





from __future__ import annotations





def   lowerCamelCase__       (       UpperCamelCase__     :    list[int]    ,      UpperCamelCase__     :    list[int]    ,      UpperCamelCase__     :    list[int]    ,      UpperCamelCase__     :    list[list[str]]    ,      UpperCamelCase__     :    int    ,      )     ->	None:



					'''simple docstring'''




					_snake_case													=			len(UpperCamelCase__  )

					# 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(UpperCamelCase__  ):
										# 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]    ,      UpperCamelCase__    ,      UpperCamelCase__    ,      )





def   lowerCamelCase__       (       UpperCamelCase__     :    int  )     ->	None:



					'''simple docstring'''




					_snake_case													=			[]
					depth_first_search([]    ,      []    ,      []    ,      UpperCamelCase__    ,      UpperCamelCase__  )

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

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


if __name__ == "__main__":
					import doctest

					doctest.testmod()
					n_queens_solution(4)










from collections.abc import Sequence





def   lowerCamelCase__       (       UpperCamelCase__     :    Sequence[float]    ,      UpperCamelCase__     :    bool = False  )     ->	float:



					'''simple docstring'''




					if not arr:
										return 0

					_snake_case													=			0 if allow_empty_subarrays else float('-inf'  )
					_snake_case													=			0.0
					for num in arr:
										_snake_case													=			max(0 if allow_empty_subarrays else num    ,      curr_sum + num  )
										_snake_case													=			max(UpperCamelCase__    ,      UpperCamelCase__  )

					return max_sum


if __name__ == "__main__":
					from doctest import testmod

					testmod()

					UpperCAmelCase_ 							=       [-2, 1, -3, 4, -1, 2, 1, -5, 4]
					print(F"{max_subarray_sum(nums) = }")



