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.

<image>


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

Constraints

* There is exactly one solution

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 '.'.

Example

Input

2
2 2
5 3


Output

......Q.
Q.......
..Q.....
.......Q
.....Q..
...Q....
.Q......
....Q...
from __future__ import division
import sys

def can_place(pos, idx, col):
    for i in range(8):
        if pos[i] is not None and pos[i] == col: return False
    for i in range(8):
        if pos[i] is not None and abs(pos[i] - col) == abs(i - idx): return False
    return True

def dfs(pos, depth):
    if 8 == depth:
        for idx, p in enumerate(pos):
            print('.' * p + 'Q' + '.' * (7 - p))
    else:
        if pos[depth] is None:
            for i in range(8):
                if can_place(pos, depth, i):
                    pos[depth] = i
                    dfs(pos, depth + 1)
                    pos[depth] = None
        else:
            return dfs(pos, depth + 1)

if __name__ == '__main__':
    n = int(sys.stdin.readline())
    pos = [None] * 8
    for _ in range(n):
        row, col = map(int, sys.stdin.readline().strip().split())
        pos[row] = col
    dfs(pos, 0)