



'''simple docstring'''


def  UpperCAmelCase_       (		lowercase__       ):


     '''simple docstring'''







     if not isinstance(lowercase__       ,	lowercase__       ):
          raise ValueError("Input series is not valid, valid series - [2, 4, 6]"       )
     if len(lowercase__       ) == 0:
          raise ValueError("Input list must be a non empty list"       )
     if len(lowercase__       ) == 1:
          return True
     a_       		=series[1] - series[0]
     for index in range(len(lowercase__       ) - 1       ):
          if series[index + 1] - series[index] != common_diff:
               return False
     return True






def  UpperCAmelCase_       (		lowercase__       ):


     '''simple docstring'''







     if not isinstance(lowercase__       ,	lowercase__       ):
          raise ValueError("Input series is not valid, valid series - [2, 4, 6]"       )
     if len(lowercase__       ) == 0:
          raise ValueError("Input list must be a non empty list"       )
     a_       		=0
     for val in series:
          answer += val
     return answer / len(lowercase__       )


if __name__ == "__main__":
 import doctest

 doctest.testmod()







'''simple docstring'''


from __future__ import annotations

lowercase							       =			[]






def  UpperCAmelCase_       (		lowercase__       ,	lowercase__       ,	lowercase__       ):


     '''simple docstring'''







     for i in range(len(lowercase__       )       ):
          if board[row][i] == 1:
               return False
     for i in range(len(lowercase__       )       ):
          if board[i][column] == 1:
               return False
     for i, j in zip(range(lowercase__       ,	-1       ,	-1       )       ,	range(lowercase__       ,	-1       ,	-1       )       ):
          if board[i][j] == 1:
               return False
     for i, j in zip(range(lowercase__       ,	-1       ,	-1       )       ,	range(lowercase__       ,	len(lowercase__       )       )       ):
          if board[i][j] == 1:
               return False
     return True






def  UpperCAmelCase_       (		lowercase__       ,	lowercase__       ):


     '''simple docstring'''







     if row >= len(lowercase__       ):
          solution.append(lowercase__       )
          printboard(lowercase__       )
          print()
          return True
     for i in range(len(lowercase__       )       ):
          if is_safe(lowercase__       ,	lowercase__       ,	lowercase__       ):
               a_       		=1
               solve(lowercase__       ,	row + 1       )
               a_       		=0
     return False






def  UpperCAmelCase_       (		lowercase__       ):


     '''simple docstring'''







     for i in range(len(lowercase__       )       ):
          for j in range(len(lowercase__       )       ):
               if board[i][j] == 1:
                    print("Q"       ,	end=" "       )
               else:
                    print("."       ,	end=" "       )
          print()


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

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


