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...
#include <iostream>
#include <cstdio>
#include <cstdlib>
#include <cmath>
#include <climits>
#include <algorithm>
#include <vector>
#include <utility>
#include <queue>
#include <stack>
#include <map>
#include <string>
using namespace std;

bool flg[8] = {};
int  pos[8] = {};

bool chk(int r)
{
    for (int i = 0; i < r; i++)
        if (pos[i] == pos[r] || abs(r - i) == abs(pos[i] - pos[r]))
            return false;
    return true;
}

bool back_track(int r)
{
    if (r == 8) return true;
    for (int c = 0; c < 8; c++) {
        if (flg[r] && c != pos[r])
            continue;
        pos[r] = c;
        if (chk(r) && back_track(r + 1)) return true;
    }
    return false;
}

int main()
{
    int k, r, c, x, y;
    cin >> k;
    while (k--) {
        cin >> r >> c;
        flg[r] = true;
        pos[r] = c;
    }
    back_track(0);
    for (r = 0; r < 8; r++) {
        for (c = 0; c < 8; c++) cout << (pos[r] == c ? 'Q' : '.');
        cout << endl;
    }
    return 0;
}