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 Java8 (OpenJDK 1.8.0) (judge verdict: Time Limit Exceeded)

import java.util.HashSet;
import java.util.Scanner;
import java.util.Set;

public class Main {

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int N = sc.nextInt();
        String S = sc.next();

        Set<Character> set = new HashSet<>();
        set.add(S.charAt(0));
        int i = dft(S,1,set);
        set.remove(S.charAt(0));

        i += dft(S,1,set);

        System.out.println(i);
    }

    static int mod = (int) (Math.pow(10,9) + 7);
    static int dft(String S, int idx , Set set){

        if(idx== S.length() ){
            if(set.size()>0) return 1;
            return 0;
        }
        char c = S.charAt(idx);

        int i =0;
        //use this char
        if(set.contains(c)){
            i += 0 ;
        }else{
            set.add(c);
            i += dft(S,idx+1,set);
            set.remove(c);
        }

        i+=dft(S,idx+1,set);

        if(i > mod ){
            return  i % mod;
        }
        return i;
    }

}