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 main(){
    vector<int> a ={0,1,2,3,4,5,6,7};
    int n;
    cin >> n;
    int b[n],c[n];
    for(int i=0;i<n;i++) cin >> b[i] >> c[i];
    do{
        int flag = 1;
        for(int i=0;i<n;i++){
            if(a[b[i]]!=c[i]) flag = 0;
        }
        if(flag){
            int map[8][8] = {};
            int flag1 = 1;
            for(int i=0;i<8;i++){
                int r=i,c=a[i];
                if(map[r][c]) flag1 = 0;
                for(int j=0;j<8;j++){
                    for(int k=0;k<8;k++){
                        if(r==j||c==k) map[j][k]=1;
                        if(abs(r-j)==abs(c-k)) map[j][k]=1; 
                    }
                }
            }
            if(flag1){
                    for(int j=0;j<8;j++){
                        for(int k=0;k<8;k++){
                            if(k==a[j]) cout << 'Q';
                            else cout << '.';
                        }
                        cout << endl;
                    }
                return 0;
            }
        }
    }while(next_permutation(a.begin(),a.end()));
}

