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 <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;
}