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>

bool rc(int);
bool board[64]{}, row[8]{}, column[8]{}, right_down[15]{}, left_down[15]{};

int main()
{
	int k, r, c;

	std::cin >> k;
	for (int i = 0; i < k; ++i)
	{
		std::cin >> r >> c;
		board[r * 8 + c] = true;
		row[r] = column[c] = true;
		right_down[7 + c - r] = left_down[r + c] = true;
	}

	rc(k);
	for (int i = 0; i < 64; ++i)
	{
		if (board[i])
			std::cout << 'Q';
		else
			std::cout << '.';
		if (i % 8 == 7)
			std::cout << std::endl;
	}

	return 0;
}

bool rc(int k)
{
	if (k == 8)
		return true;

	for (int i = 0; i < 8; ++i)
	{
		if (row[i]) continue;
		row[i] = true;
		for (int j = 0; j < 8; ++j)
		{
			if (column[j] || right_down[7 + j - i] || left_down[i + j])
				continue;
			column[j] = right_down[7 + j - i] = left_down[i + j] = true;
			board[i * 8 + j] = true;

			if (rc(k + 1))
				return true;

			column[j] = right_down[7 + j - i] = left_down[i + j] = false;
			board[i * 8 + j] = false;
		}
		row[i] = false;
		return false;
	}
}
