text: from __future__ import absolute_import, unicode_literals
  
  import abc
  from abc import abstractmethod, abstractproperty
  import collections
  import functools
  import re as stdlib_re  # Avoid confusion with the re we export.
  import sys
  import types
  try:
      import collections.abc as collections_abc
  except ImportError:
      import collections as collections_abc  # Fallback for PY3.2.
  
  
  # Please keep __all__ alphabetized within each category.
  __all__ = [
      # Super-special typing primitives.
      'Any',
      'Callable',
      'ClassVar',
      'Generic',
      'Optional',
      'Tuple',
      'Type',
      'TypeVar',
      'Union',
  
      # ABCs (from collections.abc).
      'AbstractSet',  # collections.abc.Set.
      'ByteString',
      'Container',
      'Hashable',
      'ItemsView',
      'Iterable',
      'Iterator',
      'KeysView',
      'Mapping',
      'MappingView',
      'MutableMapping',
      'MutableSequence',
      'MutableSet',
      'Sequence',
      'Sized',
      'ValuesView',
  
      # Structural checks, a.k.a. protocols.
      'Reversible',
      'SupportsAbs',
      'SupportsFloat',
      'SupportsInt',
  
      # Concrete collection types.
      'Dict',
      'DefaultDict',
      'List',
      'Set',
      'FrozenSet',
      'NamedTuple',  # Not really a type.
      'Generator',
  
      # One-off things.
      'AnyStr',
      'cast',
      'get_type_hints',
      'NewType',
      'no_type_check',
      'no_type_check_decorator',
      'overload',
      'Text',
      'TYPE_CHECKING',
  ]
  
  # The pseudo-submodules 're' and 'io' are part of the public
  # namespace, but excluded from __all__ because they might stomp on
  # legitimate imports of those modules.
  
  
  def _qualname(x):
      if sys.version_info[:2] >= (3, 3):
          return x.__qualname__
      else:
          # Fall back to just name.
          return x.__name__
  
  def _trim_name(nm):
      if nm.startswith('_') and nm not in ('_TypeAlias',
                      '_ForwardRef', '_TypingBase', '_FinalTypingBase'):
          nm = nm[1:]
      return nm
  
  
  class TypingMeta(type):
      """Metaclass for most types defined in typing module
      (not a part of public API).
  
      This also defines a dummy constructor (all the work for most typing
      constructs is done in __new__) and a nicer repr().
      """
  
      _is_protocol = False
  
      def __new__(cls, name, bases, namespace):
          return super(TypingMeta, cls).__new__(cls, str(name), bases, namespace)
  
      @classmethod
      def assert_no_subclassing(cls, bases):
          for base in bases:
              if isinstance(base, cls):
                  raise TypeError("Cannot subclass %s" %
                                  (', '.join(map(_type_repr, bases)) or '()'))
  
      def __init__(self, *args, **kwds):
          pass
  
      def _eval_type(self, globalns, localns):
          """Override this in subclasses to interpret forward references.
  
          For example, List['C'] is internally stored as
          List[_ForwardRef('C')], which should evaluate to List[C],
          where C is an object found in globalns or localns (searching
          localns first, of course).
          """
          return self
  
      def _get_type_vars(self, tvars):
          pass
  
      def __repr__(self):
          qname = _trim_name(_qualname(self))
          return '%s.%s' % (self.__module__, qname)
  
  
  class _TypingBase(object):
      """Internal indicator of special typing constructs."""
      __metaclass__ = TypingMeta
      __slots__ = ()
  
      def __init__(self, *args, **kwds):
          pass
  
      def __new__(cls, *args, **kwds):
          """Constructor.
  
          This only exists to give a better error message in case
          someone tries to subclass a special typing object (not a good idea).
          """
          if (len(args) == 3 and
                  isinstance(args[0], str) and
                  isinstance(args[1], tuple)):
              # Close enough.
              raise TypeError("Cannot subclass %r" % cls)
          return super(_TypingBase, cls).__new__(cls)
  
      # Things that are not classes also need these.
      def _eval_type(self, globalns, localns):
          return self
  
      def _get_type_vars(self, tvars):
          pass
  
      def __repr__(self):
          cls = type(self)
          qname = _trim_name(_qualname(cls))
          return '%s.%s' % (cls.__module__, qname)
  
      def __call__(self, *args, **kwds):
          raise TypeError("Cannot instantiate %r" % type(self))
  
  
  class _FinalTypingBase(_TypingBase):
      """Internal mix-in class to prevent instantiation.
  
      Prevents instantiation unless _root=True is given in class call.
      It is used to create pseudo-singleton instances Any, Union, Optional, etc.
      """
  
      __slots__ = ()
  
      def __new__(cls, *args, **kwds):
          self = super(_FinalTypingBase, cls).__new__(cls, *args, **kwds)
          if '_root' in kwds and kwds['_root'] is True:
              return self
          raise TypeError("Cannot instantiate %r" % cls)
  
      def __reduce__(self):
          return _trim_name(type(self).__name__)
  
  
  class _ForwardRef(_TypingBase):
      """Internal wrapper to hold a forward reference."""
  
      __slots__ = ('__forward_arg__', '__forward_code__',
                   '__forward_evaluated__', '__forward_value__')
  
      def __init__(self, arg):
          super(_ForwardRef, self).__init__(arg)
          if not isinstance(arg, basestring):
              raise TypeError('Forward reference must be a string -- got %r' % (arg,))
          try:
              code = compile(arg, '<string>', 'eval')
          except SyntaxError:
              raise SyntaxError('Forward reference must be an expression -- got %r' %
                                (arg,))
          self.__forward_arg__ = arg
          self.__forward_code__ = code
          self.__forward_evaluated__ = False
          self.__forward_value__ = None
  
      def _eval_type(self, globalns, localns):
          if not self.__forward_evaluated__ or localns is not globalns:
              if globalns is None and localns is None:
                  globalns = localns = {}
              elif globalns is None:
                  globalns = localns
              elif localns is None:
                  localns = globalns
              self.__forward_value__ = _type_check(
                  eval(self.__forward_code__, globalns, localns),
                  "Forward references must evaluate to types.")
              self.__forward_evaluated__ = True
          return self.__forward_value__
  
      def __instancecheck__(self, obj):
          raise TypeError("Forward references cannot be used with isinstance().")
  
      def __subclasscheck__(self, cls):
          raise TypeError("Forward references cannot be used with issubclass().")
  
      def __repr__(self):
          return '_ForwardRef(%r)' % (self.__forward_arg__,)
  
  
  class _TypeAlias(_TypingBase):
      """Internal helper class for defining generic variants of concrete types.
  
      Note that this is not a type; let's call it a pseudo-type.  It cannot
      be used in instance and subclass checks in parameterized form, i.e.
      ``isinstance(42, Match[str])`` raises ``TypeError`` instead of returning
      ``False``.
      """
  
      __slots__ = ('name', 'type_var', 'impl_type', 'type_checker')
  
  
      def __init__(self, name, type_var, impl_type, type_checker):
          """Initializer.
  
