'''simple docstring'''





from __future__ import annotations


def     __lowerCAmelCase						(       a_       ,      a_       ,      a_       ,      a_       ,      a_       ,      )      ->	None:





     '''simple docstring'''





     SCREAMING_SNAKE_CASE					:			int    	=       len(SCREAMING_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(SCREAMING_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]       ,      SCREAMING_SNAKE_CASE_       ,      SCREAMING_SNAKE_CASE_       ,      )


def     __lowerCAmelCase						(       a_		)      ->	None:





     '''simple docstring'''





     SCREAMING_SNAKE_CASE					:			list[list[str]]    	=       []
     depth_first_search([]       ,      []       ,      []       ,      SCREAMING_SNAKE_CASE_       ,      SCREAMING_SNAKE_CASE_		)

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

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


if __name__ == "__main__":
 import doctest

 doctest.testmod()
 n_queens_solution(4)




'''simple docstring'''





import unittest

from transformers import is_torch_available
from transformers.testing_utils import require_torch


if is_torch_available():
 import torch

 from transformers.activations import gelu_new, gelu_python, get_activation






@require_torch
class 				UpperCAmelCase (       unittest.TestCase ):




    '''simple docstring'''







    def       _UpperCamelCase    (       self )							-> int:
         SCREAMING_SNAKE_CASE					:			str    	=       torch.tensor([-100, -1, -0.1, 0, 0.1, 1.0, 100] )
         SCREAMING_SNAKE_CASE					:			str    	=       get_activation('gelu' )
         self.assertTrue(torch.allclose(gelu_python(lowercase__ )    ,							torch_builtin(lowercase__ ) ) )
         self.assertFalse(torch.allclose(gelu_python(lowercase__ )    ,							gelu_new(lowercase__ ) ) )






    def       _UpperCamelCase    (       self )							-> Optional[Any]:
         SCREAMING_SNAKE_CASE					:			Union[str, Any]    	=       torch.tensor([-100, -1, -0.1, 0, 0.1, 1.0, 100] )
         SCREAMING_SNAKE_CASE					:			str    	=       get_activation('gelu' )
         SCREAMING_SNAKE_CASE					:			Dict    	=       get_activation('gelu_10' )

         SCREAMING_SNAKE_CASE					:			Optional[int]    	=       torch_builtin(lowercase__ )
         SCREAMING_SNAKE_CASE					:			str    	=       geluaa(lowercase__ )

         SCREAMING_SNAKE_CASE					:			List[Any]    	=       torch.where(y_gelu_aa < 1_0.0    ,							1    ,							0 )

         self.assertTrue(torch.max(lowercase__ ).item() == 1_0.0 )
         self.assertTrue(torch.allclose(y_gelu * clipped_mask    ,							y_gelu_aa * clipped_mask ) )






    def       _UpperCamelCase    (       self )							-> Optional[Any]:
         get_activation('gelu' )
         get_activation('gelu_10' )
         get_activation('gelu_fast' )
         get_activation('gelu_new' )
         get_activation('gelu_python' )
         get_activation('gelu_pytorch_tanh' )
         get_activation('linear' )
         get_activation('mish' )
         get_activation('quick_gelu' )
         get_activation('relu' )
         get_activation('sigmoid' )
         get_activation('silu' )
         get_activation('swish' )
         get_activation('tanh' )
         with self.assertRaises(lowercase__ ):
              get_activation('bogus' )
         with self.assertRaises(lowercase__ ):
              get_activation(lowercase__ )






    def       _UpperCamelCase    (       self )							-> int:
         SCREAMING_SNAKE_CASE					:			Optional[int]    	=       get_activation('gelu' )
         SCREAMING_SNAKE_CASE					:			str    	=       1
         SCREAMING_SNAKE_CASE					:			List[str]    	=       get_activation('gelu' )
         self.assertEqual(acta.a    ,							1 )
         with self.assertRaises(lowercase__ ):
              SCREAMING_SNAKE_CASE					:			Dict    	=       acta.a



