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 <string>

using namespace std;

int ve[8],ho[8],po[15],ne[15];
string mp[8];//mp[row][col]

bool dfs(int row) {
	if(row==8) return true;
	if(ho[row] != -1) {
		return dfs(row+1);
	}
	for(int i = 0;i < 8;i++) {
		if(ve[i] == -1 && 
			po[i+row] == -1 &&
			ne[(7-i)+row] == -1) {
			mp[row][i] = 'Q';
			ho[row] = row;
			ve[i] = row;
			po[i+row] = row;
			ne[(7-i)+row] = row;
			if(dfs(row+1)) return true;
			mp[row][i] = '.';
			ho[row] = -1;
			ve[i] = -1;
			po[i+row] = -1;
			ne[(7-i)+row] = -1;
		}
	}
	return false;
}

int main() {
	for(int i = 0;i < 8;i++)mp[i]="........";
	for(int i = 0;i < 8;i++){ho[i]=-1;ve[i]=-1;}
	for(int i = 0;i < 15;i++){po[i]=-1;ne[i]=-1;}
	int n,r,c;
	cin >> n;
	for(int i = 0;i < n;i++) {
		cin >> r >> c;
		mp[r][c] = 'Q';
		ho[r]=r;ve[c]=r;po[r+c]=r;ne[(7-c)+r]=r;
	}
	dfs(0);
	for(int i = 0;i < 8;i++) cout << mp[i] << endl;
}
