






"""simple docstring"""


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



def 	lowercase_				(			__UpperCAmelCase				)						->    str:

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

      lowerCAmelCase__      :			Optional[int]   =	precision
      lowerCAmelCase__      :			Tuple   =	ceil(precision / 14				)
      lowerCAmelCase__      :			Dict   =	42_6880 * Decimal(1_0005				).sqrt()
      lowerCAmelCase__      :			List[str]   =	1
      lowerCAmelCase__      :			Tuple   =	1359_1409
      lowerCAmelCase__      :			Optional[Any]   =	Decimal(__UpperCAmelCase				)
      for k in range(1    ,		__UpperCAmelCase				):
            lowerCAmelCase__      :			Dict   =	factorial(6 * k				) // (factorial(3 * k				) * factorial(__UpperCAmelCase				) ** 3)
            linear_term += 5_4514_0134
            exponential_term *= -26_2537_4126_4076_8000
            partial_sum += Decimal(multinomial_term * linear_term				) / exponential_term
      return str(constant_term / partial_sum				)[:-1]


if __name__ == "__main__":
  _A													=      5_0
  print(f"""The first {n} digits of pi is: {pi(n)}""")











"""simple docstring"""


# This is the module that test_patching.py uses to test patch_submodule()

import os  # noqa: this is just for tests
import os as renamed_os  # noqa: this is just for tests
from os import path  # noqa: this is just for tests
from os import path as renamed_path  # noqa: this is just for tests
from os.path import join  # noqa: this is just for tests
from os.path import join as renamed_join  # noqa: this is just for tests


_A													=      open  # noqa: we just need to have a builtin inside this module to test it properly





