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;

int flag_a[8];
int flag_b[15];
int flag_c[15];
int pos[8];
int rc[8];

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

void set_board(int i) {
  for (int j = 0; j < 8; ++j) {
    if (!flag_a[j] && !flag_b[i + j] && !flag_c[i - j + 7]) {
      pos[i] = j;
      if (i == 7) {
        bool flag = false;
        for (int k = 0; k < 8; ++k) {
          if (rc[k] == -1) continue;
          if (rc[k] == pos[k]) {
            flag = true;
          } else {
            flag = false;
            break;
          }
        }
        if (flag){
          print();
          return;
        } 
      } else {
        flag_a[j] = flag_b[i + j] = flag_c[i - j + 7] = 1;
        set_board(i + 1);
        flag_a[j] = flag_b[i + j] = flag_c[i - j + 7] = 0;
      }
    }
  }
}

int main() {
  int K, r, c;
  
  for (int i = 0; i < 8; ++i) {
    flag_a[i] = 0;
    rc[i] = -1;
  }
  for (int i = 0; i < 15; ++i) {
    flag_b[i] = flag_c[i] = 0;
  }

  cin >> K;
  for (int i = 0; i < K; ++i) {
    cin >> r >> c;
    rc[r] = c;
  }

  set_board(0);

  return 0;
}
