"""simple docstring"""






import dataclasses
import json
import sys
import types
from argparse import ArgumentDefaultsHelpFormatter, ArgumentParser, ArgumentTypeError
from copy import copy
from enum import Enum
from inspect import isclass
from pathlib import Path
from typing import Any, Callable, Dict, Iterable, List, Literal, NewType, Optional, Tuple, Union, get_type_hints

import yaml


__lowerCAmelCase    :       Tuple					     =NewType("""DataClass""", Any)
__lowerCAmelCase    :       Optional[int]					     =NewType("""DataClassType""", Any)


def 			UpperCAmelCase__       (				lowerCAmelCase__     :Tuple		) ->    int:
      '''simple docstring'''


      if isinstance(lowerCAmelCase__					,		lowerCAmelCase__		):
            return v
      if v.lower() in ("yes", "true", "t", "y", "1"):
            return True
      elif v.lower() in ("no", "false", "f", "n", "0"):
            return False
      else:
            raise ArgumentTypeError(
                f'Truthy value expected: got {v} but expected one of yes/no, true/false, t/f, y/n, 1/0 (case insensitive).'		)


def 			UpperCAmelCase__       (				lowerCAmelCase__     :list		) ->    Callable[[str], Any]:
      '''simple docstring'''


      lowercase														=	{str(lowerCAmelCase__		): choice for choice in choices}
      return lambda lowerCAmelCase__		: str_to_choice.get(lowerCAmelCase__					,		lowerCAmelCase__		)


def 			UpperCAmelCase__       (				*,
    lowerCAmelCase__     :Union[str, List[str]] = None					,		lowerCAmelCase__     :str = None					,		lowerCAmelCase__     :Any = dataclasses.MISSING					,		lowerCAmelCase__     :Callable[[], Any] = dataclasses.MISSING					,		lowerCAmelCase__     :dict = None					,		**lowerCAmelCase__     :Dict					,		) ->    dataclasses.Field:
      '''simple docstring'''


      if metadata is None:
            # Important, don't use as default param in function signature because dict is mutable and shared across function calls
            lowercase														=	{}
      if aliases is not None:
            lowercase														=	aliases
      if help is not None:
            lowercase														=	help

      return dataclasses.field(metadata=lowerCAmelCase__					,		default=lowerCAmelCase__					,		default_factory=lowerCAmelCase__					,		**lowerCAmelCase__		)






class  _A						(       lowerCAmelCase	):
      snake_case__			:   Iterable[DataClassType]

      def __init__(						self		,       __lowerCAmelCase		,       **__lowerCAmelCase						):







            """simple docstring"""



            if "formatter_class" not in kwargs:
                  lowercase														=	ArgumentDefaultsHelpFormatter
            super().__init__(**__lowerCAmelCase						)
            if dataclasses.is_dataclass(__lowerCAmelCase						):
                  lowercase														=	[dataclass_types]
            lowercase														=	list(__lowerCAmelCase						)
            for dtype in self.dataclass_types:
                  self._add_dataclass_arguments(__lowerCAmelCase						)

      @staticmethod
      def 				A__       (						__lowerCAmelCase		,       __lowerCAmelCase						):







            """simple docstring"""



            lowercase														=	f'--{field.name}'
            lowercase														=	field.metadata.copy()
            # field.metadata is not used at all by Data Classes,
            # it is provided as a third-party extension mechanism.
            if isinstance(field.type		,       __lowerCAmelCase						):
                  raise RuntimeError(
                      """Unresolved type detected, which should have been done with the help of """
                      """`typing.get_type_hints` method by default"""						)

            lowercase														=	kwargs.pop("""aliases"""		,       []						)
            if isinstance(__lowerCAmelCase		,       __lowerCAmelCase						):
                  lowercase														=	[aliases]

            lowercase														=	getattr(field.type		,       """__origin__"""		,       field.type						)
            if origin_type is Union or (hasattr(__lowerCAmelCase		,       """UnionType"""						) and isinstance(__lowerCAmelCase		,       types.UnionType						)):
                  if str not in field.type.__args__ and (
                      len(field.type.__args__						) != 2 or type(__lowerCAmelCase						) not in field.type.__args__
                  ):
                        raise ValueError(
                            """Only `Union[X, NoneType]` (i.e., `Optional[X]`) is allowed for `Union` because"""
                            """ the argument parser only supports one type per argument."""
                            f' Problem encountered in field \'{field.name}\'.'						)
                  if type(__lowerCAmelCase						) not in field.type.__args__:
                        # filter `str` in Union
                        lowercase														=	field.type.__args__[0] if field.type.__args__[1] == str else field.type.__args__[1]
                        lowercase														=	getattr(field.type		,       """__origin__"""		,       field.type						)
                  elif bool not in field.type.__args__:
                        # filter `NoneType` in Union (except for `Union[bool, NoneType]`)
                        lowercase														=	(
                            field.type.__args__[0] if isinstance(__lowerCAmelCase		,       field.type.__args__[1]						) else field.type.__args__[1]
                        )
                        lowercase														=	getattr(field.type		,       """__origin__"""		,       field.type						)

