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: Runtime Error)

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();
            var dups = new int[N];
            var strTemp = str;
            for(int i =0;i<N-1;i++)
            {
                if(strTemp[i] != '_')
                {
                    var strSub = strTemp.Substring(i + 1);
                    dups[i] = strSub.Where(s => s == str[i]).Count();
                    strTemp = strTemp.Select(s => s == str[i] ? '_' : s).ToString();
                }
            }
            
            double ret = Math.Pow(2.0, N) - 1;
            for(int i=0;i<N;i++)
            {
                ret -= dups[i] == 0 ? 0 : Math.Pow(2.0, dups[i]);
            }
            Console.WriteLine(ret);
        }
    }
}