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 <bits/stdc++.h>
typedef long long ll;
using namespace std;

int N;
vector<char> S;
set<char> charset;
map<char, vector<bool>> mask_map;

ll count(int pos, const vector<bool>& mask){
    if(pos == N-1){
        if(mask[pos]) return 2;
        else return 1;
    }else{
        if(!mask[pos]){
            return count(pos+1, mask);
        }else{
            vector<bool> update_mask = mask_map[S[pos]];
            for(int i=pos;i<N;i++){
                update_mask[i] = update_mask[i] &&  mask[i];
            }
            return count(pos+1, mask) + count(pos+1, update_mask);
        }
    }
}


signed main() {
    cin >> N;
    for(int i=0;i<N;i++){
        char a;
        cin >> a;
        S.push_back(a);
        charset.insert(a);
    }
    for(char moji:charset){
        vector<bool> mask(N,true);
        mask_map[moji] = mask;
    }
    for(int id=0;id<N;id++){
        mask_map[S[id]][id] = false;
    }

    vector<bool> init_mask(N,true);
    cout << count(0, init_mask) -1  << endl;

}