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)

def printBorad():
    for i in range(8):
        s = ['.'] * 8
        s[row[i]] = 'Q'
        print(''.join(s))

def putQueen(i, j):
    row[i] = j
    col[j] = True
    left[i+j] = True
    right[7+i-j] = True

def removeQueen(i, j):
    row[i] = False
    col[j] = False
    left[i+j] = False
    right[7+i-j] = False
    


def recursive(i):
    if i == 8:
        printBorad()
        return
    
    if row[i] is not False:
        putQueen(i, row[i])
        recursive(i + 1)
    else:
        for j in range(8):        
            if col[j] or left[i+j] or right[7+i-j]:
                continue
            putQueen(i, j)
            recursive(i + 1)
            removeQueen(i, j)


if __name__ == "__main__":
    row = [False for i in range(8)]
    col = [False for i in range(8)]
    left = [False for i in range(15)]
    right = [False for i in range(15)]
    n = int(input())
    for _ in range(n):
        i, j = map(int, input().split())
        putQueen(i, j)
    
    recursive(0)