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: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Text.RegularExpressions;
using static System.Console;
using static System.Math;
using static MyIO;
using static MyUtil;
using static BinaryRepresentation;

public class D
{
	public static void Main() => (new Solver()).Solve();
}

public class Solver
{
	public void Solve()
	{
		var add = new string[10] { 
			"a", "b", "c", "d", "e", "f", "g", "h", "i", "j"
		};

		int N = GetInt();
		var list = new List<string>(){ "a" };
		for(int i = 1; i < N; i++)
		{
			var next = new List<string>();
			foreach(var s in list)
			{
				int c = count(s);
				for(int j = 0; j <= c; j++)
					next.Add(s + add[j]);
			}
			list = next;
		}
		list.Sort(StringComparer.Ordinal);
		WriteLine(string.Join("\n", list));
	}

	private int count(string S)
	{
		int flag = 0;
		for(int i = 0; i < S.Length; i++)
			flag |= (1 << (int)(S[i] - 'a'));

		return popcnt(flag);
	}
}

public static class BinaryRepresentation
{
	/*
	* initialize: array = { 0, 1, 2, ..., N - 1 } 
	* do { ... } while(nextPermutaion(ref array));
	*/
	private static bool nextPermutation(ref int[] array)
	{
		int len = array.Length;
		int i = len - 2;
		while((i >= 0) && (array[i] > array[i + 1]))
			i--;
		if(i < 0)
			return false;

		int pivot = array[i];
		int j = i + 1;
		while((j < len - 1) && (array[j + 1] > pivot))
			j++;
		
		int tmp = array[i];
		array[i] = array[j];
		array[j] = tmp;
		
		Array.Reverse(array, i + 1, len - i - 1);

		return true;
	}

	/* 
	* nCk
	* initialize: comb = (1 << k) - 1
	* while(comb < (1 << n)) { ...; comb = nextCombination(comb); };
	*/
	public static int nextCombination(int comb)
	{
		int x = comb & -comb;
		int y = comb + x;
		return (((comb & ~y) /x) >> 1) | y;
	}

	public static int popcnt(int v) {
		v = v - ((v >> 1) & 0x55555555);
		v = (v & 0x33333333) + ((v >> 2) & 0x33333333);
		return ((v + (v >> 4) & 0xF0F0F0F) * 0x1010101) >> 24;
	}

	public static long popcnt(long v) {
		v = v - ((v >> 1) & 0x5555555555555555);
		v = (v & 0x3333333333333333) + ((v >> 2) & 0x3333333333333333);
		return ((v + (v >> 4) & 0xF0F0F0F0F0F0F0F) * 0x101010101010101) >> 56;
	}
}

public static class MyIO
{
	private static string[] args = null;
	private static int num = -1;
	private static int used = -1;

	private static string getArg()
	{
		if(used == num)
		{
			args = Console.ReadLine().Split(' ');
			num = args.Length;
			used = 0;
		}
		return args[used++];
	}

	public static int GetInt() => int.Parse(getArg());
	public static long GetLong() => long.Parse(getArg());
	public static double GetDouble() => double.Parse(getArg());
	public static decimal GetDecimal() => decimal.Parse(getArg());
	public static string GetString() => getArg();
	public static char GetChar() => getArg()[0];
	public static int[] GetInts(long N) => Enumerable.Range(0, (int)N).Select(_ => GetInt()).ToArray();
	public static long[] GetLongs(long N) => Enumerable.Range(0, (int)N).Select(_ => GetLong()).ToArray();
	public static double[] GetDoubles(long N) => Enumerable.Range(0, (int)N).Select(_ => GetDouble()).ToArray();
	public static decimal[] GetDecimals(long N) => Enumerable.Range(0, (int)N).Select(_ => GetDecimal()).ToArray();
	public static string[] GetStrings(long N) => Enumerable.Range(0, (int)N).Select(_ => GetString()).ToArray();
}

public static class MyUtil
{
	public static void chmax<T>(ref T x, T y) where T : IComparable<T>
	{
		if(x.CompareTo(y) < 0)
			x = y;
	}

	public static void chmin<T>(ref T x, T y) where T : IComparable<T>
	{
		if(x.CompareTo(y) > 0)
			x = y;
	}

	public static void swap<T>(ref T x, ref T y)
	{
		T tmp = x;
		x = y;
		y = tmp;
	}
}