          return self.hashvalue
  
  def _make_key(args, kwds, typed,
               kwd_mark = (object(),),
               fasttypes = {int, str},
               tuple=tuple, type=type, len=len):
      """Make a cache key from optionally typed positional and keyword arguments
  
      The key is constructed in a way that is flat as possible rather than
      as a nested structure that would take more memory.
  
      If there is only a single argument and its data type is known to cache
      its hash value, then that argument is returned without a wrapper.  This
      saves space and improves lookup speed.
  
      """
      # All of code below relies on kwds preserving the order input by the user.
      # Formerly, we sorted() the kwds before looping.  The new way is *much*
      # faster; however, it means that f(x=1, y=2) will now be treated as a
      # distinct call from f(y=2, x=1) which will be cached separately.
      key = args
      if kwds:
          key += kwd_mark
          for item in kwds.items():
              key += item
      if typed:
          key += tuple(type(v) for v in args)
          if kwds:
              key += tuple(type(v) for v in kwds.values())
      elif len(key) == 1 and type(key[0]) in fasttypes:
          return key[0]
      return _HashedSeq(key)
  
  def lru_cache(maxsize=128, typed=False):
      """Least-recently-used cache decorator.
  
      If *maxsize* is set to None, the LRU features are disabled and the cache
      can grow without bound.
  
      If *typed* is True, arguments of different types will be cached separately.
      For example, f(3.0) and f(3) will be treated as distinct calls with
      distinct results.
  
      Arguments to the cached function must be hashable.
  
      View the cache statistics named tuple (hits, misses, maxsize, currsize)
      with f.cache_info().  Clear the cache and statistics with f.cache_clear().
      Access the underlying function with f.__wrapped__.
  
      See:  http://en.wikipedia.org/wiki/Cache_replacement_policies#Least_recently_used_(LRU)
  
      """
  
      # Users should only access the lru_cache through its public API:
      #       cache_info, cache_clear, and f.__wrapped__
      # The internals of the lru_cache are encapsulated for thread safety and
      # to allow the implementation to change (including a possible C version).
  
      if isinstance(maxsize, int):
          # Negative maxsize is treated as 0
          if maxsize < 0:
              maxsize = 0
      elif callable(maxsize) and isinstance(typed, bool):
          # The user_function was passed in directly via the maxsize argument
          user_function, maxsize = maxsize, 128
          wrapper = _lru_cache_wrapper(user_function, maxsize, typed, _CacheInfo)
          wrapper.cache_parameters = lambda : {'maxsize': maxsize, 'typed': typed}
          return update_wrapper(wrapper, user_function)
      elif maxsize is not None:
          raise TypeError(
              'Expected first argument to be an integer, a callable, or None')
  
      def decorating_function(user_function):
          wrapper = _lru_cache_wrapper(user_function, maxsize, typed, _CacheInfo)
          wrapper.cache_parameters = lambda : {'maxsize': maxsize, 'typed': typed}
          return update_wrapper(wrapper, user_function)
  
      return decorating_function
  
  def _lru_cache_wrapper(user_function, maxsize, typed, _CacheInfo):
      # Constants shared by all lru cache instances:
      sentinel = object()          # unique object used to signal cache misses
      make_key = _make_key         # build a key from the function arguments
      PREV, NEXT, KEY, RESULT = 0, 1, 2, 3   # names for the link fields
  
      cache = {}
      hits = misses = 0
      full = False
      cache_get = cache.get    # bound method to lookup a key or return None
      cache_len = cache.__len__  # get cache size without calling len()
      lock = RLock()           # because linkedlist updates aren't threadsafe
      root = []                # root of the circular doubly linked list
      root[:] = [root, root, None, None]     # initialize by pointing to self
  
      if maxsize == 0:
  
          def wrapper(*args, **kwds):
              # No caching -- just a statistics update
              nonlocal misses
              misses += 1
              result = user_function(*args, **kwds)
              return result
  
      elif maxsize is None:
  
          def wrapper(*args, **kwds):
              # Simple caching without ordering or size limit
              nonlocal hits, misses
              key = make_key(args, kwds, typed)
              result = cache_get(key, sentinel)
              if result is not sentinel:
                  hits += 1
                  return result
              misses += 1
              result = user_function(*args, **kwds)
              cache[key] = result
              return result
  
      else:
  
