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++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
#include<bits/stdc++.h>
using namespace __gnu_pbds;
using namespace std;
#define ll long long int
#define ull unsigned long long int
#define ff first 
#define ss second
#define pb(x) push_back(x)
#define pf(x) push_front(x)
#define start_routine() int begtime = clock();
#define end_routine() int endtime = clock(); \
                      cerr << "\n\n" << "Time elapsed: " << \
                      (endtime - begtime)*1000/CLOCKS_PER_SEC << " ms\n\n"; \
                      return 0
#define testcase(t) int t;cin>>t;while(t--)
#define mp(x,y) make_pair(x,y)
#define in(x) insert(x)
#define rep(i,a,b)  for (__typeof((b)) i=(a);i<=(b);i++)
#define nrep(i,a,b)  for (__typeof((b)) i=(b);i>=(a);i--)
#define PI 3.14159265358979323846
#define SP(x) setprecision(x)
#define reflex ios_base::sync_with_stdio(false);cin.tie(NULL);cout.tie(NULL)
#define M 1000000007
#define sz(a) (int)a.size()
#define endl "\n"
#define all(v) v.begin(), v.end()
#define UNIQUE(x) x.resize(distance(x.begin(), unique(all(x))))
#define mem(arr,val) memset(arr,val,sizeof(arr)) //For "0" and "-1"                  
#define inp0(a,n) rep(i,0,n-1) cin>>a[i];
#define inp1(a,n) rep(i,1,n) cin>>a[i]; 
#define prll(x) printf("%lld",x)
#define nth_ele(v,n) nth_element(v.begin(), v.begin()+n ,v.end())//O(N)
#define DEBUG(x) cerr << (#x) << ": " << (x) << endl
#define DEBUGV(x) for(auto IT:x) cout<<IT<<" "; cout<<endl;
#define minheap priority_queue <int, vector<int>, greater<int>>
typedef pair<int,int> pii;
typedef pair<ll,ll> pll;
typedef tree< int, null_type, less<int>, rb_tree_tag, tree_order_statistics_node_update> ordered_set;
ll gcd(ll n1, ll n2){if(n2!=0) return gcd(n2, n1%n2);else return n1;}
ll powerM(ll a,ll b){if(b==0) return 1;  if(b==1) return a%M; ll x=powerM(a,b/2)%M; if(b&1){return ((((a%M)*(x%M))%M)*(x%M))%M;}return ((x%M)*(x%M))%M;}
ll power(ll a,ll b){if(b==0) return 1;  if(b==1) return a; ll x=power(a,b/2); if(b&1){return ((((a)*(x)))*(x));}return ((x)*(x));}
 
const ll INF=1e18; 
const int SIZE = 100006;



int main(){
	int n;
	cin>>n;
	ll xx=(1<<(n-1))-1;
	rep(i,0,xx){
		ll mask = i;
		nrep(j,0,n-1){
			if(mask&(1<<j)) cout<<"b";
			else cout<<"a";
		}
		cout<<endl;
	}	
}