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 abc119d
{
    class Program
    {
        static void Main(string[] args)
        {
            var N = ReadInt();
            var S = Console.ReadLine();
            var lc = new int[26];
            for (int i = 0; i < N; i++)
            {
                lc[S[i]-'a']++;
            }
            var sp = lc.Where(x => x != 0).ToList();
            var count = 1;
            var dp = new int[26];
            dp[0] = sp[0];
            while (true)
            {
                dp[count] = dp[count - 1] + dp[count - 1] * sp[count] + sp[count];
                count++;
                if (count == sp.Count) break;
            }
            
            Console.WriteLine(dp[count-1]);
#if DEBUG
            Console.ReadKey();
#endif
        }

        private static bool IsRange(int a, int from, int to) => (from <= a && a <= to);
        private static int ReadInt() => int.Parse(Console.ReadLine());
        private static List<int> ReadIntList() => Console.ReadLine().Split().Select(int.Parse).ToList();
        private static double ReadDouble() => double.Parse(Console.ReadLine());
        private static List<double> ReadDoubleList() => Console.ReadLine().Split().Select(double.Parse).ToList();
        private static long ReadLong() => long.Parse(Console.ReadLine());
        private static List<long> ReadLongList() => Console.ReadLine().Split().Select(long.Parse).ToList();
        private static List<int> Int2Digits(int a) => a.ToString().ToCharArray().Select(_ => int.Parse(_.ToString())).ToList();
        private static int BinarySearch<Type>(IReadOnlyList<Type> s, Type target) // target 以下の最大要素のインデックスを返す
            where Type : IComparable
        {
            var lower = 0;
            var upper = s.Count - 1;
            while (upper - lower > 1)
            {
                var mid = lower + (upper - lower) / 2;
                if (s[mid].CompareTo(target) <= 0)
                {
                    lower = mid;
                }
                else
                {
                    upper = mid;
                }

            }
            return lower;
        }
    }
}