Problem:
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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.

For a given chess board where $k$ queens are already placed, find the solution of the 8 queens problem.

Input

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.

Output

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 '.'.

Constraints

There is exactly one solution

Sample Input 1

2
2 2
5 3

Sample Output 1

......Q.
Q.......
..Q.....
.......Q
.....Q..
...Q....
.Q......
....Q...

Solution in Python3 (judge verdict: Accepted)

from itertools import permutations

N = 8

M = [['.']*N for i in range(N)]
A0 = set()
B0 = set()

K = int(input())
R = set(range(N))
C = set(range(N))
for i in range(K):
    r, c = map(int, input().split())
    R.remove(r); C.remove(c)
    M[r][c] = 'Q'
    A0.add(r+c)
    B0.add(r-c)


for CS in permutations(C):
    A = A0.copy()
    B = B0.copy()
    ok = 1
    for r, c in zip(R, CS):
        if r+c in A:
            ok = 0
        A.add(r+c)
        if r-c in B:
            ok = 0
        B.add(r-c)
    if ok:
        for r, c in zip(R, CS):
            M[r][c] = 'Q'
        break
print(*("".join(m) for m in M), sep='\n')