        # A variable to store kwargs for a boolean field, if needed
        # so that we can init a `no_*` complement argument (see below)
            lowercase														=	{}
            if origin_type is Literal or (isinstance(field.type		,       __lowerCAmelCase						) and issubclass(field.type		,       __lowerCAmelCase						)):
                  if origin_type is Literal:
                        lowercase														=	field.type.__args__
                  else:
                        lowercase														=	[x.value for x in field.type]

                  lowercase														=	make_choice_type_function(kwargs["""choices"""]						)

                  if field.default is not dataclasses.MISSING:
                        lowercase														=	field.default
                  else:
                        lowercase														=	True
            elif field.type is bool or field.type == Optional[bool]:
                  # Copy the currect kwargs to use to instantiate a `no_*` complement argument below.
                  # We do not initialize it here because the `no_*` alternative must be instantiated after the real argument
                  lowercase														=	copy(__lowerCAmelCase						)

                  # Hack because type=bool in argparse does not behave as we want.
                  lowercase														=	string_to_bool
                  if field.type is bool or (field.default is not None and field.default is not dataclasses.MISSING):
                        # Default value is False if we have no default when of type bool.
                        lowercase														=	False if field.default is dataclasses.MISSING else field.default
                        # This is the value that will get picked if we don't include --field_name in any way
                        lowercase														=	default
                        # This tells argparse we accept 0 or 1 value after --field_name
                        lowercase														=	"""?"""
                        # This is the value that will get picked if we do --field_name (without value)
                        lowercase														=	True
            elif isclass(__lowerCAmelCase						) and issubclass(__lowerCAmelCase		,       __lowerCAmelCase						):
                  lowercase														=	field.type.__args__[0]
                  lowercase														=	"""+"""
                  if field.default_factory is not dataclasses.MISSING:
                        lowercase														=	field.default_factory()
                  elif field.default is dataclasses.MISSING:
                        lowercase														=	True
            else:
                  lowercase														=	field.type
                  if field.default is not dataclasses.MISSING:
                        lowercase														=	field.default
                  elif field.default_factory is not dataclasses.MISSING:
                        lowercase														=	field.default_factory()
                  else:
                        lowercase														=	True
            parser.add_argument(__lowerCAmelCase		,       *__lowerCAmelCase		,       **__lowerCAmelCase						)

            # Add a complement `no_*` argument for a boolean field AFTER the initial field has already been added.
            # Order is important for arguments with the same destination!
            # We use a copy of earlier kwargs because the original kwargs have changed a lot before reaching down
            # here and we do not need those changes/additional keys.
            if field.default is True and (field.type is bool or field.type == Optional[bool]):
                  lowercase														=	False
                  parser.add_argument(f'--no_{field.name}'		,       action="""store_false"""		,       dest=field.name		,       **__lowerCAmelCase						)

      def 				A__       (						self		,       __lowerCAmelCase						):







            """simple docstring"""



            if hasattr(__lowerCAmelCase		,       """_argument_group_name"""						):
                  lowercase														=	self.add_argument_group(dtype._argument_group_name						)
            else:
                  lowercase														=	self

            try:
                  lowercase														=	get_type_hints(__lowerCAmelCase						)
            except NameError:
                  raise RuntimeError(
                      f'Type resolution failed for {dtype}. Try declaring the class in global scope or '
                      """removing line of `from __future__ import annotations` which opts in Postponed """
                      """Evaluation of Annotations (PEP 563)"""						)
            except TypeError as ex:
                  # Remove this block when we drop Python 3.9 support
                  if sys.version_info[:2] < (3, 10) and "unsupported operand type(s) for |" in str(__lowerCAmelCase						):
                        lowercase														=	""".""".join(map(__lowerCAmelCase		,       sys.version_info[:3]						)						)
                        raise RuntimeError(
                            f'Type resolution failed for {dtype} on Python {python_version}. Try removing '
                            """line of `from __future__ import annotations` which opts in union types as """
                            """`X | Y` (PEP 604) via Postponed Evaluation of Annotations (PEP 563). To """
                            """support Python versions that lower than 3.10, you need to use """
                            """`typing.Union[X, Y]` instead of `X | Y` and `typing.Optional[X]` instead of """
                            """`X | None`."""						) from ex
                  raise

            for field in dataclasses.fields(__lowerCAmelCase						):
                  if not field.init:
                        continue
                  lowercase														=	type_hints[field.name]
                  self._parse_dataclass_field(__lowerCAmelCase		,       __lowerCAmelCase						)

      def 				A__       (						self		,       __lowerCAmelCase=None		,       __lowerCAmelCase=False		,       __lowerCAmelCase=True		,       __lowerCAmelCase=None		,       __lowerCAmelCase=None		,       ):







            """simple docstring"""



            if args_file_flag or args_filename or (look_for_args_file and len(sys.argv						)):
                  lowercase														=	[]

                  if args_filename:
                        args_files.append(Path(__lowerCAmelCase						)						)
                  elif look_for_args_file and len(sys.argv						):
                        args_files.append(Path(sys.argv[0]						).with_suffix(""".args"""						)						)

