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 C# (Mono 4.6.2.0) (judge verdict: Wrong Answer)

using System;
using System.Collections.Generic;
using System.IO;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace AtCoder
{
    partial class Program
    {
        static long mod = 1000000007;
        static void Swap<T>(ref T a, ref T b) { T temp = a; a = b; b = temp; }
        static void Main()
        {
            Console.SetOut(new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false });
            Solve();
            Console.Out.Flush();
            Console.ReadKey();
        }

        //ここから
        static int N;
        static void Solve()
        {
            N = GetInt();
            DFS("a");
            //Console.WriteLine(ans);
        }

        static void DFS(string s)
        {
            if (s.Length == N)
            {
                Console.WriteLine(s);
            }
            else
            {
                for(int i = 0; i <= s.Last() - 'a'+1;i++)
                {
                    DFS(s + ((char)(i + 'a')).ToString());
                }
            }
        }

    }



    //拡張メソッド
    public static class Ex
    {
        public static List<string> FastSort(this List<string> s) { s.Sort(StringComparer.Ordinal); return s.ToList(); }
        public static string yesno(this bool b) { return b ? "yes" : "no"; }
        public static string YesNo(this bool b) { return b ? "Yes" : "No"; }
        public static string YESNO(this bool b) { return b ? "YES" : "NO"; }
    }

    partial class Program
    {
        static public string GetStr() { return Console.ReadLine().Trim(); }
        static public char GetChar() { return Console.ReadLine().Trim()[0]; }
        static public int GetInt() { return int.Parse(Console.ReadLine().Trim()); }
        static public long GetLong() { return long.Parse(Console.ReadLine().Trim()); }
        static public double GetDouble() { return double.Parse(Console.ReadLine().Trim()); }
        static public string[] GetStrArray() { return Console.ReadLine().Trim().Split(' '); }
        static public int[] GetIntArray() { return Console.ReadLine().Trim().Split(' ').Select(int.Parse).ToArray(); }
        static public long[] GetLongArray() { return Console.ReadLine().Trim().Split(' ').Select(long.Parse).ToArray(); }
        static public char[] GetCharArray() { return Console.ReadLine().Trim().Split(' ').Select(char.Parse).ToArray(); }
        static public double[] GetDoubleArray() { return Console.ReadLine().Trim().Split(' ').Select(double.Parse).ToArray(); }
        static public void WriteObjects<T>(IList<T> values) { var num = values.Count; for (int i = 0; i < num; i++) { Console.Write(values[i]); if (i < num - 1) { Console.Write(" "); } } Console.WriteLine(); }

        static bool eq<T, U>() => typeof(T).Equals(typeof(U));
        static T ct<T, U>(U a) => (T)Convert.ChangeType(a, typeof(T));
        static T cv<T>(string s) => eq<T, int>() ? ct<T, int>(int.Parse(s))
                           : eq<T, long>() ? ct<T, long>(long.Parse(s))
                           : eq<T, double>() ? ct<T, double>(double.Parse(s))
                           : eq<T, char>() ? ct<T, char>(s[0])
                                             : ct<T, string>(s);
        static void Multi<T>(out T a) => a = cv<T>(GetStr());
        static void Multi<T, U>(out T a, out U b)
        {
            var ar = GetStrArray(); a = cv<T>(ar[0]); b = cv<U>(ar[1]);
        }
        static void Multi<T, U, V>(out T a, out U b, out V c)
        {
            var ar = GetStrArray(); a = cv<T>(ar[0]); b = cv<U>(ar[1]); c = cv<V>(ar[2]);
        }
        static void Multi<T, U, V, W>(out T a, out U b, out V c, out W d)
        {
            var ar = GetStrArray(); a = cv<T>(ar[0]); b = cv<U>(ar[1]); c = cv<V>(ar[2]); d = cv<W>(ar[3]);
        }
        static void Multi<T, U, V, W, X>(out T a, out U b, out V c, out W d, out X e)
        {
            var ar = GetStrArray(); a = cv<T>(ar[0]); b = cv<U>(ar[1]); c = cv<V>(ar[2]); d = cv<W>(ar[3]); e = cv<X>(ar[4]);
        }
    }
}