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 static System.Math;
using static Panasonic2020.D.Cin;
using static Panasonic2020.D.Util;
using Pair = Panasonic2020.D.VTuple<long, long>;
using Graph = System.Collections.Generic.List<System.Collections.Generic.List<long>>;
using System.Text;

namespace Panasonic2020
{
    public class D
    {
        public static void Main(string[] args)
        {
            DontAutoFlush();

            int n = ri;
            string abc = "abcdefghij";
            char[] cur = new char[n];
            cur[0] = 'a';
            Action<int, int> rec = null;
            rec = (depth, max) =>
            {
                if (depth == n)
                {
                    Console.WriteLine(cur);
                    return;
                }
                for (int j = 0; j <= max+1; j++)
                {
                    cur[depth] = abc[j];
                    rec(depth + 1, Max(j, max));
                }
            };
            rec(1, 0);
            Flush();
        }

        public struct VTuple<T1,T2>:System.IComparable<VTuple<T1,T2>>,System.IEquatable<VTuple<T1,T2>>{public T1 First;public T2 Second;public VTuple(T1 a,T2 b){First=a;Second=b;}public int CompareTo(VTuple<T1,T2>a){int b=Comparer<T1>.Default.Compare(First,a.First);if(b!=0)return b;return Comparer<T2>.Default.Compare(Second,a.Second);}public override bool Equals(object a){return a is VTuple<T1,T2>&&Equals((VTuple<T1,T2>)a);}public bool Equals(VTuple<T1,T2>a){return EqualityComparer<T1>.Default.Equals(First,a.First)&&EqualityComparer<T2>.Default.Equals(Second,a.Second);}public override int GetHashCode(){int a=First!=null?First.GetHashCode():0;int b=Second!=null?Second.GetHashCode():0;uint c=((uint)a<<5)|((uint)a>>27);return((int)c+a)^b;}}public class HashMap<K,V>:System.Collections.Generic.Dictionary<K,V>{V i;static Func<V>j=System.Linq.Expressions.Expression.Lambda<Func<V>>(System.Linq.Expressions.Expression.New(typeof(V))).Compile();public HashMap(){}public HashMap(V a){i=a;}new public V this[K a]{get{V b;if(TryGetValue(a,out b))return b;else return base[a]=i!=null?i:j();}set{base[a]=value;}}}public static class Util{public static readonly long INF=(long)1e17;public readonly static long MOD=(long)1e9+7;public readonly static int[]DXY4={0,1,0,-1,0};public readonly static int[]DXY8={1,1,0,1,-1,0,-1,-1,1};public static void DontAutoFlush(){var a=new System.IO.StreamWriter(Console.OpenStandardOutput()){AutoFlush=false};Console.SetOut(a);}public static void Flush(){Console.Out.Flush();}public static T[]Sort<T>(T[]a){Array.Sort<T>(a);return a;}public static T[]SortDecend<T>(T[]a){Array.Sort<T>(a);Array.Reverse(a);return a;}public static void Swap<T>(ref T a,ref T b){T c=a;a=b;b=c;}public static int GCD(int a,int b){return(b==0)?a:GCD(b,a%b);}public static void ChMax(ref long a,long b){if(a<b)a=b;}public static void ChMin(ref long a,long b){if(a>b)a=b;}public static long ModAdd(long a,long b){long c=a+b;if(c>=MOD)return c%MOD;return c;}public static long ModMul(long a,long b){long c=a*b;if(c>=MOD)return c%MOD;return c;}public static void ChModAdd(ref long a,long b){a+=b;if(a>=MOD)a%=MOD;}public static void ChModMul(ref long a,long b){a*=b;if(a>=MOD)a%=MOD;}public static void FillArray<T>(T[]a,T b){int c=a.Length;for(int d=0;d<c;d++)a[d]=b;}public static void FillArray<T>(T[,]a,T b){int c=a.GetLength(0);int d=a.GetLength(1);for(int e=0;e<c;e++)for(int f=0;f<d;f++){a[e,f]=b;}}public static void FillArray<T>(T[,,]a,T b){int c=a.GetLength(0);int d=a.GetLength(1);int e=a.GetLength(2);for(int f=0;f<c;f++)for(int g=0;g<d;g++){for(int h=0;h<e;h++){a[f,g,h]=b;}}}public static long[]Accumulate(long[]a){long[]b=new long[a.Length+1];for(int c=0;c<a.Length;c++)b[c+1]=b[c]+a[c];return b;}public static double[]Accumulate(double[]a){double[]b=new double[a.Length+1];for(int c=0;c<a.Length;c++)b[c+1]=b[c]+a[c];return b;}}public static class Cin{public static int ri{get{return ReadInt();}}public static int[]ria{get{return ReadIntArray();}}public static long rl{get{return ReadLong();}}public static long[]rla{get{return ReadLongArray();}}public static double rd{get{return ReadDouble();}}public static double[]rda{get{return ReadDoubleArray();}}public static string rs{get{return ReadString();}}public static string[]rsa{get{return ReadStringArray();}}public static int ReadInt(){return int.Parse(i());}public static long ReadLong(){return long.Parse(i());}public static double ReadDouble(){return double.Parse(i());}public static string ReadString(){return i();}public static int[]ReadIntArray(){g=null;return Array.ConvertAll(Console.ReadLine().Split(' '),int.Parse);}public static long[]ReadLongArray(){g=null;return Array.ConvertAll(Console.ReadLine().Split(' '),long.Parse);}public static double[]ReadDoubleArray(){g=null;return Array.ConvertAll(Console.ReadLine().Split(' '),double.Parse);}public static string[]ReadStringArray(){g=null;return Console.ReadLine().Split(' ');}public static void ReadCol(out long[]a,long b){a=new long[b];for(int c=0;c<b;c++)a[c]=ReadLong();}public static void ReadCols(out long[]a,out long[]b,long c){a=new long[c];b=new long[c];for(int d=0;d<c;d++){a[d]=ReadLong();b[d]=ReadLong();}}public static void ReadCols(out long[]a,out long[]b,out long[]c,long d){a=new long[d];b=new long[d];c=new long[d];for(int e=0;e<d;e++){a[e]=ReadLong();b[e]=ReadLong();c[e]=ReadLong();}}public static int[,]ReadIntTable(int a,int b){g=null;int[,]c=new int[a,b];for(int d=0;d<a;d++)for(int e=0;e<b;e++){c[d,e]=ReadInt();}return c;}public static long[,]ReadLongTable(long a,long b){g=null;long[,]c=new long[a,b];for(int d=0;d<a;d++)for(int e=0;e<b;e++){c[d,e]=ReadLong();}return c;}public static char[,]ReadCharTable(int a,int b){g=null;char[,]c=new char[a,b];for(int d=0;d<a;d++){var e=ReadString();for(int f=0;f<b;f++)c[d,f]=e[f];}return c;}static string[]g;static int h;static string i(){if(g==null||g.Length<=h){g=Console.ReadLine().Split(' ');h=0;}return g[h++];}}
    }
}