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;
using System.Linq;


namespace AtC
{
    class Program
    {
        static void Main(string[] args)
        {
            var N = ulong.Parse(Console.ReadLine());
            var S = Console.ReadLine();

            ulong[] counts = new ulong['z' - 'a' + 1];

            foreach (var c in S)
            {
                counts[c - 'a']++;
            }

            var list = counts.Where(val => val != 0).ToList();

            ulong count = 0;
            for (var i = 0; i < list.Count; i++)
            {
                count += Count(i + 1, list) / Factrial((ulong) (i + 1));
                count %= 1000000007;
            }

            Console.WriteLine(count);
        }

        static ulong Factrial(ulong n)
        {
            if (n <= 1) return 1;
            return n * Factrial(n - 1);
        }

        static ulong Count(int d, List<ulong> counts)
        {
            if (d == 1)
            {
                ulong count = 0;
                counts.ForEach(val => { count += val; });
                return count;
            }

            ulong c = 0;
            for (var index = 0; index < counts.Count; index++)
            {
                var count = counts[index];
                var list = counts.ToList();
                list.RemoveAt(index);
                c += count * Count(d - 1, list);
            }

            return c;
        }
    }
}