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 {
	public static final int N=8;
	public static final int free=-1;
	public static final int not_free=1;

	static int row[]=new int [N];
	static int col[]=new int [N];
	static int dpos[]=new int [2*N-1];
	static int dneg[]=new int [2*N-1];
	static boolean x[][]=new boolean [N][N];

	public static void initialize(){
		for(int i=0;i<N;i++){
			row[i]=free;
			col[i]=free;
		}
		for(int i=0;i<2*N-1;i++){
			dpos[i]=free;
			dneg[i]=free;
		}
	}
	public static void print(){
		for(int i=0;i<N;i++){
			for(int j=0;j<N;j++){
				if(x[i][j]){
					if(row[i]!=j){
						return;
					}
				}
			}
		}
		for(int i=0;i<N;i++){
			for(int j=0;j<N;j++){
				if(row[i]==j){
					System.out.print("Q");
				}else{
					System.out.print(".");
				}
			}
			System.out.println();
		}
	}
	public static void solve(int i){
		if(i==N){
			print();
			return;
		}
		for(int j=0;j<N;j++){
			if(col[j]==not_free || dpos[i+j]==not_free || dneg[i-j+N-1]==not_free)
				continue;

			row[i]=j;
			col[j]=dpos[i+j]=dneg[i-j+N-1]=not_free;

			solve(i+1);

			row[i]=col[j]=dpos[i+j]=dneg[i-j+N-1]=free;
		}
	}
	public static void main(String[] args){
		Scanner stdIn=new Scanner(System.in);
		initialize();
		for(int i=0;i<N;i++){
			for(int j=0;j<N;j++){
				x[i][j]=false;
			}
		}
		int k=stdIn.nextInt();
		for(int i=0;i<k;i++){
			int r=stdIn.nextInt();
			int c=stdIn.nextInt();
			x[r][c]=true;
		}
		solve(0);
	}
}