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: Accepted)

import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.util.HashSet;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.io.BufferedWriter;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.util.InputMismatchException;
import java.io.IOException;
import java.util.ArrayList;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author Mufaddal Naya
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        OutputWriter out = new OutputWriter(outputStream);
        DStringEquivalence solver = new DStringEquivalence();
        solver.solve(1, in, out);
        out.close();
    }

    static class DStringEquivalence {
        ArrayList<String> aa;
        HashSet<String> hs;
        int n;

        public void solve(int testNumber, InputReader c, OutputWriter w) {
            n = c.readInt();
            aa = new ArrayList<>();
            hs = new HashSet<>();
            solve_(0, "");
            for (String str : aa) {
                w.printLine(str);
            }
        }

        private void solve_(int x, String s) {
            int check[] = new int[s.length()];
            int cr = 1;
            if (x == n) {
                for (int i = 0; i < s.length(); i++) {
                    if (check[i] == 0) {
                        for (int j = 0; j < s.length(); j++) {
                            if (s.charAt(j) == s.charAt(i)) {
                                check[j] = cr;
                            }
                        }
                        cr++;
                    }
                }
                String ss = "";
                for (int i = 0; i < check.length; i++) {
                    ss += check[i];
                    ss += ",";
                }
                if (!hs.contains(ss)) {
                    aa.add(s);
                    hs.add(ss);
                }
            } else {
                for (int i = 0; i < s.length(); i++) {
                    if (check[i] == 0) {
                        for (int j = 0; j < s.length(); j++) {
                            if (s.charAt(j) == s.charAt(i)) {
                                check[j] = cr;
                            }
                        }
                        cr++;
                    }
                }
                String ss = "";
                for (int i = 0; i < check.length; i++) {
                    ss += check[i];
                    ss += ",";
                }
                if (hs.contains(ss)) {
                    return;
                } else {
                    hs.add(ss);
                    for (char ch = 'a'; ch <= 'z'; ch++) {
                        solve_(x + 1, s + "" + ch);
                    }
                }
            }
        }

    }

    static class OutputWriter {
        private final PrintWriter writer;

        public OutputWriter(OutputStream outputStream) {
            writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
        }

        public OutputWriter(Writer writer) {
            this.writer = new PrintWriter(writer);
        }

        public void print(Object... objects) {
            for (int i = 0; i < objects.length; i++) {
                if (i != 0) {
                    writer.print(' ');
                }
                writer.print(objects[i]);
            }
        }

        public void printLine(Object... objects) {
            print(objects);
            writer.println();
        }

        public void close() {
            writer.close();
        }

    }

    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private InputReader.SpaceCharFilter filter;

        public InputReader(InputStream stream) {
            this.stream = stream;
        }

        public int read() {
            if (numChars == -1) {
                throw new InputMismatchException();
            }
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 0) {
                    return -1;
                }
            }
            return buf[curChar++];
        }

        public int readInt() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            int res = 0;
            do {
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public boolean isSpaceChar(int c) {
            if (filter != null) {
                return filter.isSpaceChar(c);
            }
            return isWhitespace(c);
        }

        public static boolean isWhitespace(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);

        }

    }
}