
import numpy as np




def 				__magic_name__				(     __lowerCAmelCase			:		Optional[int]							)    ->     str:
				__lowerCamelCase					      =			np.exp(__lowerCAmelCase							)

				# Add up the all the exponentials
				__lowerCamelCase					      =			np.sum(__lowerCAmelCase							)

				# Divide every exponent by the sum of all exponents
				__lowerCamelCase					      =			exponent_vector / sum_of_exponents

				return softmax_vector


if __name__ == "__main__":
					print(softmax((0,)))





def 				__magic_name__				(     __lowerCAmelCase			:		list	,						__lowerCAmelCase			:		int	,						__lowerCAmelCase			:		int	,						__lowerCAmelCase			:		int							)    ->     int:
				__lowerCamelCase					      =			int((lower_bound + upper_bound) // 2							)
				if array[r] == value:
								return r
				if lower_bound >= upper_bound:
								return -1
				if array[r] < value:
								return binary_search(__lowerCAmelCase	,						r + 1	,						__lowerCAmelCase	,						__lowerCAmelCase							)
				else:
								return binary_search(__lowerCAmelCase	,						__lowerCAmelCase	,						r - 1	,						__lowerCAmelCase							)




def 				__magic_name__				(     __lowerCAmelCase			:		int	,						__lowerCAmelCase			:		list							)    ->     list:
				__lowerCamelCase					      =			0
				if matrix[index][0] == value:
								return [index, 0]
				while index < len(__lowerCAmelCase							) and matrix[index][0] < value:
								__lowerCamelCase					      =			binary_search(matrix[index]	,						0	,						len(matrix[index]							) - 1	,						__lowerCAmelCase							)
								if r != -1:
												return [index, r]
								index += 1
				return [-1, -1]


if __name__ == "__main__":
					import doctest

					doctest.testmod()



