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<algorithm>
using namespace std;
const int MAXN=90;
char s[MAXN][MAXN];
int k,a[MAXN],b[MAXN],c[MAXN];
void print(){
	int an=0;
		for(int i=0;i<8;i++){
		for(int j=0;j<8;j++){
			if(j==c[i]) s[i][j]='Q';
			else s[i][j]='.';
		}
	}
	for(int i=1;i<=k;i++){
		if(s[a[i]][b[i]]=='Q'){
			an++;
		}
	}
	if(an==k) {
		for(int i=0;i<8;i++){
		for(int j=0;j<8;j++){
			cout<<s[i][j];
		}
		cout<<endl;
	}
	}
	else {
		for(int i=0;i<8;i++){
		for(int j=0;j<8;j++){
			s[i][j]='.';
		}
	}
	an=0;
	}
}
void search(int r){
    if(r==8){
    	print();
        return;
    }
    for(int i=0; i<8; ++i){
        c[r] = i;
        int ok = 1;
        for(int j=0; j<r; ++j)
            if(c[r]==c[j] || r-j==c[r]-c[j] || r-j==c[j]-c[r]){
                ok = 0;
                break;
            }
        if(ok) search(r+1);
    }
}
int main(){
	cin>>k;
	for(int i=0;i<8;i++){
		for(int j=0;j<8;j++){
			s[i][j]='.';
		}
	}
	for(int i=1;i<=k;i++){
		cin>>a[i]>>b[i];
		s[a[i]][b[i]]='Q'; 
	}
	search(0);
	return 0;
}