                  # args files specified via command line flag should overwrite default args files so we add them last
                  if args_file_flag:
                        # Create special parser just to extract the args_file_flag values
                        lowercase														=	ArgumentParser()
                        args_file_parser.add_argument(__lowerCAmelCase		,       type=__lowerCAmelCase		,       action="""append"""						)

                        # Use only remaining args for further parsing (remove the args_file_flag)
                        lowercase							,							lowercase														=	args_file_parser.parse_known_args(args=__lowerCAmelCase						)
                        lowercase														=	vars(__lowerCAmelCase						).get(args_file_flag.lstrip("""-"""						)		,       __lowerCAmelCase						)

                        if cmd_args_file_paths:
                              args_files.extend([Path(__lowerCAmelCase						) for p in cmd_args_file_paths]						)

                  lowercase														=	[]
                  for args_file in args_files:
                        if args_file.exists():
                              file_args += args_file.read_text().split()

            # in case of duplicate arguments the last one has precedence
            # args specified via the command line should overwrite args from files, so we add them last
                  lowercase														=	file_args + args if args is not None else file_args + sys.argv[1:]
            lowercase							,							lowercase														=	self.parse_known_args(args=__lowerCAmelCase						)
            lowercase														=	[]
            for dtype in self.dataclass_types:
                  lowercase														=	{f.name for f in dataclasses.fields(__lowerCAmelCase						) if f.init}
                  lowercase														=	{k: v for k, v in vars(__lowerCAmelCase						).items() if k in keys}
                  for k in keys:
                        delattr(__lowerCAmelCase		,       __lowerCAmelCase						)
                  lowercase														=	dtype(**__lowerCAmelCase						)
                  outputs.append(__lowerCAmelCase						)
            if len(namespace.__dict__						) > 0:
                  # additional namespace.
                  outputs.append(__lowerCAmelCase						)
            if return_remaining_strings:
                  return (*outputs, remaining_args)
            else:
                  if remaining_args:
                        raise ValueError(f'Some specified arguments are not used by the HfArgumentParser: {remaining_args}'						)

                  return (*outputs,)

      def 				A__       (						self		,       __lowerCAmelCase		,       __lowerCAmelCase = False						):







            """simple docstring"""



            lowercase														=	set(args.keys()						)
            lowercase														=	[]
            for dtype in self.dataclass_types:
                  lowercase														=	{f.name for f in dataclasses.fields(__lowerCAmelCase						) if f.init}
                  lowercase														=	{k: v for k, v in args.items() if k in keys}
                  unused_keys.difference_update(inputs.keys()						)
                  lowercase														=	dtype(**__lowerCAmelCase						)
                  outputs.append(__lowerCAmelCase						)
            if not allow_extra_keys and unused_keys:
                  raise ValueError(f'Some keys are not used by the HfArgumentParser: {sorted(__lowerCAmelCase						)}'						)
            return tuple(__lowerCAmelCase						)

      def 				A__       (						self		,       __lowerCAmelCase		,       __lowerCAmelCase = False						):







            """simple docstring"""



            with open(Path(__lowerCAmelCase						)		,       encoding="""utf-8"""						) as open_json_file:
                  lowercase														=	json.loads(open_json_file.read()						)
            lowercase														=	self.parse_dict(__lowerCAmelCase		,       allow_extra_keys=__lowerCAmelCase						)
            return tuple(__lowerCAmelCase						)







      def 				A__       (						self		,       __lowerCAmelCase		,       __lowerCAmelCase = False						):







            """simple docstring"""



            lowercase														=	self.parse_dict(yaml.safe_load(Path(__lowerCAmelCase						).read_text()						)		,       allow_extra_keys=__lowerCAmelCase						)
            return tuple(__lowerCAmelCase						)




"""simple docstring"""






from decimal import Decimal, getcontext
from math import ceil, factorial


def 			UpperCAmelCase__       (				lowerCAmelCase__     :int		) ->    str:
      '''simple docstring'''


      if not isinstance(lowerCAmelCase__					,		lowerCAmelCase__		):
            raise TypeError("""Undefined for non-integers"""		)
      elif precision < 1:
            raise ValueError("""Undefined for non-natural numbers"""		)

      lowercase														=	precision
      lowercase														=	ceil(precision / 1_4		)
      lowercase														=	4_2_6_8_8_0 * Decimal(1_0_0_0_5		).sqrt()
      lowercase														=	1
      lowercase														=	1_3_5_9_1_4_0_9
      lowercase														=	Decimal(lowerCAmelCase__		)
      for k in range(1					,		lowerCAmelCase__		):
            lowercase														=	factorial(6 * k		) // (factorial(3 * k		) * factorial(lowerCAmelCase__		) ** 3)
            linear_term += 5_4_5_1_4_0_1_3_4
            exponential_term *= -2_6_2_5_3_7_4_1_2_6_4_0_7_6_8_0_0_0
            partial_sum += Decimal(multinomial_term * linear_term		) / exponential_term
      return str(constant_term / partial_sum		)[:-1]


if __name__ == "__main__":
       __lowerCAmelCase    :       List[Any]					     =5_0
       print(F"""The first {n} digits of pi is: {pi(n)}""")



