
import numpy as np




def  __magic_name__ (   __lowerCAmelCase	:						np.array							)			->   np.array:
				return 1 / (1 + np.exp(-vector							))




def  __magic_name__ (   __lowerCAmelCase	:						np.array							)			->   np.array:
				return vector * sigmoid(1.702 * vector							)


if __name__ == "__main__":
					import doctest

					doctest.testmod()





from __future__ import annotations

from fractions import Fraction




def  __magic_name__ (   __lowerCAmelCase	:						int		,  __lowerCAmelCase	:						int							)			->   bool:
				return (
				    num != den and num % 10 == den // 10 and (num // 10) / (den % 10) == num / den
				)




def  __magic_name__ (   __lowerCAmelCase	:						int							)			->   list[str]:
				__lowerCamelCase    					=	[]
				__lowerCamelCase    					=	11
				__lowerCamelCase    					=	int('''1''' + '''0''' * digit_len							)
				for num in range(__lowerCAmelCase		,  __lowerCAmelCase							):
								while den <= 99:
												if (num != den) and (num % 10 == den // 10) and (den % 10 != 0):
																if is_digit_cancelling(__lowerCAmelCase		,  __lowerCAmelCase							):
																				solutions.append(f'''{num}/{den}'''							)
												den += 1
								num += 1
								__lowerCamelCase    					=	10
				return solutions




def  __magic_name__ (   __lowerCAmelCase	:						int = 2							)			->   int:
				__lowerCamelCase    					=	1.0
				for fraction in fraction_list(__lowerCAmelCase							):
								__lowerCamelCase    					=	Fraction(__lowerCAmelCase							)
								result *= frac.denominator / frac.numerator
				return int(__lowerCAmelCase							)


if __name__ == "__main__":
					print(solution())



