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++ (GCC 9.2.1) (judge verdict: Accepted)

#include <bits/stdc++.h>
#define rep(i, n) for (int i = 0; i < (n); ++i)
#define zero_pad(num) setfill('0') << std::right << setw(num)
using namespace std;
using ll = long long;
using ld = long double;
using P = pair<int, int>;

int main() {
    int n;
    cin >> n;
    string s;
    cin >> s;
    map<char, int> mp;
    rep(i, n)mp[s[i]]++;
    int m = mp.size();
    vector<vector<ll>> dp(m+1, vector<ll>(2, 0));
    dp[0][0] = 1;
    ll mod = 1000000007;
    int cnt = 0;
    for(auto p : mp){
        ll c = p.second;
        dp[cnt+1][0] = (dp[cnt][0] + dp[cnt][1]) % mod;
        dp[cnt+1][1] = (dp[cnt][0] + dp[cnt][1]) % mod * c % mod;
        cnt++;
    }
    ll ans = (dp[m][0] + dp[m][1] - 1 + mod) % mod;
    cout << ans << endl;
}