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: Accepted)

using System;
using System.Collections.Generic;
using System.Diagnostics;
using System.Text;
using System.Linq;
using static System.Math;

class Program
{
    static char[] alp = "abcdefghijklmnopqrstuvwxyz".ToCharArray();

    static void Main()
    {
        int N = int.Parse(Console.ReadLine());
        string s = Console.ReadLine();
        char[] alp = "abcdefghijklmnopqrstuvwxyz".ToCharArray();
        long[] c = new long[alp.Length];

        long ans = 1;
        for (int i = 0; i < N; i++)
        {
            c[Inv(s[i])]++;
        }

        for (int i = 0; i < alp.Length; i++)
        {
            ans *= c[i] + 1;
            ans %= (long)1e9 + 7;
        }

        Console.WriteLine((ans + (long)1e9 + 6) % ((long)1e9 + 7));
    }

    static int Inv(char c)
    {
        for (int i = 0; i < alp.Length; i++)
            if (c == alp[i]) return i;
        return -1;
    }
}