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.lang.reflect.Array;
import java.util.*;

public class Main {
    public static void main(String[] args) {
        int N;
        String S;
        long MOD_NUM = 1000_000_007;
        List<Long> list = new ArrayList<>();
        try (Scanner sc = new Scanner(System.in)) {
            N = sc.nextInt();
            S = sc.next();
        }

        char[] chS = S.toCharArray();
        Set<Character> set = new HashSet<>(24);
        Map<Character, Integer> map = new HashMap<>(24);
        for (Character c : chS) {
            set.add(c);
            Integer v = map.getOrDefault(c, 0);
            map.put(c, ++v);
        }

        int typeNum = set.size();
        int[] arr = new int[typeNum];
        int index = 0;
        for (Map.Entry<Character, Integer> entry :map.entrySet()) {
            int value = entry.getValue();
            arr[index] = value;
            index++;
        }

        long result = 0;
        for (int i = 0; i < (1 << typeNum); i++) {
            long temp = 0;
            for (int j = 0; j < typeNum; j++) {
                if ((i & (1 << j)) != 0) {
                    if (temp == 0) {
                        temp = arr[j];
                    }else{
                        temp *= arr[j];
                    }
                    temp = temp % MOD_NUM;
                }
            }
            result += temp;
            result = result % MOD_NUM;
        }


        System.out.println(result);
    }


}