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.Linq;
using System.Text;
using System.IO;
static class Program{
	const int mod=1000000007;
	static void Main(){
		Sc sc=new Sc();
		int n=sc.I;
		string s=sc.S;
		s=" "+s;
		int[] h=new int[26];
		long[] dp=new long[s.Length];
		long m=0;
		for(int i=s.Length-1;i>0;i--){
			h[s[i]-'a']++;
			dp[i]=(1+m)%mod;
			if(h[s[i]-'a']>1){dp[i]=(dp[i]*Mi(h[s[i]-'a']))%mod;}
			m=(m+dp[i])%mod;
		}
		Console.WriteLine("{0}",m);
	}
	static long Mi(long a){
		long b=mod,u=1,v=0;
		while(b>0){
			long t=a/b;
			a-=t*b;a^=b;b^=a;a^=b;
			u-=t*v;u^=v;v^=u;u^=v;
		}
		u%=mod;
		if(u<0){u+=mod;}
		return u%mod;
	}
}

public class Sc{
	public int I{get{return int.Parse(Console.ReadLine());}}
	public long L{get{return long.Parse(Console.ReadLine());}}
	public double D{get{return double.Parse(Console.ReadLine());}}
	public string S{get{return Console.ReadLine();}}
	public int[] Ia{get{return Array.ConvertAll(Console.ReadLine().Split(),int.Parse);}}
	public int[] Ia2{get{return Array.ConvertAll(("0 "+Console.ReadLine()).Split(),int.Parse);}}
	public long[] La{get{return Array.ConvertAll(Console.ReadLine().Split(),long.Parse);}}
	public long[] La2{get{return Array.ConvertAll(("0 "+Console.ReadLine()).Split(),long.Parse);}}
	public double[] Da{get{return Array.ConvertAll(Console.ReadLine().Split(),double.Parse);}}
	public string[] Sa{get{return Console.ReadLine().Split();}}
}