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: Accepted)

#include <bits/stdc++.h>

using namespace std;
const int Mod = 1e9 + 7;

int n;
char s[200005];
int sum[30];

inline long long fsp(long long x, long long p) {
    long long res = 1;
    while (p) {
        if (p & 1) (res *= x) %= Mod;
        (x *= x) %= Mod;
        p >>= 1;
    }
    return res;
}

int main() {
    cin >> n;
    scanf("%s", s + 1);
    long long ans = 1;
    for (int i = 1; i <= n; ++i)
        sum[s[i] - 'a']++;
    for (int i = 0; i < 26; ++i)
        (ans *= sum[i] + 1) %= Mod;
    cout << ans - 1 << endl;
    return 0;
}