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.Scanner; 
    public class Main{ 
        static final int N = 8; 
        static boolean[] row = new boolean[N]; 
        static boolean[] col = new boolean[N]; 
        static boolean[] dpos = new boolean[2*N -1]; 
        static boolean[] dneg = new boolean[2*N -1]; 
        static boolean[][] X = new boolean[N][N]; 
        static void print_Board(){ 
            for(int i = 0; i < N; i++){ 
                for(int j = 0; j < N; j++){ 
                    if(X[i][j]){ 
                        if(j == N-1) 
                            System.out.println("Q"); 
                        else 
                            System.out.print("Q"); 
                    } 
                    else{ 
                        if(j == N-1) 
                            System.out.println("."); 
                        else System.out.print("."); 
                    } 
                } 
            } 
        } 
        static void putQueen(int i){ 
            if(i == N){ 
                print_Board(); 
                return; 
            } 
            else{ 
                for(int j = 0; j < N; j++){ 
                    if(X[i][j]) 
                        putQueen(i+1); 
                    else if(col[j] || dpos[i+j] || dneg[i-j+N-1]){ 
                        continue; 
                    } 
                    else{ 
                        row[i] = true; 
                        col[j] = true; 
                        dpos[i+j] = true; 
                        dneg[i-j+N-1] = true; 
                        X[i][j] = true; 
                        putQueen(i+1); 
                        row[i] = false; 
                        col[j] = false; 
                        dpos[i+j] = false; 
                        dneg[i-j+N-1] = false; 
                        X[i][j] = false; 
                    } 
                } 
                return; 
            } 
        } 
        public static void main(String[] args){ 
            Scanner scan = new Scanner(System.in); 
            int k = scan.nextInt(); 
            for(int i = 0; i < N; i++){ 
                row[i] = false; 
                col[i] = false; 
            } 
            for(int i = 0; i < 2*N-1; i++){ 
                dpos[i] = false; 
                dneg[i] = false; 
            } 
            for(int i = 0; i < N; i++) 
                for(int j = 0; j < N; j++) 
                    X[i][j] = false; 
            for(int i = 0; i < k; i++){ 
                int x = scan.nextInt(); 
                int y = scan.nextInt(); 
                X[x][y] = true; 
                row[x] = true; 
                col[y] = true; 
                dpos[x+y] = true; 
                dneg[x-y+N-1] = true; 
            } 
            putQueen(0); 
        } 
    }