          def wrapper(*args, **kwds):
              # Size limited caching that tracks accesses by recency
              nonlocal root, hits, misses, full
              key = make_key(args, kwds, typed)
              with lock:
                  link = cache_get(key)
                  if link is not None:
                      # Move the link to the front of the circular queue
                      link_prev, link_next, _key, result = link
                      link_prev[NEXT] = link_next
                      link_next[PREV] = link_prev
                      last = root[PREV]
                      last[NEXT] = root[PREV] = link
                      link[PREV] = last
                      link[NEXT] = root
                      hits += 1
                      return result
                  misses += 1
              result = user_function(*args, **kwds)
              with lock:
                  if key in cache:
                      # Getting here means that this same key was added to the
                      # cache while the lock was released.  Since the link
                      # update is already done, we need only return the
                      # computed result and update the count of misses.
                      pass
                  elif full:
                      # Use the old root to store the new key and result.
                      oldroot = root
                      oldroot[KEY] = key
                      oldroot[RESULT] = result
                      # Empty the oldest link and make it the new root.
                      # Keep a reference to the old key and old result to
                      # prevent their ref counts from going to zero during the
                      # update. That will prevent potentially arbitrary object
                      # clean-up code (i.e. __del__) from running while we're
                      # still adjusting the links.
                      root = oldroot[NEXT]
                      oldkey = root[KEY]
                      oldresult = root[RESULT]
                      root[KEY] = root[RESULT] = None
                      # Now update the cache dictionary.
                      del cache[oldkey]
                      # Save the potentially reentrant cache[key] assignment
                      # for last, after the root and links have been put in
                      # a consistent state.
                      cache[key] = oldroot
                  else:
                      # Put result in a new link at the front of the queue.
                      last = root[PREV]
                      link = [last, root, key, result]
                      last[NEXT] = root[PREV] = cache[key] = link
                      # Use the cache_len bound method instead of the len() function
                      # which could potentially be wrapped in an lru_cache itself.
                      full = (cache_len() >= maxsize)
              return result
  
      def cache_info():
          """Report cache statistics"""
          with lock:
              return _CacheInfo(hits, misses, maxsize, cache_len())
  
      def cache_clear():
          """Clear the cache and cache statistics"""
          nonlocal hits, misses, full
          with lock:
              cache.clear()
              root[:] = [root, root, None, None]
              hits = misses = 0
              full = False
  
      wrapper.cache_info = cache_info
      wrapper.cache_clear = cache_clear
      return wrapper
  
  try:
      from _functools import _lru_cache_wrapper
  except ImportError:
      pass
  
  
  ################################################################################
  ### singledispatch() - single-dispatch generic function decorator
  ################################################################################
  
  def _c3_merge(sequences):
      """Merges MROs in *sequences* to a single MRO using the C3 algorithm.
  
      Adapted from http://www.python.org/download/releases/2.3/mro/.
  
      """
      result = []
      while True:
          sequences = [s for s in sequences if s]   # purge empty sequences
          if not sequences:
              return result
          for s1 in sequences:   # find merge candidates among seq heads
              candidate = s1[0]
              for s2 in sequences:
                  if candidate in s2[1:]:
                      candidate = None
                      break      # reject the current head, it appears later
              else:
                  break
          if candidate is None:
              raise RuntimeError("Inconsistent hierarchy")
          result.append(candidate)
          # remove the chosen candidate
          for seq in sequences:
              if seq[0] == candidate:
                  del seq[0]
  
  def _c3_mro(cls, abcs=None):
      """Computes the method resolution order using extended C3 linearization.
  
      If no *abcs* are given, the algorithm works exactly like the built-in C3
      linearization used for method resolution.
  
      If given, *abcs* is a list of abstract base classes that should be inserted
      into the resulting MRO. Unrelated ABCs are ignored and don't end up in the
      result. The algorithm inserts ABCs where their functionality is introduced,
      i.e. issubclass(cls, abc) returns True for the class itself but returns
      False for all its direct base classes. Implicit ABCs for a given class
      (either registered or inferred from the presence of a special method like
      __len__) are inserted directly after the last ABC explicitly listed in the
      MRO of said class. If two implicit ABCs end up next to each other in the
      resulting MRO, their ordering depends on the order of types in *abcs*.
  
