



from __future__ import annotations







def       lowerCAmelCase_     (lowerCAmelCase__:						Dict						,		lowerCAmelCase__:						Union[str, Any]						,		lowerCAmelCase__:						str						,		lowerCAmelCase__:						List[str]						,		lowerCAmelCase__:						Tuple						,		):





			"""simple docstring"""


			UpperCAmelCase_:						Any					=			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       lowerCAmelCase_     (lowerCAmelCase__:						Tuple   ):





			"""simple docstring"""


			UpperCAmelCase_:						list[list[str]]					=			[]
			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"""




def lowercase_  (   _snake_case   ,_snake_case						):

							if not (isinstance(_snake_case   ,_snake_case						) and isinstance(_snake_case   ,_snake_case						)):
														raise ValueError("""longest_common_substring() takes two strings for inputs"""						)

							SCREAMING_SNAKE_CASE__						:       Optional[Any]           =   len(_snake_case						)
							SCREAMING_SNAKE_CASE__						:       int           =   len(_snake_case						)

							SCREAMING_SNAKE_CASE__						:       Dict           =   [[0] * (texta_length + 1) for _ in range(texta_length + 1						)]
							SCREAMING_SNAKE_CASE__						:       List[Any]           =   0
							SCREAMING_SNAKE_CASE__						:       Union[str, Any]           =   0

							for i in range(1   ,texta_length + 1						):
														for j in range(1   ,texta_length + 1						):
																					if texta[i - 1] == texta[j - 1]:
																												SCREAMING_SNAKE_CASE__						:       int           =   1 + dp[i - 1][j - 1]
																												if dp[i][j] > ans_length:
																																			SCREAMING_SNAKE_CASE__						:       List[Any]           =   i
																																			SCREAMING_SNAKE_CASE__						:       List[str]           =   dp[i][j]

							return texta[ans_index - ans_length : ans_index]


if __name__ == "__main__":
					import doctest

					doctest.testmod()




