






'''simple docstring'''
from __future__ import annotations





def 	_a(					UpperCamelCase__			:  List[str],		UpperCamelCase__			:  Union[str, Any],		UpperCamelCase__			:  int,		UpperCamelCase__			:  List[str]							):  # noqa: E741




      '''simple docstring'''






      while r - l > 1:
            SCREAMING_SNAKE_CASE__       :			List[str]													=(l + r) // 2
            if v[m] >= key:
                  SCREAMING_SNAKE_CASE__       :			Dict													=m
            else:
                  SCREAMING_SNAKE_CASE__       :			Any													=m  # noqa: E741
      return r





def 	_a(					UpperCamelCase__			:  list[int]							):




      '''simple docstring'''






      if len(UpperCamelCase__							) == 0:
            return 0

      SCREAMING_SNAKE_CASE__       :			List[Any]													=[0] * len(UpperCamelCase__							)
      SCREAMING_SNAKE_CASE__       :			Dict													=1

      SCREAMING_SNAKE_CASE__       :			Union[str, Any]													=v[0]

      for i in range(1,		len(UpperCamelCase__							)							):
            if v[i] < tail[0]:
                  SCREAMING_SNAKE_CASE__       :			List[Any]													=v[i]
            elif v[i] > tail[length - 1]:
                  SCREAMING_SNAKE_CASE__       :			int													=v[i]
                  length += 1
            else:
                  SCREAMING_SNAKE_CASE__       :			Union[str, Any]													=v[i]

      return length


if __name__ == "__main__":
  import doctest

  doctest.testmod()







'''simple docstring'''
from decimal import Decimal, getcontext
from math import ceil, factorial





def 	_a(					UpperCamelCase__			:  int							):




      '''simple docstring'''






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

      SCREAMING_SNAKE_CASE__       :			Optional[Any]													=precision
      SCREAMING_SNAKE_CASE__       :			int													=ceil(precision / 1_4							)
      SCREAMING_SNAKE_CASE__       :			int													=4_2_6_8_8_0 * Decimal(1_0_0_0_5							).sqrt()
      SCREAMING_SNAKE_CASE__       :			Tuple													=1
      SCREAMING_SNAKE_CASE__       :			Any													=1_3_5_9_1_4_0_9
      SCREAMING_SNAKE_CASE__       :			List[Any]													=Decimal(UpperCamelCase__							)
      for k in range(1,		UpperCamelCase__							):
            SCREAMING_SNAKE_CASE__       :			str													=factorial(6 * k							) // (factorial(3 * k							) * factorial(UpperCamelCase__							) ** 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__":
  a_					=	5_0
  print(F'''The first {n} digits of pi is: {pi(n)}''')