Problem:
Score : 400 points

Problem Statement

In this problem, we only consider strings consisting of lowercase English letters.

Strings s and t are said to be isomorphic when the following conditions are satisfied:

|s| = |t| holds.

For every pair i, j, one of the following holds:

s_i = s_j and t_i = t_j.

s_i \neq s_j and t_i \neq t_j.

For example, abcac and zyxzx are isomorphic, while abcac and ppppp are not.

A string s is said to be in normal form when the following condition is satisfied:

For every string t that is isomorphic to s, s \leq t holds. Here \leq denotes lexicographic comparison.

For example, abcac is in normal form, but zyxzx is not since it is isomorphic to abcac, which is lexicographically smaller than zyxzx.

You are given an integer N.
Print all strings of length N that are in normal form, in lexicographically ascending order.

Constraints

1 \leq N \leq 10

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N

Output

Assume that there are K strings of length N that are in normal form: w_1, \ldots, w_K in lexicographical order.
Output should be in the following format:

w_1
:
w_K

Sample Input 1

1

Sample Output 1

a

Sample Input 2

2

Sample Output 2

aa
ab

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Runtime Error)

import java.util.Arrays;
import java.util.Scanner;

public class Main {

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

        char[] c = new char[n];
        Arrays.fill(c, 'a');

        if (n == 0) {
            System.out.println("a");
            return;
        }

        solve(c, 1);
    }

    private static void solve(char[] c, int index) {

        if (index < c.length - 1) {

            while (true) {
                // 指定されたindexより先に文字が存在する場合、再帰的に呼び出す。
                solve(c, index + 1);
                //まだいける？
                if (moumuri(c, index)) {
                    break;
                }
                // 指定されているindexを1こ上げて、その先の文字を全部aにしちゃう。
                c[index]++;
                Arrays.fill(c, index + 1, c.length, 'a');
            }
        } else {

            while (true) {
                // 配列のお尻を指定されている場合、出力処理をする。
                System.out.println(String.valueOf(c));
                //まだいける？
                if (moumuri(c, index)) {
                    break;
                }
                // 指定されているindexを1こ上げる
                c[index]++;
            }
        }
    }

    private static boolean moumuri(char[] c, int index) {
        for (int i = 0; i < index; i++) {
            if (c[i] >= c[index]) {
                return false;
            }
        }
        return true;
    }
}