          Args:
              name: The name, e.g. 'Pattern'.
              type_var: The type parameter, e.g. AnyStr, or the
                  specific type, e.g. str.
              impl_type: The implementation type.
              type_checker: Function that takes an impl_type instance.
                  and returns a value that should be a type_var instance.
          """
          assert isinstance(name, basestring), repr(name)
          assert isinstance(impl_type, type), repr(impl_type)
          assert not isinstance(impl_type, TypingMeta), repr(impl_type)
          assert isinstance(type_var, (type, _TypingBase)), repr(type_var)
          self.name = name
          self.type_var = type_var
          self.impl_type = impl_type
          self.type_checker = type_checker
  
      def __repr__(self):
          return "%s[%s]" % (self.name, _type_repr(self.type_var))
  
      def __getitem__(self, parameter):
          if not isinstance(self.type_var, TypeVar):
              raise TypeError("%s cannot be further parameterized." % self)
          if self.type_var.__constraints__ and isinstance(parameter, type):
              if not issubclass(parameter, self.type_var.__constraints__):
                  raise TypeError("%s is not a valid substitution for %s." %
                                  (parameter, self.type_var))
          if isinstance(parameter, TypeVar) and parameter is not self.type_var:
              raise TypeError("%s cannot be re-parameterized." % self)
          return self.__class__(self.name, parameter,
                                self.impl_type, self.type_checker)
  
      def __instancecheck__(self, obj):
          if not isinstance(self.type_var, TypeVar):
              raise TypeError("Parameterized type aliases cannot be used "
                              "with isinstance().")
          return isinstance(obj, self.impl_type)
  
      def __subclasscheck__(self, cls):
          if not isinstance(self.type_var, TypeVar):
              raise TypeError("Parameterized type aliases cannot be used "
                              "with issubclass().")
          return issubclass(cls, self.impl_type)
  
  
  def _get_type_vars(types, tvars):
      for t in types:
          if isinstance(t, TypingMeta) or isinstance(t, _TypingBase):
              t._get_type_vars(tvars)
  
  
  def _type_vars(types):
      tvars = []
      _get_type_vars(types, tvars)
      return tuple(tvars)
  
  
  def _eval_type(t, globalns, localns):
      if isinstance(t, TypingMeta) or isinstance(t, _TypingBase):
          return t._eval_type(globalns, localns)
      return t
  
  
  def _type_check(arg, msg):
      """Check that the argument is a type, and return it (internal helper).
  
      As a special case, accept None and return type(None) instead.
      Also, _TypeAlias instances (e.g. Match, Pattern) are acceptable.
  
      The msg argument is a human-readable error message, e.g.
  
          "Union[arg, ...]: arg should be a type."
  
      We append the repr() of the actual value (truncated to 100 chars).
      """
      if arg is None:
          return type(None)
      if isinstance(arg, basestring):
          arg = _ForwardRef(arg)
      if (isinstance(arg, _TypingBase) and type(arg).__name__ == '_ClassVar' or
          not isinstance(arg, (type, _TypingBase)) and not callable(arg)):
          raise TypeError(msg + " Got %.100r." % (arg,))
      # Bare Union etc. are not valid as type arguments
      if (type(arg).__name__ in ('_Union', '_Optional')
          and not getattr(arg, '__origin__', None)
          or isinstance(arg, TypingMeta) and _gorg(arg) in (Generic, _Protocol)):
          raise TypeError("Plain %s is not valid as type argument" % arg)
      return arg
  
  
  def _type_repr(obj):
      """Return the repr() of an object, special-casing types (internal helper).
  
      If obj is a type, we return a shorter version than the default
      type.__repr__, based on the module and qualified name, which is
      typically enough to uniquely identify a type.  For everything
      else, we fall back on repr(obj).
      """
      if isinstance(obj, type) and not isinstance(obj, TypingMeta):
          if obj.__module__ == '__builtin__':
              return _qualname(obj)
          return '%s.%s' % (obj.__module__, _qualname(obj))
      if obj is Ellipsis:
          return('...')
      if isinstance(obj, types.FunctionType):
          return obj.__name__
      return repr(obj)
  
  
  class ClassVarMeta(TypingMeta):
      """Metaclass for _ClassVar"""
  
      def __new__(cls, name, bases, namespace):
          cls.assert_no_subclassing(bases)
          self = super(ClassVarMeta, cls).__new__(cls, name, bases, namespace)
          return self
  
  
  class _ClassVar(_FinalTypingBase):
      """Special type construct to mark class variables.
  
      An annotation wrapped in ClassVar indicates that a given
      attribute is intended to be used as a class variable and
      should not be set on instances of that class. Usage::
  
        class Starship:
            stats = {}  # type: ClassVar[Dict[str, int]] # class variable
            damage = 10 # type: int                      # instance variable
  
      ClassVar accepts only types and cannot be further subscribed.
  
      Note that ClassVar is not a class itself, and should not
      be used with isinstance() or issubclass().
      """
  
      __metaclass__ = ClassVarMeta
      __slots__ = ('__type__',)
  
      def __init__(self, tp=None, _root=False):
          self.__type__ = tp
  
      def __getitem__(self, item):
          cls = type(self)
          if self.__type__ is None:
              return cls(_type_check(item,
                         '{} accepts only types.'.format(cls.__name__[1:])),
                         _root=True)
          raise TypeError('{} cannot be further subscripted'
                          .format(cls.__name__[1:]))
  
      def _eval_type(self, globalns, localns):
          return type(self)(_eval_type(self.__type__, globalns, localns),
                            _root=True)
  
      def __repr__(self):
          r = super(_ClassVar, self).__repr__()
          if self.__type__ is not None:
              r += '[{}]'.format(_type_repr(self.__type__))
          return r
  
      def __hash__(self):
          return hash((type(self).__name__, self.__type__))
  
      def __eq__(self, other):
          if not isinstance(other, _ClassVar):
              return NotImplemented
          if self.__type__ is not None:
              return self.__type__ == other.__type__
          return self is other
  
  ClassVar = _ClassVar(_root=True)
  
  
  class AnyMeta(TypingMeta):
      """Metaclass for Any."""
  
      def __new__(cls, name, bases, namespace):
          cls.assert_no_subclassing(bases)
          self = super(AnyMeta, cls).__new__(cls, name, bases, namespace)
          return self
  
  
  class _Any(_FinalTypingBase):
      """Special type indicating an unconstrained type.
  
      - Any is compatible with every type.
      - Any assumed to have all methods.
      - All values assumed to be instances of Any.
  
      Note that all the above statements are true from the point of view of
      static type checkers. At runtime, Any should not be used with instance
      or class checks.
      """
      __metaclass__ = AnyMeta
      __slots__ = ()
  
      def __instancecheck__(self, obj):
          raise TypeError("Any cannot be used with isinstance().")
  
      def __subclasscheck__(self, cls):
          raise TypeError("Any cannot be used with issubclass().")
  
  
  Any = _Any(_root=True)
  
  
  class TypeVarMeta(TypingMeta):
      def __new__(cls, name, bases, namespace):
          cls.assert_no_subclassing(bases)
          return super(TypeVarMeta, cls).__new__(cls, name, bases, namespace)
  
  
  class TypeVar(_TypingBase):
      """Type variable.
  
      Usage::
  
        T = TypeVar('T')  # Can be anything
        A = TypeVar('A', str, bytes)  # Must be str or bytes
  
      Type variables exist primarily for the benefit of static type
      checkers.  They serve as the parameters for generic types as well
      as for generic function definitions.  See class Generic for more
      information on generic types.  Generic functions work as follows:
  
        def repeat(x: T, n: int) -> List[T]:
            '''Return a list containing n references to x.'''
            return [x]*n
  
        def longest(x: A, y: A) -> A:
            '''Return the longest of two strings.'''
            return x if len(x) >= len(y) else y
  
      The latter example's signature is essentially the overloading
      of (str, str) -> str and (bytes, bytes) -> bytes.  Also note
      that if the arguments are instances of some subclass of str,
      the return type is still plain str.
  
      At runtime, isinstance(x, T) and issubclass(C, T) will raise TypeError.
  
      Type variables defined with covariant=True or contravariant=True
      can be used do declare covariant or contravariant generic types.
      See PEP 484 for more details. By default generic types are invariant
      in all type variables.
  
