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: Wrong Answer)

import java.io.PrintStream;
import java.util.ArrayList;
import java.util.Collections;
import java.util.Scanner;

public class Main {
	public static void main(String[] args) throws Exception{
		new Main(new Scanner(System.in), System.out, System.err).exec();
	}
	public final Scanner sc;
	public final PrintStream out, err;
	public Main(final Scanner sc, final PrintStream out, final PrintStream err) {
		this.sc = sc;this.out = out;this.err = err;
	}
	static public final long pair(int a, int b) {return (((long)a) << 32) + b;}
	static public final int getPair1(long v) {return (int)(v >> 32);}
	static public final int getPair2(long v) {return (int)(v & 0xFFFFFFFF);}

	static public final long quad(long a, long b, long c, long d) {
		return ((a&0xFFFF)<< 48) + ((b&0xFFFF)<< 32) + ((c&0xFFFF)<< 16) +(d&0xFFFF);}
	static public final int getQuad1(long v) {return (int)( v >> 48          );}
	static public final int getQuad2(long v) {return (int)((v >> 32) & 0xFFFF);}
	static public final int getQuad3(long v) {return (int)((v >> 16) & 0xFFFF);}
	static public final int getQuad4(long v) {return (int)( v        & 0xFFFF);}

	static public final long record(int e, int m, int i) {
		return quad(-1, e, m, i);
	}
	static public final int re(long record) {
		return getQuad2(record);
	}
	static public final int rm(long record) {
		return getQuad3(record);
	}
	static public final int ri(long record) {
		return getQuad4(record);
	}

	//------------------------------------------

	private int p;
	private int[] inv;
	private int[] fact;
	private int[] finv;
	public final int mod(long v) {
		return mod(v, p);
	}
	static public final int mod(long v, int M) {
		v %= M;
		return (int)(v < 0 ? v+M : v);
	}
	/**
	 * a * b (mod p)
	 * 事前にinitFactを行うこと。
	 */
	public final int mul(long a, long b) {
		return mod(a*b);
	}
	public final void initFact(double limit, double p) {
		initFact((int)limit, (int)p);
	}
	/**
	 * 集合数nの組み合わせ計算を高速化するため、事前に計算を行う。
	 * 組み合わせ数はpで割った余りを算出する。
	 */
	public final void initFact(int n, int p) {
		this.p = p;
		this.inv = new int[n+1];
		this.fact = new int[n+1];
		this.finv = new int[n+1];
		fact[1] = finv[1] = inv[0] = inv[1] = 1;
		for(int i=2;i<=n;i++) {
			int a = p / i;
			int b = p % i;
			inv[i]  = mul(-a, inv[b]);
			fact[i] = mul(fact[i-1], i);
			finv[i] = mul(finv[i-1], inv[i]);
		}
	}
	/**
	 * mCnを計算する。事前にinitFactを実行すること。
	 */
	public final int comb(int m, int n) {
		return mul(mul(fact[m], finv[n]), finv[m-n]);
	}
	/**
	 * a^b (mod M)を計算する。
	 */
	public static long pow(long a, long b, int M) {
		long ret = 1;
		long tmp = a;
		while (b > 0) {
			if ((b & 1) == 1) {
				ret = (ret * tmp) % M;
			}
			tmp = (tmp * tmp) % M;
			b = b >> 1;
		}
		return ret;
	}
	/**
	 * nCk (mod M)を計算する。
	 */
	public static int nCk(int n, int k, int M) {
		long ret = 1;
		int min = Math.min(k, n - k);
		// 分母
		for (int i = 1; i <= min; i++) {
			// a^-1 ≡ a^M-2  ※フェルマーの小定理
			ret = (ret * pow(i, M - 2, M)) % M;
		}
		// 分子
		for (int i = n - min + 1; i <= n; i++) {
			ret = (ret * i) % M;
		}
		return (int) ret;
	}
	//------------------------------------------
	static long lcm (long a, long b) {
		long temp;
		long c = a;
		c *= b;
		while((temp = a%b)!=0) {
			a = b;
			b = temp;
		}
		return (long)(c/b);
	}

	//------------------------------------------

	static class DisjointSetUnion {
		public int[] parent;
		public int[] weight;
		public int count;

		public DisjointSetUnion(int nodes) {
			count = nodes;
			parent = new int[nodes];
			weight = new int[nodes];
			for (int i = 0; i < nodes; i++) {
				parent[i] = i;
				weight[i] = 1;
			}
		}
		//"find"
		public int root(int p) {
			while (p != parent[p]) {
				p = parent[p];
			}
			return p;
		}

		//"union"
		public void connect(int p, int q) {
			int rootP = root(p);
			int rootQ = root(q);
			if (rootP == rootQ) return;
			if (weight[rootP] < weight[rootQ]) {
				parent[rootP] = rootQ;
				weight[rootQ] += weight[rootP];
			} else {
				parent[rootQ] = rootP;
				weight[rootP] += weight[rootQ];
			}
			count--;
		}

		public boolean connected(int p, int q) {
			return root(p) == root(q);
		}
	}
	static class IntList{
		int tail = 0;
		final int[] element;
		public IntList(int cap) {
			element = new int[cap];
		}
		public int size() {
			return tail;
		}
		public int get(int index) {
			return element[index];
		}
		public void reset() {
			tail = 0;
		}
		public void add(int v) {
			element[tail++] = v;
		}
	}

	public void exec() throws Exception{
		final int N = sc.nextInt();
		final int max = 1 << (N-1);
		ArrayList<String> list = new ArrayList<>(1024);
		StringBuilder sb = new StringBuilder();
		for(int i=0;i<max;i++) {
			sb.append("a");
			int mask = i;
			char c[] = new char[] {'a', 'b'};
			int index = 0;
			for(int n=0;n<N-1;n++) {
				if((mask & 0x1) == 1) {
					index = (index+1) & 0x1;
				}
				sb.append(c[index]);
				mask = (mask >> 1);
			}
			list.add(sb.toString());
			sb.setLength(0);
		}
		Collections.sort(list);
		for(String str : list) {
			out.println(str);
		}
	}
}