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;
#define MAX 20

int con;
int eq[MAX][MAX], hoge[4][MAX];

bool check(int y, int x){
	return hoge[0][y]||hoge[1][x]||hoge[2][y-x+8]||hoge[3][y+x]||eq[y][x];
}

void mark(int y, int x, bool tf){
	bool z = tf;
	eq[y][x] = z;
	hoge[0][y] = hoge[1][x] = hoge[2][y-x+8] = hoge[3][y+x] = z;
}

bool fuga(int z){
	while(hoge[0][z] == 1) z++;
	if(z>=8)return true;
	for(int i = 0; i < 8; i++){
		if(!check(z,i)){
			mark(z,i,true);
			if(fuga(z+1) == false) mark(z,i,false);
			else return true;
		}
	}
	return false;
}

int main(){
	int k, x, y;
	
	cin>>k;
	
	for(int i = 0; i < k; i++){
		cin>>y>>x;
		mark(y,x,true);
	}
	
	fuga(0);
	
	for(int i = 0; i < 8; i++){
		for(int j = 0; j < 8; j++){
			cout<<(eq[i][j]?"Q":".");
		}cout<<endl;
	}
	return 0;
}
