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...
//ALDS1_13_A
#include <iostream>
#include <vector>
using namespace std;

void printChess(int chess[]){
	for(int i=0;i<8;i++){
		for(int j=0;j<8;j++){
			if(j == chess[i])
				cout<<"Q";
			else
				cout<<".";
		}
		cout<<endl;
	}
}

bool isBlank(int chess[], int &r){
	for(int i=0;i<8;i++){
		if(chess[i] == 100){
			r = i;
			return true;
		}
	}
	return false;
}

bool setQ(int chess[], int r, int c){
	for(int i=0;i<8;i++){
		if(chess[i] == c)
			return false;
		if(i+chess[i] == r+c)
			return false;
		if(i-chess[i] == r-c)
			return false;
	}
	return true;
}

void solve(int chess[]){
	int r;
	if(isBlank(chess, r)){
		for(int c=0;c<8;c++){
			if(setQ(chess, r, c)){
				chess[r] = c;
				solve(chess);
				chess[r] = 100;
			}
		}
	}else{
		printChess(chess);
	}
}

int main(){
	int k, r, c, chess[8];
	
	for(int i=0;i<8;i++)
		chess[i] = 100;

	cin>>k;
	for(int i=0;i<k;i++){
		cin>>r>>c;
		chess[r] = c;
	}

	solve(chess);

	return 0;
}