      Type variables can be introspected. e.g.:
  
        T.__name__ == 'T'
        T.__constraints__ == ()
        T.__covariant__ == False
        T.__contravariant__ = False
        A.__constraints__ == (str, bytes)
      """
  
      __metaclass__ = TypeVarMeta
      __slots__ = ('__name__', '__bound__', '__constraints__',
                   '__covariant__', '__contravariant__')
  
      def __init__(self, name, *constraints, **kwargs):
          super(TypeVar, self).__init__(name, *constraints, **kwargs)
          bound = kwargs.get('bound', None)
          covariant = kwargs.get('covariant', False)
          contravariant = kwargs.get('contravariant', False)
          self.__name__ = name
          if covariant and contravariant:
              raise ValueError("Bivariant types are not supported.")
          self.__covariant__ = bool(covariant)
          self.__contravariant__ = bool(contravariant)
          if constraints and bound is not None:
              raise TypeError("Constraints cannot be combined with bound=...")
          if constraints and len(constraints) == 1:
              raise TypeError("A single constraint is not allowed")
          msg = "TypeVar(name, constraint, ...): constraints must be types."
          self.__constraints__ = tuple(_type_check(t, msg) for t in constraints)
          if bound:
              self.__bound__ = _type_check(bound, "Bound must be a type.")
          else:
              self.__bound__ = None
  
      def _get_type_vars(self, tvars):
          if self not in tvars:
              tvars.append(self)
  
      def __repr__(self):
          if self.__covariant__:
              prefix = '+'
          elif self.__contravariant__:
              prefix = '-'
          else:
              prefix = '~'
          return prefix + self.__name__
  
      def __instancecheck__(self, instance):
          raise TypeError("Type variables cannot be used with isinstance().")
  
      def __subclasscheck__(self, cls):
          raise TypeError("Type variables cannot be used with issubclass().")
  
  
  # Some unconstrained type variables.  These are used by the container types.
  # (These are not for export.)
  T = TypeVar('T')  # Any type.
  KT = TypeVar('KT')  # Key type.
  VT = TypeVar('VT')  # Value type.
  T_co = TypeVar('T_co', covariant=True)  # Any type covariant containers.
  V_co = TypeVar('V_co', covariant=True)  # Any type covariant containers.
  VT_co = TypeVar('VT_co', covariant=True)  # Value type covariant containers.
  T_contra = TypeVar('T_contra', contravariant=True)  # Ditto contravariant.
  
  # A useful type variable with constraints.  This represents string types.
  # (This one *is* for export!)
  AnyStr = TypeVar('AnyStr', bytes, unicode)
  
  
  def _replace_arg(arg, tvars, args):
      """An internal helper function: replace arg if it is a type variable
      found in tvars with corresponding substitution from args or
      with corresponding substitution sub-tree if arg is a generic type.
      """
  
      if tvars is None:
          tvars = []
      if hasattr(arg, '_subs_tree'):
          return arg._subs_tree(tvars, args)
      if isinstance(arg, TypeVar):
          for i, tvar in enumerate(tvars):
              if arg == tvar:
                  return args[i]
      return arg
  
  
  def _subs_tree(cls, tvars=None, args=None):
      """An internal helper function: calculate substitution tree
      for generic cls after replacing its type parameters with
      substitutions in tvars -> args (if any).
      Repeat the same following __origin__'s.
  
      Return a list of arguments with all possible substitutions
      performed. Arguments that are generic classes themselves are represented
      as tuples (so that no new classes are created by this function).
      For example: _subs_tree(List[Tuple[int, T]][str]) == [(Tuple, int, str)]
      """
  
      if cls.__origin__ is None:
          return cls
      # Make of chain of origins (i.e. cls -> cls.__origin__)
      current = cls.__origin__
      orig_chain = []
      while current.__origin__ is not None:
          orig_chain.append(current)
          current = current.__origin__
      # Replace type variables in __args__ if asked ...
      tree_args = []
      for arg in cls.__args__:
          tree_args.append(_replace_arg(arg, tvars, args))
      # ... then continue replacing down the origin chain.
      for ocls in orig_chain:
          new_tree_args = []
          for i, arg in enumerate(ocls.__args__):
              new_tree_args.append(_replace_arg(arg, ocls.__parameters__, tree_args))
          tree_args = new_tree_args
      return tree_args
  
  
  def _remove_dups_flatten(parameters):
      """An internal helper for Union creation and substitution: flatten Union's
      among parameters, then remove duplicates and strict subclasses.
      """
  
      # Flatten out Union[Union[...], ...].
      params = []
      for p in parameters:
          if isinstance(p, _Union) and p.__origin__ is Union:
              params.extend(p.__args__)
          elif isinstance(p, tuple) and len(p) > 0 and p[0] is Union:
              params.extend(p[1:])
          else:
              params.append(p)
      # Weed out strict duplicates, preserving the first of each occurrence.
      all_params = set(params)
      if len(all_params) < len(params):
          new_params = []
          for t in params:
              if t in all_params:
                  new_params.append(t)
                  all_params.remove(t)
          params = new_params
          assert not all_params, all_params
      # Weed out subclasses.
      # E.g. Union[int, Employee, Manager] == Union[int, Employee].
      # If object is present it will be sole survivor among proper classes.
      # Never discard type variables.
      # (In particular, Union[str, AnyStr] != AnyStr.)
      all_params = set(params)
      for t1 in params:
          if not isinstance(t1, type):
              continue
          if any(isinstance(t2, type) and issubclass(t1, t2)
                 for t2 in all_params - {t1}
                 if not (isinstance(t2, GenericMeta) and
                         t2.__origin__ is not None)):
              all_params.remove(t1)
      return tuple(t for t in params if t in all_params)
  
  
  def _check_generic(cls, parameters):
      # Check correct count for parameters of a generic cls (internal helper).
      if not cls.__parameters__:
          raise TypeError("%s is not a generic class" % repr(cls))
      alen = len(parameters)
      elen = len(cls.__parameters__)
      if alen != elen:
          raise TypeError("Too %s parameters for %s; actual %s, expected %s" %
                          ("many" if alen > elen else "few", repr(cls), alen, elen))
  
  
  _cleanups = []
  
  
  def _tp_cache(func):
      maxsize = 128
      cache = {}
      _cleanups.append(cache.clear)
  
      @functools.wraps(func)
      def inner(*args):
          key = args
          try:
              return cache[key]
          except TypeError:
              # Assume it's an unhashable argument.
              return func(*args)
          except KeyError:
              value = func(*args)
              if len(cache) >= maxsize:
                  # If the cache grows too much, just start over.
                  cache.clear()
              cache[key] = value
              return value
  
      return inner
  
  
  class UnionMeta(TypingMeta):
      """Metaclass for Union."""
  
      def __new__(cls, name, bases, namespace):
          cls.assert_no_subclassing(bases)
          return super(UnionMeta, cls).__new__(cls, name, bases, namespace)
  
  
  class _Union(_FinalTypingBase):
      """Union type; Union[X, Y] means either X or Y.
  
      To define a union, use e.g. Union[int, str].  Details:
  
      - The arguments must be types and there must be at least one.
  
      - None as an argument is a special case and is replaced by
        type(None).
  
      - Unions of unions are flattened, e.g.::
  
          Union[Union[int, str], float] == Union[int, str, float]
  
      - Unions of a single argument vanish, e.g.::
  
          Union[int] == int  # The constructor actually returns int
  
      - Redundant arguments are skipped, e.g.::
  
          Union[int, str, int] == Union[int, str]
  
      - When comparing unions, the argument order is ignored, e.g.::
  
          Union[int, str] == Union[str, int]
  
      - When two arguments have a subclass relationship, the least
        derived argument is kept, e.g.::
  
          class Employee: pass
          class Manager(Employee): pass
          Union[int, Employee, Manager] == Union[int, Employee]
          Union[Manager, int, Employee] == Union[int, Employee]
          Union[Employee, Manager] == Employee
  
      - Similar for object::
  
          Union[int, object] == object
  
      - You cannot subclass or instantiate a union.
  