      """
      for i, base in enumerate(reversed(cls.__bases__)):
          if hasattr(base, '__abstractmethods__'):
              boundary = len(cls.__bases__) - i
              break   # Bases up to the last explicit ABC are considered first.
      else:
          boundary = 0
      abcs = list(abcs) if abcs else []
      explicit_bases = list(cls.__bases__[:boundary])
      abstract_bases = []
      other_bases = list(cls.__bases__[boundary:])
      for base in abcs:
          if issubclass(cls, base) and not any(
                  issubclass(b, base) for b in cls.__bases__
              ):
              # If *cls* is the class that introduces behaviour described by
              # an ABC *base*, insert said ABC to its MRO.
              abstract_bases.append(base)
      for base in abstract_bases:
          abcs.remove(base)
      explicit_c3_mros = [_c3_mro(base, abcs=abcs) for base in explicit_bases]
      abstract_c3_mros = [_c3_mro(base, abcs=abcs) for base in abstract_bases]
      other_c3_mros = [_c3_mro(base, abcs=abcs) for base in other_bases]
      return _c3_merge(
          [[cls]] +
          explicit_c3_mros + abstract_c3_mros + other_c3_mros +
          [explicit_bases] + [abstract_bases] + [other_bases]
      )
  
  def _compose_mro(cls, types):
      """Calculates the method resolution order for a given class *cls*.
  
      Includes relevant abstract base classes (with their respective bases) from
      the *types* iterable. Uses a modified C3 linearization algorithm.
  
      """
      bases = set(cls.__mro__)
      # Remove entries which are already present in the __mro__ or unrelated.
      def is_related(typ):
          return (typ not in bases and hasattr(typ, '__mro__')
                                   and issubclass(cls, typ))
      types = [n for n in types if is_related(n)]
      # Remove entries which are strict bases of other entries (they will end up
      # in the MRO anyway.
      def is_strict_base(typ):
          for other in types:
              if typ != other and typ in other.__mro__:
                  return True
          return False
      types = [n for n in types if not is_strict_base(n)]
      # Subclasses of the ABCs in *types* which are also implemented by
      # *cls* can be used to stabilize ABC ordering.
      type_set = set(types)
      mro = []
      for typ in types:
          found = []
          for sub in typ.__subclasses__():
              if sub not in bases and issubclass(cls, sub):
                  found.append([s for s in sub.__mro__ if s in type_set])
          if not found:
              mro.append(typ)
              continue
          # Favor subclasses with the biggest number of useful bases
          found.sort(key=len, reverse=True)
          for sub in found:
              for subcls in sub:
                  if subcls not in mro:
                      mro.append(subcls)
      return _c3_mro(cls, abcs=mro)
  
  def _find_impl(cls, registry):
      """Returns the best matching implementation from *registry* for type *cls*.
  
      Where there is no registered implementation for a specific type, its method
      resolution order is used to find a more generic implementation.
  
      Note: if *registry* does not contain an implementation for the base
      *object* type, this function may return None.
  
      """
      mro = _compose_mro(cls, registry.keys())
      match = None
      for t in mro:
          if match is not None:
              # If *match* is an implicit ABC but there is another unrelated,
              # equally matching implicit ABC, refuse the temptation to guess.
              if (t in registry and t not in cls.__mro__
                                and match not in cls.__mro__
                                and not issubclass(match, t)):
                  raise RuntimeError("Ambiguous dispatch: {} or {}".format(
                      match, t))
              break
          if t in registry:
              match = t
      return registry.get(match)
  
  def singledispatch(func):
      """Single-dispatch generic function decorator.
  
      Transforms a function into a generic function, which can have different
      behaviours depending upon the type of its first argument. The decorated
      function acts as the default implementation, and additional
      implementations can be registered using the register() attribute of the
      generic function.
      """
      # There are many programs that use functools without singledispatch, so we
      # trade-off making singledispatch marginally slower for the benefit of
      # making start-up of such applications slightly faster.
      import types, weakref
  
      registry = {}
      dispatch_cache = weakref.WeakKeyDictionary()
      cache_token = None
  
      def dispatch(cls):
          """generic_func.dispatch(cls) -> <function implementation>
  
          Runs the dispatch algorithm to return the best available implementation
          for the given *cls* registered on *generic_func*.
  
          """
          nonlocal cache_token
          if cache_token is not None:
              current_token = get_cache_token()
              if cache_token != current_token:
                  dispatch_cache.clear()
                  cache_token = current_token
          try:
              impl = dispatch_cache[cls]
          except KeyError:
              try:
                  impl = registry[cls]
              except KeyError:
                  impl = _find_impl(cls, registry)
              dispatch_cache[cls] = impl
          return impl
  
      def register(cls, func=None):
          """generic_func.register(cls, func) -> func
  
          Registers a new implementation for the given *cls* on a *generic_func*.
  
