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<cstring>
#include<algorithm>
using namespace std;
#define MAXN 10
bool hxh[10],hxs[10],hxx1[16],hxx2[16];
int n;
int q=0;
char map1[MAXN][MAXN];
void input(){
	cin>>n;
	int xx,yy;
	for(int i=0;i<n;++i){
	    cin>>xx>>yy;
	    map1[xx][yy]='Q';
	    hxh[xx]=1;
	    hxs[yy]=1;
	    hxx1[xx+yy]=1;
	    hxx2[7-xx+yy]=1;
	}
}
void syf(int x){
	if(hxh[x]==1) syf(x+1);
	if(x==8){
		for(int i=0;i<8;++i){
			for(int j=0;j<8;++j){
				if(map1[i][j]==0) cout<<".";
				else cout<<map1[i][j];
			}
			cout<<endl;
		}
		q=1;
		return;
	}
	if(q==1) return;
	for(int i=0;i<8;++i){
		if(!hxs[i]&&!hxx1[x+i]&&!hxx2[7-x+i]){
			hxs[i]=1;
			hxx1[x+i]=1;
			hxx2[7-x+i]=1;
			map1[x][i]='Q';
			syf(x+1);
			hxs[i]=0;
			hxx1[x+i]=0;
			hxx2[7-x+i]=0;
			map1[x][i]=0;
		}
	}
}
int main(){
	input();
	syf(0);
	return 0;
}