

from __future__ import annotations




def 					_lowercase     (				a_					,a_					,a_					,a_					,a_					,)				->	List[Any]:




					'''simple docstring'''







					__magic_name__							=    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 					_lowercase     (				a_				)				->	Any:




					'''simple docstring'''







					__magic_name__							=    []
					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)







import unittest

from transformers import is_torch_available
from transformers.testing_utils import require_sentencepiece, require_tokenizers, require_torch, slow, torch_device


if is_torch_available():
						from transformers import AutoModelForSeqaSeqLM, AutoTokenizer

@require_torch
@require_sentencepiece
@require_tokenizers
class 				__UpperCamelCase				(					unittest.TestCase			):







	@slow
	def 	_SCREAMING_SNAKE_CASE							(   self: Tuple      ):

						'''simple docstring'''





						__magic_name__							=    AutoModelForSeqaSeqLM.from_pretrained('google/mt5-small'  , return_dict=__UpperCamelCase      ).to(__UpperCamelCase      )
						__magic_name__							=    AutoTokenizer.from_pretrained('google/mt5-small'      )

						__magic_name__							=    tokenizer('Hello there'  , return_tensors='pt'      ).input_ids
						__magic_name__							=    tokenizer('Hi I am'  , return_tensors='pt'      ).input_ids

						__magic_name__							=    model(input_ids.to(__UpperCamelCase      )  , labels=labels.to(__UpperCamelCase      )      ).loss
						__magic_name__							=    -(labels.shape[-1] * loss.item())

						__magic_name__							=    -84.9127
						self.assertTrue(abs(mtf_score - EXPECTED_SCORE      ) < 1E-4      )




