"""simple docstring"""







from __future__ import annotations
def 						__UpperCAmelCase       (					UpperCAmelCase_					:       Optional[int]    ,							UpperCAmelCase_					:       Optional[int]    ,							UpperCAmelCase_					:       Dict    ,							UpperCAmelCase_					:       Any    ,							UpperCAmelCase_					:       Any    ,							)							->    Union[str, Any]:

	'''simple docstring'''





	__snake_case    :							Tuple   	=				len(_snake_case						)

	# If row is equal to the size of the board it means there are a queen in each row in
	# the current board (possible_board)
	if row == n:
		# We convert the variable possible_board that looks like this: [1, 3, 0, 2] to
		# this: ['. Q . . ', '. . . Q ', 'Q . . . ', '. . Q . ']
		boards.append(['. ' * i + 'Q ' + '. ' * (n - 1 - i) for i in possible_board]						)
		return

	# We iterate each column in the row to find all possible results in each row
	for col in range(_snake_case						):
		# We apply that we learned previously. First we check that in the current board
		# (possible_board) there are not other same value because if there is it means
		# that there are a collision in vertical. Then we apply the two formulas we
		# learned before:
		#
		# 45º: y - x = b or 45: row - col = b
		# 135º: y + x = b or row + col = b.
		#
		# And we verify if the results of this two formulas not exist in their variables
		# respectively.  (diagonal_right_collisions, diagonal_left_collisions)
		#
		# If any or these are True it means there is a collision so we continue to the
		# next value in the for loop.
		if (
		    col in possible_board
		    or row - col in diagonal_right_collisions
		    or row + col in diagonal_left_collisions
		):
			continue

		# If it is False we call dfs function again and we update the inputs
		depth_first_search(
		    [*possible_board, col]    ,							[*diagonal_right_collisions, row - col]    ,							[*diagonal_left_collisions, row + col]    ,							_snake_case    ,							_snake_case    ,							)
def 						__UpperCAmelCase       (					UpperCAmelCase_					:       Optional[int]						)							->    str:

	'''simple docstring'''





	__snake_case    :							Tuple   	=				[]
	depth_first_search([]    ,							[]    ,							[]    ,							_snake_case    ,							_snake_case						)

	# Print all the boards
	for board in boards:
		for column in board:
			print(_snake_case						)
		print(''						)

	print(len(_snake_case						)    ,							'solutions were found.'						)


if __name__ == "__main__":
	import doctest

	doctest.testmod()
	n_queens_solution(4)
"""simple docstring"""







import numpy as np
def 						__UpperCAmelCase       (					UpperCAmelCase_					:       np.array						)							->    np.array:

	'''simple docstring'''





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


if __name__ == "__main__":
	import doctest

	doctest.testmod()





