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']
  
  try:
      from _functools import reduce
  except ImportError:
      pass
  from abc import get_cache_token
  from collections import namedtuple
  from types import MappingProxyType
  from weakref import WeakKeyDictionary
  try:
      from _thread import RLock
  except:
      class RLock:
          'Dummy reentrant lock for builds without threads'
          def __enter__(self): pass
          def __exit__(self, exctype, excinst, exctb): pass
  
  
  ################################################################################
  ### 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):
      '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 NotImplemented
      return not op_result and self != other
  
  def _le_from_lt(self, other):
      '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):
      'Return a >= b.  Computed by @total_ordering from (not a < b).'
      op_result = self.__lt__(other)
      if op_result is NotImplemented:
          return NotImplemented
      return not op_result
  
  def _ge_from_le(self, other):
      '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 NotImplemented
      return not op_result or self == other
  
  def _lt_from_le(self, other):
      'Return a < b.  Computed by @total_ordering from (a <= b) and (a != b).'
      op_result = self.__le__(other)
      if op_result is NotImplemented:
          return NotImplemented
      return op_result and self != other
  
  def _gt_from_le(self, other):
      'Return a > b.  Computed by @total_ordering from (not a <= b).'
      op_result = self.__le__(other)
      if op_result is NotImplemented:
          return NotImplemented
      return not op_result
  
  def _lt_from_gt(self, other):
      '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 NotImplemented
      return not op_result and self != other
  
  def _ge_from_gt(self, other):
      '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):
      'Return a <= b.  Computed by @total_ordering from (not a > b).'
      op_result = self.__gt__(other)
      if op_result is NotImplemented:
          return NotImplemented
      return not op_result
  
  def _le_from_ge(self, other):
      '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 NotImplemented
      return not op_result or self == other
  
  def _gt_from_ge(self, other):
      'Return a > b.  Computed by @total_ordering from (a >= b) and (a != b).'
      op_result = self.__ge__(other)
      if op_result is NotImplemented:
          return NotImplemented
      return op_result and self != other
  
  def _lt_from_ge(self, other):
      'Return a < b.  Computed by @total_ordering from (not a >= b).'
      op_result = self.__ge__(other)
      if op_result is NotImplemented:
          return NotImplemented
      return not op_result
  
  def total_ordering(cls):
      """Class decorator that fills in missing ordering methods"""
      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)]
      }
      # 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
          def __ne__(self, other):
              return mycmp(self.obj, other.obj) != 0
          __hash__ = None
      return K
  
  try:
      from _functools import cmp_to_key
  except ImportError:
      pass
  
  
  ################################################################################
  ### partial() argument application
  ################################################################################
  
  # Purely functional, no descriptor behaviour
  def partial(func, *args, **keywords):
      """New function with partial application of the given arguments
      and keywords.
      """
      def newfunc(*fargs, **fkeywords):
          newkeywords = keywords.copy()
          newkeywords.update(fkeywords)
          return func(*(args + fargs), **newkeywords)
      newfunc.func = func
      newfunc.args = args
      newfunc.keywords = keywords
      return newfunc
  
  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.copy()
              self.keywords.update(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__.__name__,
                                      func=self.func,
                                      args=args,
                                      keywords=keywords)
  
      def _make_unbound_method(self):
          def _method(*args, **keywords):
              call_keywords = self.keywords.copy()
              call_keywords.update(keywords)
              cls_or_self, *rest = args
              call_args = (cls_or_self,) + self.args + tuple(rest)
              return self.func(*call_args, **call_keywords)
          _method.__isabstractmethod__ = self.__isabstractmethod__
          _method._partialmethod = self
          return _method
  
      def __get__(self, obj, cls):
          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)
  
  
  ################################################################################
  ### 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, frozenset, type(None)},
               sorted=sorted, 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.
  
      """
      key = args
      if kwds:
          sorted_items = sorted(kwds.items())
          key += kwd_mark
          for item in sorted_items:
              key += item
      if typed:
          key += tuple(type(v) for v in args)
          if kwds:
              key += tuple(type(v) for k, v in sorted_items)
      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_algorithms#Least_Recently_Used
  
      """
  
      # 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).
  
      # Early detection of an erroneous call to @lru_cache without any arguments
      # resulting in the inner function being passed to maxsize instead of an
      # integer or None.
      if maxsize is not None and not isinstance(maxsize, int):
          raise TypeError('Expected maxsize to be an integer or None')
  
      # 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
  
      def decorating_function(user_function):
          cache = {}
          hits = misses = 0
          full = False
          cache_get = cache.get    # bound method to lookup a key or return None
          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 after a successful call
                  nonlocal misses
                  result = user_function(*args, **kwds)
                  misses += 1
                  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
                  result = user_function(*args, **kwds)
                  cache[key] = result
                  misses += 1
                  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
                  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
                          full = (len(cache) >= maxsize)
                      misses += 1
                  return result
  
          def cache_info():
              """Report cache statistics"""
              with lock:
                  return _CacheInfo(hits, misses, maxsize, len(cache))
  
          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 update_wrapper(wrapper, user_function)
  
      return decorating_function
  
  
  ################################################################################
  ### 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.
  
      """
      registry = {}
      dispatch_cache = 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:
              return lambda f: register(cls, f)
          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):
          return dispatch(args[0].__class__)(*args, **kw)
  
      registry[object] = func
      wrapper.register = register
      wrapper.dispatch = dispatch
      wrapper.registry = MappingProxyType(registry)
      wrapper._clear_cache = dispatch_cache.clear
      update_wrapper(wrapper, func)
      return wrapper
  