output_description: Print a $8 \times 8$ chess board by strings where a square with a queen is
  represented by 'Q' and an empty square is represented by '.'.
input_description: In the first line, an integer $k$ is given. In the following $k$ lines, each
  square where a queen is already placed is given by two integers $r$ and $c$.
  $r$ and $c$ respectively denotes the row number and the column number. The
  row/column numbers start with 0.
attempt: from itertools import permutations
  
  k = int(input())
  
  points = {tuple(map(int, input().split())) for _ in range(k)}
  
  for perm in permutations(range(8), 8):
      test = {(i, perm[i]) for i in range(8)}
      if test & points == points:
          flg = 0
          for x, y in test:
              diag = (
                  {(x - i, y - i) for i in range(1, min(x, y) + 1)}
                  | {(x + i, y + i) for i in range(1, min(7 - x, 7 - y) + 1)}
                  | {(x - i, y + i) for i in range(1, min(x, 7 - y) + 1)}
                  | {(x - i, y + i) for i in range(1, min(7 - x, y) + 1)}
              )
              if diag & test == set():
                  flg += 1
          if flg == 8:
              ans = test
              break
  
  for i in range(8):
      col = ""
      for j in range(8):
          if (i, j) in ans:
              col += "Q"
          else:
              col += "."
      print(col)
  
problem_description: 8 Queens Problem
  
  The goal of 8 Queens Problem is to put eight queens on a chess-board such that
  none of them threatens any of others. A queen threatens the squares in the
  same row, in the same column, or on the same diagonals as shown in the
  following figure.
  
  ![](https://judgeapi.u-aizu.ac.jp/resources/images/IMAGE2_ALDS1_13_A_8queens)  
  
  For a given chess board where $k$ queens are already placed, find the solution
  of the 8 queens problem.
samples: [{"input": "2\n    2 2\n    5 3", "output": "......Q.\n    Q.......\n    ..Q.....\n    .......Q\n    .....Q..\n    ...Q....\n    .Q......\n    ....Q..."}]