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;

#define N 8
#define FREE -1
bool board[N][N];
int  row[N];
bool col[N], dp[2*N-1], dn[2*N-1]; // 横, 右斜め、左斜めのクイーンの利き

void print()
{
	for(int i=0; i<N; i++)
	{
		for(int j=0; j<N; j++)
		{
			if(board[i][j] && row[i] != j)
			{
				return;
			}
		}
	}

	for(int i=0; i<N; i++)
	{
		for(int j=0; j<N; j++)
		{
			cout << ((row[i] == j) ? 'Q' : '.');
		}
		cout << endl;
	}
}

void queeeeeen(int i)
{
	if(i == N)
	{
		print();
		return;
	}
	
	for(int j = 0; j < N; j++)
	{
		// クイーンが利いていない
		if(!col[j] && !dp[i + j] && !dn[i - j + N - 1])
		{
			// クイーンを置く
			row[i] = j;
			col[j] = dp[i + j] = dn[i - j + N - 1] = true;
			
			// 再起呼び出し
			queeeeeen(i + 1);
			
			// クイーンを戻す
			row[i] = FREE;
			col[j] = dp[i + j] = dn[i - j + N - 1] = false;
		}
	}
}

int main()
{
	for(int i=0; i<N; i++)
	{
		row[i] = FREE;
		col[i] = false;
	}
	for(int i=0; i<2*N-1; i++)
	{
		dp[i] = dn[i] = false;
	}
	
	for(int i=0; i<N; i++)
	{
		for(int j=0; j<N; j++)
		{
			board[i][j] = false;
		}
	}
	
	int k;
	cin >> k;
	
	for(int i = 0; i < k; i++)
	{
		int r,c;
		cin >> r >> c;
		board[r][c] = true;
	}
	
	queeeeeen(0);
	
	return 0;
}


