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;
bool row[8];//yoko i
bool col[8];//tate j
bool dpos[14];// / x=i+j
bool dneg[14];// \ x=i-j+(N-1)
bool boad[8][8];
bool canput(int i,int j){
  if(row[i])return false;
  if(col[j])return false;
  if(dpos[i+j])return false;
  if(dneg[i-j+7])return false;
  return true;
}
void put(int i,int j,bool x){
  row[i]=x;
  col[j]=x;
  dpos[i+j]=x;
  dneg[i-j+(8-1)]=x;
  boad[i][j]=x;
}
void print(){
  for(int i=0;i<8;i++){
    for(int j=0;j<8;j++){
      cout << (boad[i][j] ? 'Q':'.');
    }
    cout << endl;
  }
}
void dfs(int i){
  if(i==8){
    print();
    return;
  }
  if(row[i])dfs(i+1);
  for(int j=0;j<8;j++){
    if(canput(i,j)){
      put(i,j,1);
      dfs(i+1);
      put(i,j,0);
    }
  }
}
    

int main(){
  int n;
  cin >> n;
  for(int i=0;i<n;i++){
    int I,J;
    cin >> I >> J;
    put(I,J,1);
  }
  dfs(0);
  return 0;
}