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>
using namespace std;
int k, C[10], C2[10], ans, is;
char map[10][10];
void dfs(int cur){
	if(cur == 8){
		for(int i = 0; i < 8; i++){
			for(int j = 0; j < 8; j++)cout<<map[i][j];
			cout<<"\n";
		}
		is = 1;
	}
	else for(int i = 0; i < 8; i++){
		bool ok = true;
		for(int j = 0; j < cur; j++)
			if(C[j]==i || cur-i==j-C[j] || cur+i==j+C[j])
				{ok = false; break;}
		if(C2[cur]!=0 && C2[cur] != i)ok = false;
		if(ok && !is){
			map[cur][i] = 'Q';
			C[cur] = i;
			dfs(cur+1);
			map[cur][i] = '.';
		}
	}
}
int main(){
	for(int i = 0; i < 8; i++)
		for(int j = 0; j < 8; j++)
			map[i][j] = '.';
	cin>>k;
	for(int i = 0; i < k; i++){
		int a, b;
		cin>>a>>b;
		C2[a] = b;
		map[a][b] = 'Q';
	}
	dfs(0);
	return 0;
}