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: Time Limit Exceeded)

using System;
using System.Collections.Generic;
class Program
{
    static void Main(string[] args)
    {
        int len = int.Parse(Console.ReadLine());
        string input = Console.ReadLine();
        List<string> result = new List<string>();
        Dictionary<int, List<string>> dic = new Dictionary<int, List<string>>();

        for (int i = len - 1; i >= 0; i--) {
            List<string> list = new List<string>();
            string c = input.Substring(i, 1);
            list.Add(c);
            result.Add(c);
            for (int j = i + 1; j <= len - 1; j++) {
                if (dic.ContainsKey(j)) {
                    var temp = dic[j];
                    foreach (var data in temp) {
                        if (data.IndexOf(c) >= 0) {
                            continue;
                        }
                        var word = c + data;
                        list.Add(word);
                        result.Add(word);
                    }
                }
            }
            dic.Add(i, list);
        }

        Console.WriteLine(result.Count % (Math.Pow(10, 9) + 7));
    }
}