      - You can use Optional[X] as a shorthand for Union[X, None].
      """
  
      __metaclass__ = UnionMeta
      __slots__ = ('__parameters__', '__args__', '__origin__', '__tree_hash__')
  
      def __new__(cls, parameters=None, origin=None, *args, **kwds):
          self = super(_Union, cls).__new__(cls, parameters, origin, *args, **kwds)
          if origin is None:
              self.__parameters__ = None
              self.__args__ = None
              self.__origin__ = None
              self.__tree_hash__ = hash(frozenset(('Union',)))
              return self
          if not isinstance(parameters, tuple):
              raise TypeError("Expected parameters=<tuple>")
          if origin is Union:
              parameters = _remove_dups_flatten(parameters)
              # It's not a union if there's only one type left.
              if len(parameters) == 1:
                  return parameters[0]
          self.__parameters__ = _type_vars(parameters)
          self.__args__ = parameters
          self.__origin__ = origin
          # Pre-calculate the __hash__ on instantiation.
          # This improves speed for complex substitutions.
          subs_tree = self._subs_tree()
          if isinstance(subs_tree, tuple):
              self.__tree_hash__ = hash(frozenset(subs_tree))
          else:
              self.__tree_hash__ = hash(subs_tree)
          return self
  
      def _eval_type(self, globalns, localns):
          if self.__args__ is None:
              return self
          ev_args = tuple(_eval_type(t, globalns, localns) for t in self.__args__)
          ev_origin = _eval_type(self.__origin__, globalns, localns)
          if ev_args == self.__args__ and ev_origin == self.__origin__:
              # Everything is already evaluated.
              return self
          return self.__class__(ev_args, ev_origin, _root=True)
  
      def _get_type_vars(self, tvars):
          if self.__origin__ and self.__parameters__:
              _get_type_vars(self.__parameters__, tvars)
  
      def __repr__(self):
          if self.__origin__ is None:
              return super(_Union, self).__repr__()
          tree = self._subs_tree()
          if not isinstance(tree, tuple):
              return repr(tree)
          return tree[0]._tree_repr(tree)
  
      def _tree_repr(self, tree):
          arg_list = []
          for arg in tree[1:]:
              if not isinstance(arg, tuple):
                  arg_list.append(_type_repr(arg))
              else:
                  arg_list.append(arg[0]._tree_repr(arg))
          return super(_Union, self).__repr__() + '[%s]' % ', '.join(arg_list)
  
      @_tp_cache
      def __getitem__(self, parameters):
          if parameters == ():
              raise TypeError("Cannot take a Union of no types.")
          if not isinstance(parameters, tuple):
              parameters = (parameters,)
          if self.__origin__ is None:
              msg = "Union[arg, ...]: each arg must be a type."
          else:
              msg = "Parameters to generic types must be types."
          parameters = tuple(_type_check(p, msg) for p in parameters)
          if self is not Union:
              _check_generic(self, parameters)
          return self.__class__(parameters, origin=self, _root=True)
  
      def _subs_tree(self, tvars=None, args=None):
          if self is Union:
              return Union  # Nothing to substitute
          tree_args = _subs_tree(self, tvars, args)
          tree_args = _remove_dups_flatten(tree_args)
          if len(tree_args) == 1:
              return tree_args[0]  # Union of a single type is that type
          return (Union,) + tree_args
  
      def __eq__(self, other):
          if not isinstance(other, _Union):
              return self._subs_tree() == other
          return self.__tree_hash__ == other.__tree_hash__
  
      def __hash__(self):
          return self.__tree_hash__
  
      def __instancecheck__(self, obj):
          raise TypeError("Unions cannot be used with isinstance().")
  
      def __subclasscheck__(self, cls):
          raise TypeError("Unions cannot be used with issubclass().")
  
  
  Union = _Union(_root=True)
  
  
  class OptionalMeta(TypingMeta):
      """Metaclass for Optional."""
  
      def __new__(cls, name, bases, namespace):
          cls.assert_no_subclassing(bases)
          return super(OptionalMeta, cls).__new__(cls, name, bases, namespace)
  
  
  class _Optional(_FinalTypingBase):
      """Optional type.
  
      Optional[X] is equivalent to Union[X, None].
      """
  
      __metaclass__ = OptionalMeta
      __slots__ = ()
  
      @_tp_cache
      def __getitem__(self, arg):
          arg = _type_check(arg, "Optional[t] requires a single type.")
          return Union[arg, type(None)]
  
  
  Optional = _Optional(_root=True)
  
  
  def _gorg(a):
      """Return the farthest origin of a generic class (internal helper)."""
      assert isinstance(a, GenericMeta)
      while a.__origin__ is not None:
          a = a.__origin__
      return a
  
  
  def _geqv(a, b):
      """Return whether two generic classes are equivalent (internal helper).
  
      The intention is to consider generic class X and any of its
      parameterized forms (X[T], X[int], etc.) as equivalent.
  
      However, X is not equivalent to a subclass of X.
  
      The relation is reflexive, symmetric and transitive.
      """
      assert isinstance(a, GenericMeta) and isinstance(b, GenericMeta)
      # Reduce each to its origin.
      return _gorg(a) is _gorg(b)
  
  
  def _next_in_mro(cls):
      """Helper for Generic.__new__.
  
      Returns the class after the last occurrence of Generic or
      Generic[...] in cls.__mro__.
      """
      next_in_mro = object
      # Look for the last occurrence of Generic or Generic[...].
      for i, c in enumerate(cls.__mro__[:-1]):
          if isinstance(c, GenericMeta) and _gorg(c) is Generic:
              next_in_mro = cls.__mro__[i+1]
      return next_in_mro
  
  
  def _valid_for_check(cls):
      """An internal helper to prohibit isinstance([1], List[str]) etc."""
      if cls is Generic:
          raise TypeError("Class %r cannot be used with class "
                          "or instance checks" % cls)
      if (cls.__origin__ is not None and
          sys._getframe(3).f_globals['__name__'] not in ['abc', 'functools']):
          raise TypeError("Parameterized generics cannot be used with class "
                          "or instance checks")
  
  
  def _make_subclasshook(cls):
      """Construct a __subclasshook__ callable that incorporates
      the associated __extra__ class in subclass checks performed
      against cls.
      """
      if isinstance(cls.__extra__, abc.ABCMeta):
          # The logic mirrors that of ABCMeta.__subclasscheck__.
          # Registered classes need not be checked here because
          # cls and its extra share the same _abc_registry.
          def __extrahook__(cls, subclass):
              _valid_for_check(cls)
              res = cls.__extra__.__subclasshook__(subclass)
              if res is not NotImplemented:
                  return res
              if cls.__extra__ in getattr(subclass, '__mro__', ()):
                  return True
              for scls in cls.__extra__.__subclasses__():
                  if isinstance(scls, GenericMeta):
                      continue
                  if issubclass(subclass, scls):
                      return True
              return NotImplemented
      else:
          # For non-ABC extras we'll just call issubclass().
          def __extrahook__(cls, subclass):
              _valid_for_check(cls)
              if cls.__extra__ and issubclass(subclass, cls.__extra__):
                  return True
              return NotImplemented
      return classmethod(__extrahook__)
  
  
  class GenericMeta(TypingMeta, abc.ABCMeta):
      """Metaclass for generic types."""
  
      def __new__(cls, name, bases, namespace,
                  tvars=None, args=None, origin=None, extra=None, orig_bases=None):
          if tvars is not None:
              # Called from __getitem__() below.
              assert origin is not None
              assert all(isinstance(t, TypeVar) for t in tvars), tvars
          else:
              # Called from class statement.
              assert tvars is None, tvars
              assert args is None, args
              assert origin is None, origin
  
