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.Scanner;

public class Main {
  final static int MOD = 1000000007;

  public static void main (String[] args) {
    Scanner in = new Scanner(System.in);

    while (in.hasNext()) {
      int N = in.nextInt();
      String S = in.next();
      boolean[] discovered = new boolean[26];
      long count = count(0, S, discovered) % MOD;

      System.out.println(count);
    }
  }

  private static long count (int cur, String s,boolean[] discovered) {
    if (cur == s.length()) {
      for (int i = 0; i < discovered.length; ++i) {
        if (discovered[i]) {
          return 1;
        }
      }
      
      return 0;
    } else {
      boolean isAllDiscovered = true;
      
      for (int i = 0; i < discovered.length; ++i) {
        if (discovered[i] == false) {
          isAllDiscovered = false;
          break;
        }
      }

      if (isAllDiscovered) {
        return 1;
      } else {
        long num = 0;
        if (discovered[s.charAt(cur) - 'a'] == false) {
          discovered[s.charAt(cur) - 'a'] = true;
          num += count(cur + 1, s, discovered) % MOD;
          discovered[s.charAt(cur) - 'a'] = false;
        }

        num += count(cur + 1, s, discovered) % MOD;

        return num % MOD;
      }
    }
  }
}