






import numpy as np

def   __lowercase       (			snake_case			):







				"""simple docstring"""






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

def   __lowercase       (			snake_case			):







				"""simple docstring"""






				return vector * sigmoid(snake_case			)


if __name__ == "__main__":
					import doctest

					doctest.testmod()









from __future__ import annotations





def 	__a     (      A__			:  list[int | str]       ):
    create_state_space_tree(A__			,  []			,  0			,  [0 for i in range(len(A__       )       )]       )





def 	__a     (      A__			:  list[int | str]			,  A__			:  list[int | str]			,  A__			:  int			,  A__			:  list[int]			,  ):

    if index == len(A__       ):
        print(A__       )
        return

    for i in range(len(A__       )       ):
        if not index_used[i]:
            current_sequence.append(sequence[i]       )
            SCREAMING_SNAKE_CASE										=   True
            create_state_space_tree(A__			,  A__			,  index + 1			,  A__       )
            current_sequence.pop()
            SCREAMING_SNAKE_CASE										=   False
__A			:					list[int | str]						=			[3, 1, 2, 4]
generate_all_permutations(sequence)

__A			:					list[int | str]						=			["A", "B", "C"]





generate_all_permutations(sequence_a)