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 <bits/stdc++.h>
using namespace std;

bool done = false;
map<int, int> mp;
string ans = "";

bool check(string s)
{
	int x = s.size() - 1;
	int y = s[s.size() - 1] - '0';
	for (int i = 0; i < s.size() - 1; i++)
	{
		if (x == i || y == s[i] - '0' || abs(i - x) == abs(s[i] - '0' - y))
			return false;
	}
	return true;
}

void solve(int ind)
{
	if (ind == 8)
	{
		done = true;
		return;
	}

	if (mp.count(ind))
	{
		int x = mp[ind];
		if (check(ans + to_string(x)))
		{
			ans += to_string(x);
			solve(ind + 1);
			if (done)
				return;
			else
				ans.pop_back();
		}
	}
	else
	{
		for (int x = 0; x < 8; x++)
		{
			if (check(ans + to_string(x)))
			{
				ans += to_string(x);
				solve(ind + 1);
				if (done)
					return;
				else
					ans.pop_back();
			}
		}
	}
}

int main()
{
	int k;
	cin >> k;
	while (k--)
	{
		int a, b;
		cin >> a >> b;
		mp[a] = b;
	}
	
	solve(0);

	for (int i = 0; i < 8; i++)
	{
		for (int j = 0; j < 8; j++)
		{
			if (j == ans[i] - '0')
				cout << 'Q';
			else
				cout << '.';
		}
		cout << endl;
	}

	return 0;
}