              # Get the full set of tvars from the bases.
              tvars = _type_vars(bases)
              # Look for Generic[T1, ..., Tn].
              # If found, tvars must be a subset of it.
              # If not found, tvars is it.
              # Also check for and reject plain Generic,
              # and reject multiple Generic[...].
              gvars = None
              for base in bases:
                  if base is Generic:
                      raise TypeError("Cannot inherit from plain Generic")
                  if (isinstance(base, GenericMeta) and
                          base.__origin__ is Generic):
                      if gvars is not None:
                          raise TypeError(
                              "Cannot inherit from Generic[...] multiple types.")
                      gvars = base.__parameters__
              if gvars is None:
                  gvars = tvars
              else:
                  tvarset = set(tvars)
                  gvarset = set(gvars)
                  if not tvarset <= gvarset:
                      raise TypeError(
                          "Some type variables (%s) "
                          "are not listed in Generic[%s]" %
                          (", ".join(str(t) for t in tvars if t not in gvarset),
                           ", ".join(str(g) for g in gvars)))
                  tvars = gvars
  
          initial_bases = bases
          if extra is None:
              extra = namespace.get('__extra__')
          if extra is not None and type(extra) is abc.ABCMeta and extra not in bases:
              bases = (extra,) + bases
          bases = tuple(_gorg(b) if isinstance(b, GenericMeta) else b for b in bases)
  
          # remove bare Generic from bases if there are other generic bases
          if any(isinstance(b, GenericMeta) and b is not Generic for b in bases):
              bases = tuple(b for b in bases if b is not Generic)
          self = super(GenericMeta, cls).__new__(cls, name, bases, namespace)
  
          self.__parameters__ = tvars
          # Be prepared that GenericMeta will be subclassed by TupleMeta
          # and CallableMeta, those two allow ..., (), or [] in __args___.
          self.__args__ = tuple(Ellipsis if a is _TypingEllipsis else
                                () if a is _TypingEmpty else
                                a for a in args) if args else None
          self.__origin__ = origin
          self.__extra__ = extra
          # Speed hack (https://github.com/python/typing/issues/196).
          self.__next_in_mro__ = _next_in_mro(self)
          # Preserve base classes on subclassing (__bases__ are type erased now).
          if orig_bases is None:
              self.__orig_bases__ = initial_bases
  
          # This allows unparameterized generic collections to be used
          # with issubclass() and isinstance() in the same way as their
          # collections.abc counterparts (e.g., isinstance([], Iterable)).
          if ('__subclasshook__' not in namespace and extra  # allow overriding
              or hasattr(self.__subclasshook__, '__name__') and
              self.__subclasshook__.__name__ == '__extrahook__'):
              self.__subclasshook__ = _make_subclasshook(self)
  
          if origin and hasattr(origin, '__qualname__'):  # Fix for Python 3.2.
              self.__qualname__ = origin.__qualname__
          self.__tree_hash__ = hash(self._subs_tree()) if origin else hash((self.__name__,))
          return self
  
      def __init__(self, *args, **kwargs):
          super(GenericMeta, self).__init__(*args, **kwargs)
          if isinstance(self.__extra__, abc.ABCMeta):
              self._abc_registry = self.__extra__._abc_registry
  
      def _get_type_vars(self, tvars):
          if self.__origin__ and self.__parameters__:
              _get_type_vars(self.__parameters__, tvars)
  
      def _eval_type(self, globalns, localns):
          ev_origin = (self.__origin__._eval_type(globalns, localns)
                       if self.__origin__ else None)
          ev_args = tuple(_eval_type(a, globalns, localns) for a
                          in self.__args__) if self.__args__ else None
          if ev_origin == self.__origin__ and ev_args == self.__args__:
              return self
          return self.__class__(self.__name__,
                                self.__bases__,
                                dict(self.__dict__),
                                tvars=_type_vars(ev_args) if ev_args else None,
                                args=ev_args,
                                origin=ev_origin,
                                extra=self.__extra__,
                                orig_bases=self.__orig_bases__)
  
      def __repr__(self):
          if self.__origin__ is None:
              return super(GenericMeta, self).__repr__()
          return self._tree_repr(self._subs_tree())
  
      def _tree_repr(self, tree):
          arg_list = []
          for arg in tree[1:]:
              if arg == ():
                  arg_list.append('()')
              elif not isinstance(arg, tuple):
                  arg_list.append(_type_repr(arg))
              else:
                  arg_list.append(arg[0]._tree_repr(arg))
          return super(GenericMeta, self).__repr__() + '[%s]' % ', '.join(arg_list)
  
      def _subs_tree(self, tvars=None, args=None):
          if self.__origin__ is None:
              return self
          tree_args = _subs_tree(self, tvars, args)
          return (_gorg(self),) + tuple(tree_args)
  
      def __eq__(self, other):
          if not isinstance(other, GenericMeta):
              return NotImplemented
          if self.__origin__ is None or other.__origin__ is None:
              return self is other
          return self.__tree_hash__ == other.__tree_hash__
  
      def __hash__(self):
          return self.__tree_hash__
  
      @_tp_cache
      def __getitem__(self, params):
          if not isinstance(params, tuple):
              params = (params,)
          if not params and not _gorg(self) is Tuple:
              raise TypeError(
                  "Parameter list to %s[...] cannot be empty" % _qualname(self))
          msg = "Parameters to generic types must be types."
          params = tuple(_type_check(p, msg) for p in params)
          if self is Generic:
              # Generic can only be subscripted with unique type variables.
              if not all(isinstance(p, TypeVar) for p in params):
                  raise TypeError(
                      "Parameters to Generic[...] must all be type variables")
              if len(set(params)) != len(params):
                  raise TypeError(
                      "Parameters to Generic[...] must all be unique")
              tvars = params
              args = params
          elif self in (Tuple, Callable):
              tvars = _type_vars(params)
              args = params
          elif self is _Protocol:
              # _Protocol is internal, don't check anything.
              tvars = params
              args = params
          elif self.__origin__ in (Generic, _Protocol):
              # Can't subscript Generic[...] or _Protocol[...].
              raise TypeError("Cannot subscript already-subscripted %s" %
                              repr(self))
          else:
              # Subscripting a regular Generic subclass.
              _check_generic(self, params)
              tvars = _type_vars(params)
              args = params
          return self.__class__(self.__name__,
                                self.__bases__,
                                dict(self.__dict__),
                                tvars=tvars,
                                args=args,
                                origin=self,
                                extra=self.__extra__,
                                orig_bases=self.__orig_bases__)
  
      def __instancecheck__(self, instance):
          # Since we extend ABC.__subclasscheck__ and
          # ABC.__instancecheck__ inlines the cache checking done by the
          # latter, we must extend __instancecheck__ too. For simplicity
          # we just skip the cache check -- instance checks for generic
          # classes are supposed to be rare anyways.
          if not isinstance(instance, type):
              return issubclass(instance.__class__, self)
          return False
  
      def __copy__(self):
          return self.__class__(self.__name__, self.__bases__, dict(self.__dict__),
                                self.__parameters__, self.__args__, self.__origin__,
                                self.__extra__, self.__orig_bases__)
  
  
  # Prevent checks for Generic to crash when defining Generic.
  Generic = None
  
  
  def _generic_new(base_cls, cls, *args, **kwds):
      # Assure type is erased on instantiation,
      # but attempt to store it in __orig_class__
      if cls.__origin__ is None:
          return base_cls.__new__(cls)
      else:
          origin = _gorg(cls)
          obj = base_cls.__new__(origin)
          try:
              obj.__orig_class__ = cls
          except AttributeError:
              pass
          obj.__init__(*args, **kwds)
          return obj
  
  
  class Generic(object):
      """Abstract base class for generic types.
  
      A generic type is typically declared by inheriting from
      this class parameterized with one or more type variables.
      For example, a generic mapping type might be defined as::
  
        class Mapping(Generic[KT, VT]):
            def __getitem__(self, key: KT) -> VT:
                ...
            # Etc.
  
