Problem:
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8 Queens Problem

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.

For a given chess board where $k$ queens are already placed, find the solution of the 8 queens problem.

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 '.'.

Constraints

There is exactly one solution

Sample Input 1

2
2 2
5 3

Sample Output 1

......Q.
Q.......
..Q.....
.......Q
.....Q..
...Q....
.Q......
....Q...

Solution in JAVA (judge verdict: Accepted)

import java.util.*;
public class Main {

	static int[] pos=new int[8];
	static boolean[] row=new boolean[8],
			rup=new boolean[15],
			rdown=new boolean[15];
	static boolean[][] def=new boolean[8][8];

	public static void main(String[] args) {
		Scanner in=new Scanner(System.in);
		int n=in.nextInt();

		for(int i=0;i<n;i++) {
			int r=Integer.parseInt(in.next()),c=Integer.parseInt(in.next());
			def[c][r]=true;
			row[r]=true;
			rup[c+r]=true;
			rdown[c-r+7]=true;
		}
		set(0);
	}

	static void set(int i) {
		for(int j=0;j<8;j++) {
			if(!row[j] && !rup[i+j] && !rdown[i-j+7]) {
				pos[i]=j;

				if(i==7) {
					print();
				}
				else {
					row[j]=rup[i+j]=rdown[i-j+7]=true;
					set(i+1);
					row[j]=rup[i+j]=rdown[i-j+7]=false;
				}
			}
			else if(def[i][j]){
				pos[i]=j;
				if(i==7)print();
				else set(i+1);
			}
		}
	}

	static void print() {
		for(int i=0;i<8;i++) {
			for(int j=0;j<8;j++)System.out.print((pos[j]==i)? "Q":".");
			System.out.println();
		}
	}

}