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

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

Examples

Input

1


Output

a


Input

2


Output

aa
ab
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.NoSuchElementException;

class Main {
	public static void main(String[] args) {
		new Main().run();
	}
	
	ArrayList<Long> list=new ArrayList<>();
	long[] p26=new long[10];
	{
		p26[0]=1;
		for(int i=1;i<p26.length;++i)p26[i]=26*p26[i-1];
	}
	void dfs(int mask,int cur,long v,int n) {
		if(mask==0) {
			list.add(v);
			return;
		}
		int p=n-1;
		while((mask&(1<<p))==0)--p;
		int nmask=mask^(1<<p);
		for(int s=nmask;s>=0;s=(s-1)&nmask) {
			long nv=v+p26[p]*cur;
			for(int shift=0;shift<n;++shift) {
				if((s&(1<<shift))>0)nv+=p26[shift]*cur;
			}
			dfs(nmask^s,cur+1,nv,n);
			if(s==0)break;
		}
	}
	
	void run() {
		FastScanner sc=new FastScanner();
		int N=sc.nextInt();
		dfs((1<<N)-1,0,0,N);
		Collections.sort(list);
		ArrayList<String> slist=new ArrayList<>();
		PrintWriter pw=new PrintWriter(System.out);
		for(long v:list) {
			String ans="";
			for(int i=0;i<N;++i) {
				ans=String.valueOf((char)('a'+v%26))+ans;
				v/=26;
			}
			slist.add(ans);
		}
		Collections.sort(slist);
		for(int i=0;i<slist.size();++i) {
			pw.println(slist.get(i));
		}
		pw.close();
	}
	
	void tr(Object...objects) {System.out.println(Arrays.deepToString(objects));}
}


class FastScanner {
    private final InputStream in = System.in;
    private final byte[] buffer = new byte[1024];
    private int ptr = 0;
    private int buflen = 0;
    private boolean hasNextByte() {
        if (ptr < buflen) {
            return true;
        }else{
            ptr = 0;
            try {
                buflen = in.read(buffer);
            } catch (IOException e) {
                e.printStackTrace();
            }
            if (buflen <= 0) {
                return false;
            }
        }
        return true;
    }
    private int readByte() { if (hasNextByte()) return buffer[ptr++]; else return -1;}
    private static boolean isPrintableChar(int c) { return 33 <= c && c <= 126;}
    public boolean hasNext() { while(hasNextByte() && !isPrintableChar(buffer[ptr])) ptr++; return hasNextByte();}
    public String next() {
        if (!hasNext()) throw new NoSuchElementException();
        StringBuilder sb = new StringBuilder();
        int b = readByte();
        while(isPrintableChar(b)) {
            sb.appendCodePoint(b);
            b = readByte();
        }
        return sb.toString();
    }
    public long nextLong() {
        if (!hasNext()) throw new NoSuchElementException();
        long n = 0;
        boolean minus = false;
        int b = readByte();
        if (b == '-') {
            minus = true;
            b = readByte();
        }
        if (b < '0' || '9' < b) {
            throw new NumberFormatException();
        }
        while(true){
            if ('0' <= b && b <= '9') {
                n *= 10;
                n += b - '0';
            }else if(b == -1 || !isPrintableChar(b)){
                return minus ? -n : n;
            }else{
                throw new NumberFormatException();
            }
            b = readByte();
        }
    }
    public int nextInt() {
        long nl = nextLong();
        if (nl < Integer.MIN_VALUE || nl > Integer.MAX_VALUE) throw new NumberFormatException();
        return (int) nl;
    }
    public double nextDouble() { return Double.parseDouble(next());}
}