      This class can then be used as follows::
  
        def lookup_name(mapping: Mapping[KT, VT], key: KT, default: VT) -> VT:
            try:
                return mapping[key]
            except KeyError:
                return default
      """
  
      __metaclass__ = GenericMeta
      __slots__ = ()
  
      def __new__(cls, *args, **kwds):
          if _geqv(cls, Generic):
              raise TypeError("Type Generic cannot be instantiated; "
                              "it can be used only as a base class")
          return _generic_new(cls.__next_in_mro__, cls, *args, **kwds)
  
  
  class _TypingEmpty(object):
      """Internal placeholder for () or []. Used by TupleMeta and CallableMeta
      to allow empty list/tuple in specific places, without allowing them
      to sneak in where prohibited.
      """
  
  
  class _TypingEllipsis(object):
      """Internal placeholder for ... (ellipsis)."""
  
  
  class TupleMeta(GenericMeta):
      """Metaclass for Tuple (internal)."""
  
      @_tp_cache
      def __getitem__(self, parameters):
          if self.__origin__ is not None or not _geqv(self, Tuple):
              # Normal generic rules apply if this is not the first subscription
              # or a subscription of a subclass.
              return super(TupleMeta, self).__getitem__(parameters)
          if parameters == ():
              return super(TupleMeta, self).__getitem__((_TypingEmpty,))
          if not isinstance(parameters, tuple):
              parameters = (parameters,)
          if len(parameters) == 2 and parameters[1] is Ellipsis:
              msg = "Tuple[t, ...]: t must be a type."
              p = _type_check(parameters[0], msg)
              return super(TupleMeta, self).__getitem__((p, _TypingEllipsis))
          msg = "Tuple[t0, t1, ...]: each t must be a type."
          parameters = tuple(_type_check(p, msg) for p in parameters)
          return super(TupleMeta, self).__getitem__(parameters)
  
      def __instancecheck__(self, obj):
          if self.__args__ == None:
              return isinstance(obj, tuple)
          raise TypeError("Parameterized Tuple cannot be used "
                          "with isinstance().")
  
      def __subclasscheck__(self, cls):
          if self.__args__ == None:
              return issubclass(cls, tuple)
          raise TypeError("Parameterized Tuple cannot be used "
                          "with issubclass().")
  
  
  class Tuple(tuple):
      """Tuple type; Tuple[X, Y] is the cross-product type of X and Y.
  
      Example: Tuple[T1, T2] is a tuple of two elements corresponding
      to type variables T1 and T2.  Tuple[int, float, str] is a tuple
      of an int, a float and a string.
  
      To specify a variable-length tuple of homogeneous type, use Tuple[T, ...].
      """
  
      __metaclass__ = TupleMeta
      __extra__ = tuple
      __slots__ = ()
  
      def __new__(cls, *args, **kwds):
          if _geqv(cls, Tuple):
              raise TypeError("Type Tuple cannot be instantiated; "
                              "use tuple() instead")
          return _generic_new(tuple, cls, *args, **kwds)
  
  
  class CallableMeta(GenericMeta):
      """ Metaclass for Callable."""
  
      def __repr__(self):
          if self.__origin__ is None:
              return super(CallableMeta, self).__repr__()
          return self._tree_repr(self._subs_tree())
  
      def _tree_repr(self, tree):
          if _gorg(self) is not Callable:
              return super(CallableMeta, self)._tree_repr(tree)
          # For actual Callable (not its subclass) we override
          # super(CallableMeta, self)._tree_repr() for nice formatting.
          arg_list = []
          for arg in tree[1:]:
              if not isinstance(arg, tuple):
                  arg_list.append(_type_repr(arg))
              else:
                  arg_list.append(arg[0]._tree_repr(arg))
          if arg_list[0] == '...':
              return repr(tree[0]) + '[..., %s]' % arg_list[1]
          return (repr(tree[0]) +
                  '[[%s], %s]' % (', '.join(arg_list[:-1]), arg_list[-1]))
  
      def __getitem__(self, parameters):
          """A thin wrapper around __getitem_inner__ to provide the latter
          with hashable arguments to improve speed.
          """
  
          if  self.__origin__ is not None or not _geqv(self, Callable):
              return super(CallableMeta, self).__getitem__(parameters)
          if not isinstance(parameters, tuple) or len(parameters) != 2:
              raise TypeError("Callable must be used as "
                              "Callable[[arg, ...], result].")
          args, result = parameters
          if args is Ellipsis:
              parameters = (Ellipsis, result)
          else:
              if not isinstance(args, list):
                  raise TypeError("Callable[args, result]: args must be a list."
                                  " Got %.100r." % (args,))
              parameters = (tuple(args), result)
          return self.__getitem_inner__(parameters)
  
      @_tp_cache
      def __getitem_inner__(self, parameters):
          args, result = parameters
          msg = "Callable[args, result]: result must be a type."
          result = _type_check(result, msg)
          if args is Ellipsis:
              return super(CallableMeta, self).__getitem__((_TypingEllipsis, result))
          msg = "Callable[[arg, ...], result]: each arg must be a type."
          args = tuple(_type_check(arg, msg) for arg in args)
          parameters = args + (result,)
          return super(CallableMeta, self).__getitem__(parameters)
  
  
  class Callable(object):
      """Callable type; Callable[[int], str] is a function of (int) -> str.
  
      The subscription syntax must always be used with exactly two
      values: the argument list and the return type.  The argument list
      must be a list of types or ellipsis; the return type must be a single type.
  
      There is no syntax to indicate optional or keyword arguments,
      such function types are rarely used as callback types.
      """
  
      __metaclass__ = CallableMeta
      __extra__ = collections_abc.Callable
      __slots__ = ()
  
      def __new__(cls, *args, **kwds):
          if _geqv(cls, Callable):
              raise TypeError("Type Callable cannot be instantiated; "
                              "use a non-abstract subclass instead")
          return _generic_new(cls.__next_in_mro__, cls, *args, **kwds)
  
  
  def cast(typ, val):
      """Cast a value to a type.
  
      This returns the value unchanged.  To the type checker this
      signals that the return value has the designated type, but at
      runtime we intentionally don't check anything (we want this
      to be as fast as possible).
      """
      return val
  
  
  def _get_defaults(func):
      """Internal helper to extract the default arguments, by name."""
      code = func.__code__
      pos_count = code.co_argcount
      arg_names = code.co_varnames
      arg_names = arg_names[:pos_count]
      defaults = func.__defaults__ or ()
      kwdefaults = func.__kwdefaults__
      res = dict(kwdefaults) if kwdefaults else {}
      pos_offset = pos_count - len(defaults)
      for name, value in zip(arg_names[pos_offset:], defaults):
          assert name not in res
          res[name] = value
      return res
  
  
  def get_type_hints(obj, globalns=None, localns=None):
      """In Python 2 this is not supported and always returns None."""
      return None
  
  
  def no_type_check(arg):
      """Decorator to indicate that annotations are not type hints.
  
      The argument must be a class or function; if it is a class, it
      applies recursively to all methods and classes defined in that class
      (but not to methods defined in its superclasses or subclasses).
  
      This mutates the function(s) or class(es) in place.
      """
      if isinstance(arg, type):
          arg_attrs = arg.__dict__.copy()
          for attr, val in arg.__dict__.items():
              if val in arg.__bases__:
                  arg_attrs.pop(attr)
          for obj in arg_attrs.values():
              if isinstance(obj, types.FunctionType):
                  obj.__no_type_check__ = True
              if isinstance(obj, type):
                  no_type_check(obj)
      try:
          arg.__no_type_check__ = True
      except TypeError: # built-in classes
          pass
      return arg
  
  
  def no_type_check_decorator(decorator):
      """Decorator to give another decorator the @no_type_check effect.
  
