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 <stdio.h>
#include <iostream>

using namespace std;

int T;
int w[10][10];

int test(int r, int c) {
	for(int i=0; i<8; i++) {
		if(i == c)continue;
		if(w[r][i])return 0;
	}
	for(int i=0; i<8; i++) {
		if(i == r)continue;
		if(w[i][c])return 0;
	}
	for(int i=-7; i<8; i++) {
		if(i == 0 || r+i < 0 || r+i>7 || c-i < 0 || c-i > 7)continue;
		//cout<<r+i<<" "<<c-i<<" "<<w[r+i][c-i]<<endl;
		if(w[r+i][c-i])return 0;
	}
	for(int i=-7; i<8; i++) {
		if(i == 0 || r+i < 0 || r+i>7 || c+i < 0 || c+i > 7)continue;
		//cout<<r+i<<" "<<c-i<<" "<<w[r+i][c-i]<<endl;
		if(w[r+i][c+i])return 0;
	}
	return 1;
}

int dfs(int r) {
	if(r == 8)return 1;
	for(int c=0; c < 8 ;c++) {
		//if(r==4)cout<<r<<" "<<c<<" "<<w[r][c]<<endl;
		if(test(r, c)) {
			int f=0;
			if(w[r][c])f=1;
			w[r][c] = 1;
			if(dfs(r+1))return 1;
			if(!f)w[r][c] = 0;
		}
	}
	return 0;
}

int main() {
	int k, r, c;
	scanf("%d", &k);
	for(int i=0; i<8; i++)
		for(int j=0; j<8; j++)w[i][j] = 0;
	for(int i=0; i<k; i++) {
		scanf("%d%d", &r, &c);
		w[r][c] = 1;
	}
	dfs(0);
	for(int i=0; i<8; i++) {
		for(int j=0; j<8; j++) {
			if(w[i][j] == 0)printf(".");
			if(w[i][j] == 1)printf("Q");
		}
		puts("");
	}
	return 0;
}

