

"""simple docstring"""



from __future__ import annotations

SCREAMING_SNAKE_CASE_    :		Dict							     =  []





def        _snake_case   (			UpperCAmelCase_     :    list[list[int]]    ,      UpperCAmelCase_     :    int    ,      UpperCAmelCase_     :    int	):
     for i in range(len(UpperCAmelCase__	)	):
          if board[row][i] == 1:
               return False
     for i in range(len(UpperCAmelCase__	)	):
          if board[i][column] == 1:
               return False
     for i, j in zip(range(UpperCAmelCase__    ,      -1    ,      -1	)    ,      range(UpperCAmelCase__    ,      -1    ,      -1	)	):
          if board[i][j] == 1:
               return False
     for i, j in zip(range(UpperCAmelCase__    ,      -1    ,      -1	)    ,      range(UpperCAmelCase__    ,      len(UpperCAmelCase__	)	)	):
          if board[i][j] == 1:
               return False
     return True





def        _snake_case   (			UpperCAmelCase_     :    list[list[int]]    ,      UpperCAmelCase_     :    int	):
     if row >= len(UpperCAmelCase__	):
          solution.append(UpperCAmelCase__	)
          printboard(UpperCAmelCase__	)
          print()
          return True
     for i in range(len(UpperCAmelCase__	)	):
          if is_safe(UpperCAmelCase__    ,      UpperCAmelCase__    ,      UpperCAmelCase__	):
               A__								=     1
               solve(UpperCAmelCase__    ,      row + 1	)
               A__								=     0
     return False





def        _snake_case   (			UpperCAmelCase_     :    list[list[int]]	):
     for i in range(len(UpperCAmelCase__	)	):
          for j in range(len(UpperCAmelCase__	)	):
               if board[i][j] == 1:
                    print("""Q"""    ,      end=""" """	)
               else:
                    print("""."""    ,      end=""" """	)
          print()


# n=int(input("The no. of queens"))
SCREAMING_SNAKE_CASE_    :		Dict							     =  8
SCREAMING_SNAKE_CASE_    :		Optional[int]							     =  [[0 for i in range(n)] for j in range(n)]
solve(board, 0)

print('The total no. of solutions are :', len(solution))







'''simple docstring'''




_lowercase						: str						=						tuple[float, float, float]
_lowercase						: List[Any]						=						tuple[float, float, float]




def 							lowerCamelCase	(      UpperCAmelCase__       :					Pointad      ,      UpperCAmelCase__       :					Pointad )			->      Vectorad:
							lowercase_					:			List[str]										=       end_pointa[0] - end_pointa[0]
							lowercase_					:			Union[str, Any]										=       end_pointa[1] - end_pointa[1]
							lowercase_					:			List[Any]										=       end_pointa[2] - end_pointa[2]
							return (x, y, z)




def 							lowerCamelCase	(      UpperCAmelCase__       :					Vectorad      ,      UpperCAmelCase__       :					Vectorad )			->      Vectorad:
							lowercase_					:			List[Any]										=       ab[1] * ac[2] - ab[2] * ac[1]  # *i
							lowercase_					:			Union[str, Any]										=       (ab[0] * ac[2] - ab[2] * ac[0]) * -1  # *j
							lowercase_					:			List[str]										=       ab[0] * ac[1] - ab[1] * ac[0]  # *k
							return (x, y, z)




def 							lowerCamelCase	(      UpperCAmelCase__       :					Vectorad      ,      UpperCAmelCase__       :					int )			->      bool:
							return tuple(round(UpperCAmelCase__      ,      UpperCAmelCase__ ) for x in vector ) == (0, 0, 0)




def 							lowerCamelCase	(      UpperCAmelCase__       :					Pointad      ,      UpperCAmelCase__       :					Pointad      ,      UpperCAmelCase__       :					Pointad      ,      UpperCAmelCase__       :					int = 10 )			->      bool:
							lowercase_					:			Dict										=       create_vector(UpperCAmelCase__      ,      UpperCAmelCase__ )
							lowercase_					:			Optional[int]										=       create_vector(UpperCAmelCase__      ,      UpperCAmelCase__ )
							return is_zero_vector(get_ad_vectors_cross(UpperCAmelCase__      ,      UpperCAmelCase__ )      ,      UpperCAmelCase__ )





