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>

using namespace std;

const int N = 8;
int rows[8];
bool cols[8];
bool dpos[15];
bool dneg[15];
bool skip[8];

void displayBoard(){
	for(auto i = 0; i < N; ++i){
		for(auto j = 0; j < N; ++j){
			if(j == rows[i] && cols[j]) cout << 'Q';
			else cout << '.';
		}
		cout << endl;
	}
}

void putQueen(int i){
	if(i == N){
		displayBoard();
		return;
	}
	if(skip[i]){
		putQueen(i + 1);
		return;
	}
	for(auto j = 0; j < N; ++j){
		if(cols[j] || dpos[i + j] || dneg[i - j + N - 1]) continue;
		rows[i] = j;
		cols[j] = dpos[i + j] = dneg[i - j + N - 1] = true;
		putQueen(i + 1);
		cols[j] = dpos[i + j] = dneg[i - j + N - 1] = false;
	}
}

int main(){
	for(auto i = 0; i < N; ++i){
		rows[i] = 0;
		cols[i] = false;
		skip[i] = false;
	}
	for(auto i = 0; i < 2 * N - 1; ++i){
		dpos[i] = false;
		dneg[i] = false;
	}
	// memset(rows, 0, sizeof(rows));
	// memset(cols, false, sizeof(cols));
	// memset(dpos, false, sizeof(dpos));
	// memset(dneg, false, sizeof(dneg));

	int k;
	cin >> k;
	for(auto i = 0; i < k; ++i){
		int r, c;
		cin >> r >> c;
		skip[r] = true;
		rows[r] = c;
		cols[c] = dpos[r + c] = dneg[r - c + N - 1] = true;
	}
	// displayBoard();
	putQueen(0);
}
