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;
using System.Text;
using System.Threading.Tasks;

namespace Grand031
{
    class Program
    {
        static void Main(string[] args)
        {
            var N = int.Parse(Console.ReadLine());
            var str = Console.ReadLine().ToArray();
            var dups = new int[N];
            int ret = 1; //last 1 char
            for(int i =0;i<N-1;i++)
            {
                var strTemp = str;
                int thisRet = 1;
                for(int j = i + 1; j < N; j++)
                {
                    if (strTemp[j] != '_' && strTemp[j] != str[i])
                    {
                        var strSub = strTemp;
                        var dup = strSub.ToArray().Where((s,k) => s == str[j] && k>=i).ToArray().Length - 1;
                        strTemp = strTemp.Select(s => s == str[j] ? '_' : s).ToArray();
                        thisRet *= dup == 0 ? 2 : dup + 2;
                    }
                }
                ret += thisRet;
                
            }
            Console.WriteLine(ret);
        }
    }
}