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# (Mono 4.6.2.0) (judge verdict: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Linq;

class Program
{
    static int N;
    static char[] chr;
    static int count = 0;
    static void Main(string[] args) {
        N = int.Parse(Console.ReadLine());
        chr = Console.ReadLine().ToCharArray();
        int mod = 1000000007;
        Console.WriteLine(dfs(0, 0)%mod);
    }
    static int dfs(int n, int m) {//n=スタートの文字, m=現在の位置
        if (n == N-1) {
            count ++;
            return count;
        }
        for (int i = m; i<N; i ++) {
            if (i > 0 && chr[n]==chr[m]) break;
            else {
                count ++;
                dfs(n, m+1);
            }
        }
        return count;
    }
}