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 <assert.h>
using namespace std;

bool r[8],c[8],dl[15],dr[15],T[8][8];
int k;

bool tryput(int i){
  if (r[i])return tryput(i+1);
  if (i>7) return true;
  for (int j=0;j<8;j++){
    if (c[j]||dl[i+j]||dr[i-j+7])continue;
    T[i][j]=true;
    r[i]=c[j]=dl[i+j]=dr[i-j+7]=true;
    if (tryput(i+1))return true;
    r[i]=c[j]=dl[i+j]=dr[i-j+7]=false;
    T[i][j]=false;
  }
  return false;
}

int main(){
  int x,y;
  
  cin >>k;
  for (int i=0;i<k;i++){
    cin >>y>>x;
    T[y][x]=true;
    r[y]=c[x]=dl[x+y]=dr[y-x+7]=true;
  }
  
  tryput(0);

  for (int i=0;i<8;i++){
    for (int j=0;j<8;j++){
      if (T[i][j]) cout << "Q";
      else cout << ".";
    }
    cout << endl;
  }
  
  return 0;
}