


from __future__ import annotations

import math







def        SCREAMING_SNAKE_CASE_						(			__A :			int  ,    __A :			int  ,    __A :			bool  ,    __A :			list[int]  ,    __A :			float				)	->		int:

       """simple docstring"""

       if depth < 0:
              raise ValueError('Depth cannot be less than 0'				)

       if len(__A				) == 0:
              raise ValueError('Scores cannot be empty'				)

       if depth == height:
              return scores[node_index]

       if is_max:
              return max(
                  minimax(depth + 1  ,    node_index * 2  ,    __A  ,    __A  ,    __A				)  ,    minimax(depth + 1  ,    node_index * 2 + 1  ,    __A  ,    __A  ,    __A				)  ,    )

       return min(
           minimax(depth + 1  ,    node_index * 2  ,    __A  ,    __A  ,    __A				)  ,    minimax(depth + 1  ,    node_index * 2 + 1  ,    __A  ,    __A  ,    __A				)  ,    )







def        SCREAMING_SNAKE_CASE_						(			)	->		None:

       """simple docstring"""

       a_					:		Dict							=  [90, 23, 6, 33, 21, 65, 1_23, 3_44_23]
       a_					:		int							=  math.log(len(__A				)  ,    2				)
       print('Optimal value : '  ,    end=''				)
       print(minimax(0  ,    0  ,    __A  ,    __A  ,    __A				)				)


if __name__ == "__main__":
   import doctest

   doctest.testmod()
   main()






from __future__ import annotations

UpperCAmelCase_      : Tuple  					=       []







def        SCREAMING_SNAKE_CASE_						(			__A :			list[list[int]]  ,    __A :			int  ,    __A :			int				)	->		bool:

       """simple docstring"""

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







def        SCREAMING_SNAKE_CASE_						(			__A :			list[list[int]]  ,    __A :			int				)	->		bool:

       """simple docstring"""

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







def        SCREAMING_SNAKE_CASE_						(			__A :			list[list[int]]				)	->		None:

       """simple docstring"""

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


# n=int(input("The no. of queens"))
UpperCAmelCase_      : List[str]  					=       8
UpperCAmelCase_      : str  					=       [[0 for i in range(n)] for j in range(n)]
solve(board, 0)
print('The total no. of solutions are :', len(solution))


