



'''simple docstring'''


import doctest
from collections import deque

import numpy as np







class 	UpperCAmelCase	:


 '''simple docstring'''




 def __init__(   self) ->      None:



      """simple docstring"""







      a_       		=[2, 1, 2, -1]
      a_       		=[1, 2, 3, 4]




 def       lowercase_  (   self) ->      list[float]:



      """simple docstring"""







      a_       		=len(self.first_signal)
      a_       		=len(self.second_signal)

      a_       		=max(lowerCAmelCase_							,  lowerCAmelCase_)

      # create a zero matrix of max_length x max_length
      a_       		=[[0] * max_length for i in range(lowerCAmelCase_)]

      # fills the smaller signal with zeros to make both signals of same length
      if length_first_signal < length_second_signal:
           self.first_signal += [0] * (max_length - length_first_signal)
      elif length_first_signal > length_second_signal:
           self.second_signal += [0] * (max_length - length_second_signal)
      for i in range(lowerCAmelCase_):
           a_       		=deque(self.second_signal)
           rotated_signal.rotate(lowerCAmelCase_)
           for j, item in enumerate(lowerCAmelCase_):
                matrix[i][j] += item

        # multiply the matrix with the first signal
      a_       		=np.matmul(np.transpose(lowerCAmelCase_)							,  np.transpose(self.first_signal))

      # rounding-off to two decimal places
      return [round(lowerCAmelCase_							,  2) for i in final_signal]


if __name__ == "__main__":
 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))


