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: Wrong Answer)

import java.util.Map;
import java.util.Scanner;
import java.util.TreeMap;

public class Main {

	public static void main(String[] args) {
		Scanner in = new Scanner(System.in);
		long n = in.nextLong();
		String s = in.next();
		long ret = 1;
		Map<Character, Integer> found = new TreeMap<>();

		for (int i = 0; i < n; i++) {
			// ただし以前に現れた文字だった場合はその組み合わせの数だけ減る
			char c = s.charAt(i);
			Integer cnt = found.get(c);
			//System.out.printf("r: %d\n", ret);
			if (cnt == null) {
				found.put(c, 1);
				//System.out.printf("! [%d] : '%c'\n", i, c);

				// とる場合ととらない場合の2倍ずつ増える
				ret *= (2);
			} else {
				found.put(c, cnt + 1);
				//System.out.printf("# [%d] : '%c' (%d)\n", i, c, cnt);
				// 今回取らない場合は全採用できる。少なくとも1倍以上。
				// 今回取る場合、以前に現れた同じ字がすべてOFFの場合、残りの文字数の組み合わせの数だけ増える。
				ret += Math.pow(2, i - cnt) - 1;
			}
		}
		// 最後に長さ0の数を惹く。
		ret --;
		ret %= (1_000_000_000L + 7);
		System.out.println(ret);
	}

}