      This wraps the decorator with something that wraps the decorated
      function in @no_type_check.
      """
  
      @functools.wraps(decorator)
      def wrapped_decorator(*args, **kwds):
          func = decorator(*args, **kwds)
          func = no_type_check(func)
          return func
  
      return wrapped_decorator
  
  
  def _overload_dummy(*args, **kwds):
      """Helper for @overload to raise when called."""
      raise NotImplementedError(
          "You should not call an overloaded function. "
          "A series of @overload-decorated functions "
          "outside a stub module should always be followed "
          "by an implementation that is not @overload-ed.")
  
  
  def overload(func):
      """Decorator for overloaded functions/methods.
  
      In a stub file, place two or more stub definitions for the same
      function in a row, each decorated with @overload.  For example:
  
        @overload
        def utf8(value: None) -> None: ...
        @overload
        def utf8(value: bytes) -> bytes: ...
        @overload
        def utf8(value: str) -> bytes: ...
  
      In a non-stub file (i.e. a regular .py file), do the same but
      follow it with an implementation.  The implementation should *not*
      be decorated with @overload.  For example:
  
        @overload
        def utf8(value: None) -> None: ...
        @overload
        def utf8(value: bytes) -> bytes: ...
        @overload
        def utf8(value: str) -> bytes: ...
        def utf8(value):
            # implementation goes here
      """
      return _overload_dummy
  
  
  class _ProtocolMeta(GenericMeta):
      """Internal metaclass for _Protocol.
  
      This exists so _Protocol classes can be generic without deriving
      from Generic.
      """
  
      def __instancecheck__(self, obj):
          if _Protocol not in self.__bases__:
              return super(_ProtocolMeta, self).__instancecheck__(obj)
          raise TypeError("Protocols cannot be used with isinstance().")
  
      def __subclasscheck__(self, cls):
          if not self._is_protocol:
              # No structural checks since this isn't a protocol.
              return NotImplemented
  
          if self is _Protocol:
              # Every class is a subclass of the empty protocol.
              return True
  
          # Find all attributes defined in the protocol.
          attrs = self._get_protocol_attrs()
  
          for attr in attrs:
              if not any(attr in d.__dict__ for d in cls.__mro__):
                  return False
          return True
  
      def _get_protocol_attrs(self):
          # Get all Protocol base classes.
          protocol_bases = []
          for c in self.__mro__:
              if getattr(c, '_is_protocol', False) and c.__name__ != '_Protocol':
                  protocol_bases.append(c)
  
          # Get attributes included in protocol.
          attrs = set()
          for base in protocol_bases:
              for attr in base.__dict__.keys():
                  # Include attributes not defined in any non-protocol bases.
                  for c in self.__mro__:
                      if (c is not base and attr in c.__dict__ and
                              not getattr(c, '_is_protocol', False)):
                          break
                  else:
                      if (not attr.startswith('_abc_') and
                              attr != '__abstractmethods__' and
                              attr != '_is_protocol' and
                              attr != '__dict__' and
                              attr != '__args__' and
                              attr != '__slots__' and
                              attr != '_get_protocol_attrs' and
                              attr != '__next_in_mro__' and
                              attr != '__parameters__' and
                              attr != '__origin__' and
                              attr != '__orig_bases__' and
                              attr != '__extra__' and
                              attr != '__tree_hash__' and
                              attr != '__module__'):
                          attrs.add(attr)
  
          return attrs
  
  
  class _Protocol(object):
      """Internal base class for protocol classes.
  
      This implements a simple-minded structural issubclass check
      (similar but more general than the one-offs in collections.abc
      such as Hashable).
      """
  
      __metaclass__ = _ProtocolMeta
      __slots__ = ()
  
      _is_protocol = True
  
  
  # Various ABCs mimicking those in collections.abc.
  # A few are simply re-exported for completeness.
  
  Hashable = collections_abc.Hashable  # Not generic.
  
  
  class Iterable(Generic[T_co]):
      __slots__ = ()
      __extra__ = collections_abc.Iterable
  
  
  class Iterator(Iterable[T_co]):
      __slots__ = ()
      __extra__ = collections_abc.Iterator
  
  
  class SupportsInt(_Protocol):
      __slots__ = ()
  
      @abstractmethod
      def __int__(self):
          pass
  
  
  class SupportsFloat(_Protocol):
      __slots__ = ()
  
      @abstractmethod
      def __float__(self):
          pass
  
  
  class SupportsComplex(_Protocol):
      __slots__ = ()
  
      @abstractmethod
      def __complex__(self):
          pass
  
  
  class SupportsAbs(_Protocol[T_co]):
      __slots__ = ()
  
      @abstractmethod
      def __abs__(self):
          pass
  
  
  if hasattr(collections_abc, 'Reversible'):
      class Reversible(Iterable[T_co]):
          __slots__ = ()
          __extra__ = collections_abc.Reversible
  else:
      class Reversible(_Protocol[T_co]):
          __slots__ = ()
  
          @abstractmethod
          def __reversed__(self):
              pass
  
  
  Sized = collections_abc.Sized  # Not generic.
  
  
  class Container(Generic[T_co]):
      __slots__ = ()
      __extra__ = collections_abc.Container
  
  
  # Callable was defined earlier.
  
  
  class AbstractSet(Sized, Iterable[T_co], Container[T_co]):
      __slots__ = ()
      __extra__ = collections_abc.Set
  
  
  class MutableSet(AbstractSet[T]):
      __slots__ = ()
      __extra__ = collections_abc.MutableSet
  
  
  # NOTE: It is only covariant in the value type.
  class Mapping(Sized, Iterable[KT], Container[KT], Generic[KT, VT_co]):
      __slots__ = ()
      __extra__ = collections_abc.Mapping
  
  
  class MutableMapping(Mapping[KT, VT]):
      __slots__ = ()
      __extra__ = collections_abc.MutableMapping
  
  
  if hasattr(collections_abc, 'Reversible'):
      class Sequence(Sized, Reversible[T_co], Container[T_co]):
          __slots__ = ()
          __extra__ = collections_abc.Sequence
  else:
      class Sequence(Sized, Iterable[T_co], Container[T_co]):
          __slots__ = ()
          __extra__ = collections_abc.Sequence
  
  
  class MutableSequence(Sequence[T]):
      __slots__ = ()
      __extra__ = collections_abc.MutableSequence
  
  
  class ByteString(Sequence[int]):
      pass
  
  
  ByteString.register(str)
  ByteString.register(bytearray)
  
  
  class List(list, MutableSequence[T]):
      __slots__ = ()
      __extra__ = list
  
      def __new__(cls, *args, **kwds):
          if _geqv(cls, List):
              raise TypeError("Type List cannot be instantiated; "
                              "use list() instead")
          return _generic_new(list, cls, *args, **kwds)
  
  
  class Set(set, MutableSet[T]):
      __slots__ = ()
      __extra__ = set
  
      def __new__(cls, *args, **kwds):
          if _geqv(cls, Set):
              raise TypeError("Type Set cannot be instantiated; "
                              "use set() instead")
          return _generic_new(set, cls, *args, **kwds)
  
  
  class FrozenSet(frozenset, AbstractSet[T_co]):
      __slots__ = ()
      __extra__ = frozenset
  
      def __new__(cls, *args, **kwds):
          if _geqv(cls, FrozenSet):
              raise TypeError("Type FrozenSet cannot be instantiated; "
                              "use frozenset() instead")
          return _generic_new(frozenset, cls, *args, **kwds)
  
  
  class MappingView(Sized, Iterable[T_co]):
      __slots__ = ()
      __extra__ = collections_abc.MappingView
  
  
  class KeysView(MappingView[KT], AbstractSet[KT]):
      __slots__ = ()
      __extra__ = collections_abc.KeysView
  
  
  class ItemsView(MappingView[Tuple[KT, VT_co]],
                  AbstractSet[Tuple[KT, VT_co]],
                  Generic[KT, VT_co]):
      __slots__ = ()
      __extra__ = collections_abc.ItemsView
  
  
  class ValuesView(MappingView[VT_co]):
      __slots__ = ()
      __extra__ = collections_abc.ValuesView
  
  
  class Dict(dict, MutableMapping[KT, VT]):
      __slots__ = ()
      __extra__ = dict
  
      def __new__(cls, *args, **kwds):
          if _geqv(cls, Dict):
              raise TypeError("Type Dict cannot be instantiated; "
                              "use dict() instead")
          return _generic_new(dict, cls, *args, **kwds)
  
  
  class DefaultDict(collections.defaultdict, MutableMapping[KT, VT]):
      __slots__ = ()
      __extra__ = collections.defaultdict
  
      def __new__(cls, *args, **kwds):
          if _geqv(cls, DefaultDict):
              raise TypeError("Type DefaultDict cannot be instantiated; "
                              "use collections.defaultdict() instead")
          return _generic_new(collections.defaultdict, cls, *args, **kwds)
  
