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 <cmath>
using namespace std;

int a[8],u[8];
bool pp(){
    for(int i=0;i<7;i++){
        for(int j=i+1;j<8;j++){
            if(a[i]==a[j]||abs(a[i]-a[j])==j-i){
                return false;
            }
        }
    }
    return true;
}
void qq(int f){
    if(f==8){
        if(pp()){
            for(int i=0;i<8;i++){
                for(int j=0;j<8;j++){
                    if(a[i]==j){
                        cout<<"Q";
                    }
                    else{
                        cout<<".";
                    }
                }
                cout<<endl;
            }
        }
        return;
    }
    if(u[f]==1){
        qq(f+1);
    }
    else{
        for(int i=0;i<8;i++){
            a[f]=i;
            qq(f+1);
        }
    }
}
int main(){
    for(int i=0;i<8;i++){
        a[i]=-1;
        u[i]=0;
    }
    int k,r,c;
    cin>>k;
    for(int i=0;i<k;i++){
        cin>>r>>c;
        a[r]=c;
        u[r]=1;
    }
    qq(0);
    return 0;
}
