


'''simple docstring'''



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



def      UpperCAmelCase__   (      UpperCAmelCase_       :							int				)	->						str:

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

     __lowerCamelCase  :      List[Any]														=						precision
     __lowerCamelCase  :      Tuple														=						ceil(precision / 14				)
     __lowerCamelCase  :      Union[str, Any]														=						42_68_80 * Decimal(1_00_05				).sqrt()
     __lowerCamelCase  :      List[str]														=						1
     __lowerCamelCase  :      Dict														=						13_59_14_09
     __lowerCamelCase  :      Union[str, Any]														=						Decimal(UpperCAmelCase_				)
     for k in range(1 ,       UpperCAmelCase_				):
          __lowerCamelCase  :      List[Any]														=						factorial(6 * k				) // (factorial(3 * k				) * factorial(UpperCAmelCase_				) ** 3)
          linear_term += 5_45_14_01_34
          exponential_term *= -26_25_37_41_26_40_76_80_00
          partial_sum += Decimal(multinomial_term * linear_term				) / exponential_term
     return str(constant_term / partial_sum				)[:-1]


if __name__ == "__main__":
      A__						:   Any				=    50
      print(f'''The first {n} digits of pi is: {pi(n)}''')














def 		lowercase__  (				_UpperCamelCase       ,							_UpperCamelCase) ->			bool:
      """simple docstring"""

      return numa ^ numa < 0


if __name__ == "__main__":
       import doctest

       doctest.testmod()



