Problem:
Score : 200 points

Problem Statement

You are given a string S of length N.
Among its subsequences, count the ones such that all characters are different, modulo 10^9+7. Two subsequences are considered different if their characters come from different positions in the string, even if they are the same as strings.

Here, a subsequence of a string is a concatenation of one or more characters from the string without changing the order.

Constraints

1 \leq N \leq 100000

S consists of lowercase English letters.

|S|=N

Input

Input is given from Standard Input in the following format:

N
S

Output

Print the number of the subsequences such that all characters are different, modulo 10^9+7.

Sample Input 1

4
abcd

Sample Output 1

15

Since all characters in S itself are different, all its subsequences satisfy the condition.

Sample Input 2

3
baa

Sample Output 2

5

The answer is five: b, two occurrences of a, two occurrences of ba. Note that we do not count baa, since it contains two as.

Sample Input 3

5
abcab

Sample Output 3

17

Solution in C++14 (GCC 5.4.1) (judge verdict: Time Limit Exceeded)

#include<algorithm>
#include<complex>
#include<ctype.h>
#include<iomanip>
#include<iostream>
#include<fstream>
#include<map>
#include<math.h>
#include<numeric>
#include<queue>
#include<set>
#include<stack>
#include<stdio.h>
#include<string>
#include<string>
#include<vector>

using namespace std;
typedef long long ll;

#define FOR(i,a,b) for(ll i=(a);i<(b);++i)
#define ALL(v) (v).begin(), (v).end()
#define p(s) cout<<(s)<<endl
#define p2(s, t) cout << (s) << " " << (t) << endl
#define br() p("")
#define pn(s) cout << (#s) << " " << (s) << endl
#define p_yes() p("Yes")
#define p_no() p("No")

const ll mod = 1e9 + 7;
const ll inf = 1e18;

template < typename T >
void vprint(T &V){
	for(auto v : V){
    	cout << v << " ";
	}
	cout << endl;
}

int main(){
    cin.tie(0);
    ios::sync_with_stdio(false);

    // input
    ll N;
    cin >> N;

    string s;
    cin >> s;

    map<char, ll> mp;
    for(char c : s){
        mp[c]++;
    }

    ll L = mp.size();
    vector<ll> A;
    for(auto p : mp){
        ll count = p.second;
        A.push_back(count);
    }

    ll sum = 0;
    FOR(i, 1, 1<<L){
        ll a = 1;
        FOR(j, 0, L){
            if(i>>j & 1){
                // j番目を使う
                a *= A[j];
                a %= mod;
            }
        }
        sum += a;
        sum %= mod;
    }

    p(sum);
    
    return 0;
}