          """
          nonlocal cache_token
          if func is None:
              if isinstance(cls, type):
                  return lambda f: register(cls, f)
              ann = getattr(cls, '__annotations__', {})
              if not ann:
                  raise TypeError(
                      f"Invalid first argument to `register()`: {cls!r}. "
                      f"Use either `@register(some_class)` or plain `@register` "
                      f"on an annotated function."
                  )
              func = cls
  
              # only import typing if annotation parsing is necessary
              from typing import get_type_hints
              argname, cls = next(iter(get_type_hints(func).items()))
              if not isinstance(cls, type):
                  raise TypeError(
                      f"Invalid annotation for {argname!r}. "
                      f"{cls!r} is not a class."
                  )
          registry[cls] = func
          if cache_token is None and hasattr(cls, '__abstractmethods__'):
              cache_token = get_cache_token()
          dispatch_cache.clear()
          return func
  
      def wrapper(*args, **kw):
          if not args:
              raise TypeError(f'{funcname} requires at least '
                              '1 positional argument')
  
          return dispatch(args[0].__class__)(*args, **kw)
  
      funcname = getattr(func, '__name__', 'singledispatch function')
      registry[object] = func
      wrapper.register = register
      wrapper.dispatch = dispatch
      wrapper.registry = types.MappingProxyType(registry)
      wrapper._clear_cache = dispatch_cache.clear
      update_wrapper(wrapper, func)
      return wrapper
  
  
  # Descriptor version
  class singledispatchmethod:
      """Single-dispatch generic method descriptor.
  
      Supports wrapping existing descriptors and handles non-descriptor
      callables as instance methods.
      """
  
      def __init__(self, func):
          if not callable(func) and not hasattr(func, "__get__"):
              raise TypeError(f"{func!r} is not callable or a descriptor")
  
          self.dispatcher = singledispatch(func)
          self.func = func
  
      def register(self, cls, method=None):
          """generic_method.register(cls, func) -> func
  
          Registers a new implementation for the given *cls* on a *generic_method*.
          """
          return self.dispatcher.register(cls, func=method)
  
      def __get__(self, obj, cls=None):
          def _method(*args, **kwargs):
              method = self.dispatcher.dispatch(args[0].__class__)
              return method.__get__(obj, cls)(*args, **kwargs)
  
          _method.__isabstractmethod__ = self.__isabstractmethod__
          _method.register = self.register
          update_wrapper(_method, self.func)
          return _method
  
      @property
      def __isabstractmethod__(self):
          return getattr(self.func, '__isabstractmethod__', False)
  
  
  ################################################################################
  ### cached_property() - computed once per instance, cached as attribute
  ################################################################################
  
  _NOT_FOUND = object()
  
  
  class cached_property:
      def __init__(self, func):
          self.func = func
          self.attrname = None
          self.__doc__ = func.__doc__
          self.lock = RLock()
  
      def __set_name__(self, owner, name):
          if self.attrname is None:
              self.attrname = name
          elif name != self.attrname:
              raise TypeError(
                  "Cannot assign the same cached_property to two different names "
                  f"({self.attrname!r} and {name!r})."
              )
  
      def __get__(self, instance, owner=None):
          if instance is None:
              return self
          if self.attrname is None:
              raise TypeError(
                  "Cannot use cached_property instance without calling __set_name__ on it.")
          try:
              cache = instance.__dict__
          except AttributeError:  # not all objects have __dict__ (e.g. class defines slots)
              msg = (
                  f"No '__dict__' attribute on {type(instance).__name__!r} "
                  f"instance to cache {self.attrname!r} property."
              )
              raise TypeError(msg) from None
          val = cache.get(self.attrname, _NOT_FOUND)
          if val is _NOT_FOUND:
              with self.lock:
                  # check if another thread filled cache while we awaited lock
                  val = cache.get(self.attrname, _NOT_FOUND)
                  if val is _NOT_FOUND:
                      val = self.func(instance)
                      try:
                          cache[self.attrname] = val
                      except TypeError:
                          msg = (
                              f"The '__dict__' attribute on {type(instance).__name__!r} instance "
                              f"does not support item assignment for caching {self.attrname!r} property."
                          )
                          raise TypeError(msg) from None
          return val
  