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 C# (judge verdict: Accepted)

using System;

public class A13{
  static int N = 8;
  static int NOFREE = -1;
  static int FREE = 0;
  static int[] row = new int[N];
  static int[] col = new int[N];
  static int[] rsla = new int[2 * N - 1];
  static int[] lsla = new int[2 * N - 1];
  static bool[,] board = new bool[N,N];

  public static void Main(){
    int input1 = int.Parse(Console.ReadLine());
    for(int i = 0;i < input1;i++){
      int[] input2 = Array.ConvertAll(Console.ReadLine().Split(' '),int.Parse);
      board[input2[0],input2[1]] = true;
    }
    Calc(0);
  }

  static void Calc(int i){
    if(i == N){
      Print();
      return;
    }
    for(int j = 0;j < N;j++){
      if(NOFREE == col[j] ||
      NOFREE == rsla[i + j] ||
      NOFREE == lsla[i - j + N - 1]) continue;

      row[i] = j;
      col[j] = rsla[i + j] = lsla[i - j + N -1] = NOFREE;
      Calc(i + 1);
      row[i] = col[j] = rsla[i + j] = lsla[i - j + N - 1] = FREE;
    }
  }

  static void Print(){
    for(int i = 0;i < N;i++){
      for(int j = 0;j < N;j++){
      if(board[i,j] && row[i] != j) return;
      }
    }
  for(int i = 0;i < N;i++){
    for(int j = 0;j < N;j++){
      Console.Write((row[i] == j) ? "Q" : ".");
    }
    Console.WriteLine();
  }
}
}