






def 							lowerCamelCase__ (       __lowerCamelCase     :	int = 10**12						):
  __UpperCAmelCase				:      Optional[Any]	 =    1
  __UpperCAmelCase				:      List[str]	 =    0

  __UpperCAmelCase				:      Any	 =    1
  __UpperCAmelCase				:      int	 =    1

  while numerator <= 2 * min_total - 1:
    prev_numerator += 2 * numerator
    numerator += 2 * prev_numerator

    prev_denominator += 2 * denominator
    denominator += 2 * prev_denominator

  return (denominator + 1) // 2


if __name__ == "__main__":
       print(f"""{solution() = }""")





"""simple docstring"""




import numpy as np

def 						A							(  snake_case__     ):




			'''simple docstring'''


			return (2 / (1 + np.exp(-2 * vector     ))) - 1


if __name__ == "__main__":
						import doctest

						doctest.testmod()