  
  # Determine what base class to use for Generator.
  if hasattr(collections_abc, 'Generator'):
      # Sufficiently recent versions of 3.5 have a Generator ABC.
      _G_base = collections_abc.Generator
  else:
      # Fall back on the exact type.
      _G_base = types.GeneratorType
  
  
  class Generator(Iterator[T_co], Generic[T_co, T_contra, V_co]):
      __slots__ = ()
      __extra__ = _G_base
  
      def __new__(cls, *args, **kwds):
          if _geqv(cls, Generator):
              raise TypeError("Type Generator cannot be instantiated; "
                              "create a subclass instead")
          return _generic_new(_G_base, cls, *args, **kwds)
  
  
  # Internal type variable used for Type[].
  CT_co = TypeVar('CT_co', covariant=True, bound=type)
  
  
  # This is not a real generic class.  Don't use outside annotations.
  class Type(Generic[CT_co]):
      """A special construct usable to annotate class objects.
  
      For example, suppose we have the following classes::
  
        class User: ...  # Abstract base for User classes
        class BasicUser(User): ...
        class ProUser(User): ...
        class TeamUser(User): ...
  
      And a function that takes a class argument that's a subclass of
      User and returns an instance of the corresponding class::
  
        U = TypeVar('U', bound=User)
        def new_user(user_class: Type[U]) -> U:
            user = user_class()
            # (Here we could write the user object to a database)
            return user
  
        joe = new_user(BasicUser)
  
      At this point the type checker knows that joe has type BasicUser.
      """
      __slots__ = ()
      __extra__ = type
  
  
  def NamedTuple(typename, fields):
      """Typed version of namedtuple.
  
      Usage::
  
          Employee = typing.NamedTuple('Employee', [('name', str), 'id', int)])
  
      This is equivalent to::
  
          Employee = collections.namedtuple('Employee', ['name', 'id'])
  
      The resulting class has one extra attribute: _field_types,
      giving a dict mapping field names to types.  (The field names
      are in the _fields attribute, which is part of the namedtuple
      API.)
      """
      fields = [(n, t) for n, t in fields]
      cls = collections.namedtuple(typename, [n for n, t in fields])
      cls._field_types = dict(fields)
      # Set the module to the caller's module (otherwise it'd be 'typing').
      try:
          cls.__module__ = sys._getframe(1).f_globals.get('__name__', '__main__')
      except (AttributeError, ValueError):
          pass
      return cls
  
  
  def NewType(name, tp):
      """NewType creates simple unique types with almost zero
      runtime overhead. NewType(name, tp) is considered a subtype of tp
      by static type checkers. At runtime, NewType(name, tp) returns
      a dummy function that simply returns its argument. Usage::
  
          UserId = NewType('UserId', int)
  
          def name_by_id(user_id):
              # type: (UserId) -> str
              ...
  
          UserId('user')          # Fails type check
  
          name_by_id(42)          # Fails type check
          name_by_id(UserId(42))  # OK
  
          num = UserId(5) + 1     # type: int
      """
  
      def new_type(x):
          return x
  
      # Some versions of Python 2 complain because of making all strings unicode
      new_type.__name__ = str(name)
      new_type.__supertype__ = tp
      return new_type
  
  
  # Python-version-specific alias (Python 2: unicode; Python 3: str)
  Text = unicode
  
  
  # Constant that's True when type checking, but False here.
  TYPE_CHECKING = False
  
  
  class IO(Generic[AnyStr]):
      """Generic base class for TextIO and BinaryIO.
  
      This is an abstract, generic version of the return of open().
  
      NOTE: This does not distinguish between the different possible
      classes (text vs. binary, read vs. write vs. read/write,
      append-only, unbuffered).  The TextIO and BinaryIO subclasses
      below capture the distinctions between text vs. binary, which is
      pervasive in the interface; however we currently do not offer a
      way to track the other distinctions in the type system.
      """
  
      __slots__ = ()
  
      @abstractproperty
      def mode(self):
          pass
  
      @abstractproperty
      def name(self):
          pass
  
      @abstractmethod
      def close(self):
          pass
  
      @abstractmethod
      def closed(self):
          pass
  
      @abstractmethod
      def fileno(self):
          pass
  
      @abstractmethod
      def flush(self):
          pass
  
      @abstractmethod
      def isatty(self):
          pass
  
      @abstractmethod
      def read(self, n = -1):
          pass
  
      @abstractmethod
      def readable(self):
          pass
  
      @abstractmethod
      def readline(self, limit = -1):
          pass
  
      @abstractmethod
      def readlines(self, hint = -1):
          pass
  
      @abstractmethod
      def seek(self, offset, whence = 0):
          pass
  
      @abstractmethod
      def seekable(self):
          pass
  
      @abstractmethod
      def tell(self):
          pass
  
      @abstractmethod
      def truncate(self, size = None):
          pass
  
      @abstractmethod
      def writable(self):
          pass
  
      @abstractmethod
      def write(self, s):
          pass
  
      @abstractmethod
      def writelines(self, lines):
          pass
  
      @abstractmethod
      def __enter__(self):
          pass
  
      @abstractmethod
      def __exit__(self, type, value, traceback):
          pass
  
  
  class BinaryIO(IO[bytes]):
      """Typed version of the return of open() in binary mode."""
  
      __slots__ = ()
  
      @abstractmethod
      def write(self, s):
          pass
  
      @abstractmethod
      def __enter__(self):
          pass
  
  
  class TextIO(IO[unicode]):
      """Typed version of the return of open() in text mode."""
  
      __slots__ = ()
  
      @abstractproperty
      def buffer(self):
          pass
  
      @abstractproperty
      def encoding(self):
          pass
  
      @abstractproperty
      def errors(self):
          pass
  
      @abstractproperty
      def line_buffering(self):
          pass
  
      @abstractproperty
      def newlines(self):
          pass
  
      @abstractmethod
      def __enter__(self):
          pass
  
  
  class io(object):
      """Wrapper namespace for IO generic classes."""
  
      __all__ = ['IO', 'TextIO', 'BinaryIO']
      IO = IO
      TextIO = TextIO
      BinaryIO = BinaryIO
  
  io.__name__ = __name__ + b'.io'
  sys.modules[io.__name__] = io
  
  
  Pattern = _TypeAlias('Pattern', AnyStr, type(stdlib_re.compile('')),
                       lambda p: p.pattern)
  Match = _TypeAlias('Match', AnyStr, type(stdlib_re.match('', '')),
                     lambda m: m.re.pattern)
  
  
  class re(object):
      """Wrapper namespace for re type aliases."""
  
      __all__ = ['Pattern', 'Match']
      Pattern = Pattern
      Match = Match
  
  re.__name__ = __name__ + b'.re'
  sys.modules[re.__name__] = re
  