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>
using namespace std;

#define S 8
#define FREE -1
#define NOFREE 1

int row[S],col[S],dpos[2*S-1],dneg[2*S-1];
bool X[S][S];

void initialize(){
    for(int i=0;i<S;i++){
        row[i]=FREE;
        col[i]=FREE;
    }
    for(int i=0;i<2*S-1;i++){
        dpos[i]=FREE;
        dneg[i]=FREE;
    }
}

void prnt(){
    for(int i=0;i<S;i++){
        for(int j=0;j<S;j++){
            if(X[i][j] && row[i]!=j)return;
        }
    }
    for(int i=0;i<S;i++){
        for(int j=0;j<S;j++){
            cout<<((row[i]==j)?"Q":".");
        }
        cout<<endl;
    }
}

void rec(int i){
    if(i==S){
        prnt();
        return;
    }
    for(int j=0;j<S;j++){
        if(NOFREE==col[j] || NOFREE==dpos[i+j] ||
        NOFREE==dneg[i-j+S-1])continue;

        row[i]=j;
        col[j]=dpos[i+j]=dneg[i-j+S-1]=NOFREE;
        rec(i+1);
        row[i]=col[j]=dpos[i+j]=dneg[i-j+S-1]=FREE;
    }
}
int main(){
    initialize();
    for(int i=0;i<S;i++){
        for(int j=0;j<S;j++)X[i][j]=false;
    }
    int k;
    cin>>k;
    for(int i=0;i<k;i++){
        int r,c;
        cin>>r>>c;
        X[r][c]=true;
    }
    rec(0);
    return 0;
}
