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: Runtime Error)

using System;
using System.Collections;
using System.Collections.Generic;

namespace 練習問題
{
    class Program {
        static void Main(string[] args) {
            List<int> pattern = new List<int>();
            long a = 0;
            long b = 0;
            var sw = new System.Diagnostics.Stopwatch();
            TimeSpan TLE = new TimeSpan(0,0,2);
            debug Debug = new debug();
            if (args.Length == 0){
                Debug.FlagFalse();
                //*
                string[] input = Console.ReadLine().Split(' ');
                a = long.Parse(input[0]);
                b = long.Parse(input[1]);
                //*/
                // c = int.Parse(Console.ReadLine());

                // string d = Console.ReadLine();

                //string[] input = Console.ReadLine().Split(' ');
            } else {
                Debug.FlagTrue();
                if (args[0] == "1"){
                    a = 4;
                    b = 5;
                } else if (args[0] == "2"){
                    a = 7;
                    b = 3;
                } else if (args [0] == "3"){
                    a = 1000000000;
                    b = 1000000000;
                } else {
                    a = 3;
                    b = 2;
                }
            }
            sw.Start(); //2秒以内ですねスタート
            long result = 0;
            if (a == 1 && b == 1){
                result = 1;
            } else if (a % 2 == 1) {
                if (b % 2 == 1) {
                    result += (a + 1) / 2 * (b + 1) / 2 + (a - 1) / 2 * (b - 1) / 2;
                } else {
                    result += (a + 1) / 2 * b / 2 + (a - 1) / 2 * b / 2;
                }
            } else {
                result += a / 2 * b;
            }
            Console.WriteLine(result);
            sw.Stop();
            TimeSpan ts = sw.Elapsed;
            // Console.WriteLine($"{ts}");
        }
        
        static int intPow(int target,int kaisu){
            int startTarget = target;
            for (int i = 1; i < kaisu; i++)
            {
                target *= startTarget;
            }
            return target;
        }

        static void bubble_sort(List<List<int>> a) {
            int count=0;
            for (int i = 0; i < a.Count; i++) {
                for (int j = 0; j < a.Count-i-1; j++) {
                    // if (a[j] == a[a.Count - 1]){
                    //     continue;
                    // }
                    count++;
                    if (a[j][1] > a[j+1][1]){
                        int localsave = 0;
                        localsave = a[j+1][1];
                        a[j+1][1] = a[j][1];
                        a[j][1] = localsave;
                        localsave = a[j][0];
                        a[j][0] = a[j+1][0];
                        a[j+1][0] = localsave;
                    }
                }
                //debug(a,"途中" + i);
            }
            // debug(a,"result");
            //Console.WriteLine("回数"+count);
            for (int i = 0; i < a.Count; i++)
            {
                Console.WriteLine(a[i][0]+" "+a[i][1]);
            }
        }
        /* 標準入力と標準出力が使えるかのチェック
        static void echo() {
            string echotest = Console.ReadLine();
            Console.WriteLine(echotest);
        }

        static void HelloWorld(){
            Console.WriteLine("Hello World!");
        }
        */
    }

    public class debug{ //宣言時は、「 debug Debug = new debug(); 」推奨
        bool debug_flag = true;
        public void Log(string str){
            if (debug_flag == true){
                Console.WriteLine(str);
            }
        }
        public void Log(int str){
            if (debug_flag == true){
                Console.WriteLine(str);
            }
        }
        public void Log(float str){
            if (debug_flag == true){
                Console.WriteLine(str);
            }
        }
        public void Log(object obj){
            if (debug_flag == true){
                Console.WriteLine(obj);
            }
        }

        public void Log(int[] arr){
            if (debug_flag == true){
                Console.WriteLine(string.Join(",", arr));
            }
        }
        public void Log(string[] arr){
            if (debug_flag == true){
                Console.WriteLine(string.Join(",", arr));
            }
        }
        public void Log(List<int> arr){
            if (debug_flag == true){
                string shuturyoku = "";
                for (int i = 0; i < arr.Count; i++) {
                    shuturyoku += arr[i] + ",";
                }
                Console.WriteLine(shuturyoku.TrimEnd(','));
            }
        }

        public void Log(List<string> arr){
            if (debug_flag == true){
                string shuturyoku = "";
                for (int i = 0; i < arr.Count; i++) {
                    shuturyoku += arr[i] + ",";
                }
                Console.WriteLine(shuturyoku.TrimEnd(','));
            }
        }

        public void Log(List<float> arr){
            if (debug_flag == true){
                string shuturyoku = "";
                for (int i = 0; i < arr.Count; i++) {
                    shuturyoku += arr[i] + ",";
                }
                Console.WriteLine(shuturyoku.TrimEnd(','));
            }
        }
        public void Log(){
            if (debug_flag == true){
                Console.WriteLine("アタイイレナサイ");
            }
        }
        public void FlagFalse(){
            debug_flag = false;
        }
        public void FlagTrue(){
            debug_flag = true;
        }
    }
}