import java.util.ArrayList;
import java.util.List;
import java.util.Scanner;

/**
 * Program to solve the n-queens problem.
 * 
 * @author Scot Drysdale
 * 12/2011, minor modification to output 2/22/2013.
 * @author Minor changes by Tom Cormen
 */
public class NQueens {  
  /**
   * Solves the n-queens problem recursively.
   * 
   * @param partialSol the current partial solution (first position-1 places
   *   are valid).  Its length is the problem size.
   * @param position the next position to be assigned.
   * @param List of solutions found so far
   */
  public static void solve(int [] partialSol, int position, List<int []> solList) {
    if (position >= partialSol.length)
      solList.add(partialSol.clone());  // must clone so doesn't change
    else
      for (int i = 1; i <= partialSol.length; i++) {  // try all possible values
        partialSol[position] = i;
        if (noConflict(partialSol, position))
          solve(partialSol, position+1, solList);
      }   
  }
  
  /**
   * Determines if value in given position conflicts with earlier values
   * 
   * @param partialSol the current partial solution
   * @param position the position to be tested for conflict with earlier values
   */
  public static boolean noConflict(int [] partialSol, int position) {
    for (int i = 0; i < position; i++) {
      if (partialSol[position] == partialSol[i] ||                        // same row?
          Math.abs(partialSol[position] - partialSol[i]) == position - i) // same diagonal?
        return false;
    }
    return true;
  }
  
  public static void main(String[] args) {
    int n;                  // Problem size
    
    Scanner input = new Scanner(System.in);
    System.out.print("Number of queens (< 1 to quit): ");
    n = input.nextInt();
    
    while (n > 0) {
      int [] partialSol = new int[n];
      List<int []> solList  = new ArrayList<int []>();

      solve(partialSol, 0, solList);

      for (int [] sol : solList) {
        for (int i = 0; i < sol.length; i++)
          System.out.print(sol[i] + " "); 

        System.out.println();
      }

      System.out.println("\nNumber of solutions for n = " + n + " is " + solList.size());
      
      System.out.print("\nNumber of queens: ");
      n = input.nextInt();
    }
  }
}