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...
import java.util.*;

class Main {
    
    static int[][] queen = new int[8][8];
    static int[][] ok = new int[8][8];
    static int cnt = 0;
    
    static void mark(int a, int b, int x){
        for(int i = 0; i < 8; i++){
            for(int j = 0; j < 8; j++){
                if(i == a || j == b || Math.abs(i - a) == Math.abs(j - b)){
                    ok[i][j] += x;
                }
            }
        }
    }
    
    static void dfs(int a){
        
        if(cnt == 8) return;
        if(a == 64) return;
        
        int i = a / 8;
        int j = a % 8;
        if(ok[i][j] == 0){
            
            mark(i, j, 1);
            queen[i][j] = 1;
            cnt++;
            dfs(a + 1);
            if(cnt == 8) return;
            
            mark(i, j, -1);
            queen[i][j] = 0;
            cnt--;
            dfs(a + 1);
            if(cnt == 8) return;
        }else{
            dfs(a + 1);
            if(cnt == 8) return;
        }
    }
    
    public static void main(String[] args) throws Exception {
        Scanner sc = new Scanner(System.in);
        int k = sc.nextInt();
        for(int i = 0; i < k; i++){
            int r = sc.nextInt();
            int c = sc.nextInt();
            mark(r, c, 1);
            queen[r][c] = 1;
        }
        cnt = k;
        dfs(0);
        for(int i = 0; i < 8; i++){
            for(int j = 0; j < 8; j++){
                if(queen[i][j] == 1){
                    System.out.print("Q");
                }else{
                    System.out.print(".");
                }
            }
            System.out.println();
        }
    }
}
