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 <cmath>
using namespace std;

const int INF = -100;
int k, r, c;
int a[8] = { INF, INF, INF, INF, INF, INF, INF, INF };
bool b[8] = { 0, 0, 0, 0, 0, 0, 0, 0 };

bool check() {
	for (int i = 0; i < 7; i++) {
		for (int j = i + 1; j < 8; j++)
			if (a[i] == a[j] || j - i == abs(a[i] - a[j]))
				return false;
	}
	return true;
}

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

	if (b[i])
		set(i + 1);
	else {
		for (int j = 0; j < 8; j++) {
			a[i] = j;
			set(i + 1);
		}
	}
}

int main()
{
	cin >> k;

	for (int i = 0; i < k; i++) {
		cin >> r >> c;
		a[r] = c;
		b[r] = 1;
	}

	set(0);

	return 0;
}
