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 <algorithm>
#include <cassert>
#include <cctype>
#include <climits>
#include <cmath>
#include <complex>
#include <cstdio>
#include <cstring>
#include <deque>
#include <functional>
#include <iomanip>
#include <iostream>
#include <map>
#include <numeric>
#include <queue>
#include <random>
#include <set>
#include <stack>
#include <string>
#include <tuple>
#include <vector>
#define rep(i, n) for (int i = 0; i < (int)(n); ++i)
//#define cerr if(false) cerr
#define show(...) cerr << #__VA_ARGS__ << " = ",debug(__VA_ARGS__);
using namespace std;
using ll = long long;
using pii = pair<int,int>;
template<typename T, typename S>
ostream &operator<<(ostream &os,pair<T,S>a){
    os << '(' << a.first << ',' << a.second << ')';
    return os;
}
template<typename T>
ostream &operator<<(ostream &os, vector<T> v){
    for(auto x:v)os << x << ' ';
    return os;
}
void debug(){cerr << '\n';}
template<typename H, typename... T>
void debug(H a, T... b){
    cerr << a;
    if(sizeof...(b))cerr << ", ";
    debug(b...);
}
ll mod=1000000007;
ll combi(ll N_, ll C_) {
    const int NUM_=400001;
    static ll fact[NUM_+1],factr[NUM_+1],inv[NUM_+1];
    if (fact[0]==0) {
        inv[1]=fact[0]=factr[0]=1;
        for (int i=2;i<=NUM_;++i) inv[i] = inv[mod % i] * (mod - mod / i) % mod;
        for (int i=1;i<=NUM_;++i) fact[i]=fact[i-1]*i%mod, factr[i]=factr[i-1]*inv[i]%mod;
    }
    if(C_<0 || C_>N_) return 0;
    return factr[C_]*fact[N_]%mod*factr[N_-C_]%mod;
}
ll hcomb(ll P_, ll Q_) { return (P_==0&&Q_==0)?1:combi(P_+Q_-1,Q_);}

ll modpow(ll a, ll n = mod-2) {
    ll r=1;
    while(n) r=r*((n%2)?a:1)%mod,a=a*a%mod,n>>=1;
    return r;
}
int main(){
    int n;
    string s;
    cin >> n >> s;
    ll cnt[26] = {};
    rep(i,n)cnt[s[i]-'a']++;
    int num = 0;
    rep(i,26)cnt[i]++;
    ll ans = 1;
    rep(i,26){
        ans = (ans * cnt[i]) % mod;
    }
    cout << (ans -1 + mod)%mod << endl;
    
}