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 functools import lru_cache
cc = [["." for i in range(8)] for j in range(8)]

def check(cc,a,b):
    ss = list(zip(*cc))
    if 'Q' in cc[a]: return False
    if 'Q' in ss[b]: return False
    d = []
    for i in range(8):
        for j in range(8):
            try:
                if j + (a - i) == b: 
                    d.append(cc[i][j])
                if j -  (a - i) == b:
                    d.append(cc[i][j])
                if j + (i - a) == b: 
                    d.append(cc[i][j])
                if j -  (i - a) == b:
                    d.append(cc[i][j])
            except IndexError: continue
    if 'Q' in d: return False
    return True

def chess(s,queen):
    if queen == 8:
        return s
    for i in range(8):
        for j in range(8):
            if check(s,i,j):
                sol = s
                sol[i][j] = 'Q'
                if chess(sol,queen+1) != [[]]:
                    return sol
                else: sol[i][j] = "."
    return [[]]


k = int(input())
for i in range(k):
    a, b = input().split()
    cc[int(a)][int(b)] = 'Q'
ans = chess(cc,k)
print('\n'.join(list(map(lambda x: ''.join(x),ans))) )