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 <vector>
using namespace std;
#define FREE -1
#define EXIST 1
#define SUCCESS 1
#define SIZE 8
int row[10], col[10];
int crsR[20], crsL[20];

int solve(int r) {
  if (r == SIZE) {
    return SUCCESS; 
  } else if (row[r] != FREE) {
    return solve(r+1);
  } else {
    for (int c = 0; c < SIZE; c++) {
      if (col[c] == FREE && crsR[r+c] == FREE && crsL[r-c+SIZE-1] == FREE) {
        row[r] = c;
        col[c] = r;
        crsR[r+c] = EXIST;
        crsL[r-c+SIZE-1] = EXIST;
        if (solve(r+1) == SUCCESS) {
          return SUCCESS;
        }
        col[c] = FREE;
        crsR[r+c] = FREE;
        crsL[r-c+SIZE-1] = FREE;
      }
    }
    row[r] = FREE;
    return 0;
  }
}

int main() {
  for (int i = 0; i < SIZE; i++) {
    row[i] = col[i] = FREE;
  }
  for (int i = 0; i < SIZE*2; i++) {
    crsR[i] = crsL[i] = FREE;
  }
  
  int N; cin >> N;
  for (int i = 0; i < N; i++) {
    int r, c;
    cin >> r >> c;
    row[r] = c;
    col[c] = r;
    crsR[r+c] = EXIST;
    crsL[r-c+SIZE-1] = EXIST;
  }

  solve(0);

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


