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 Java8 (OpenJDK 1.8.0) (judge verdict: Runtime Error)

import java.io.File;
import java.util.ArrayList;
import java.util.HashMap;
import java.util.HashSet;
import java.util.List;
import java.util.Map;
import java.util.Properties;
import java.util.Scanner;
import java.util.Set;
import java.util.Stack;

public class Main {
	static Scanner sc = new Scanner(System.in);
	static Properties pps = System.getProperties();
	static boolean dbg = true;

	static long mod=1000000007;
	
	public static void main(String[] args) {
		// TODO Auto-generated method stub
		ns();
		String str=ns();
		solve(str);
	}


	private static long helper(long a) {
		long all=0;
		long a1=1;
		long a2=1;
		long b1=1;
		while(a!=0) {
			a1=a1*a;
			a2=a2*b1;
			b1++;
			long tmp=a1/a2;
			a--;
			all=(all+tmp)%mod;
		}
		return all;
	}
	

	
	private static void solve(String str) {
		// TODO Auto-generated method stub
		long count=helper(str.length());
		Map<Character,Long> m=new HashMap();
		for(char c:str.toCharArray()) {
			long k=m.getOrDefault(c, (long) 0)+1;
			m.put(c,k);
		}

		
		
		
		List<Character> l=new ArrayList();
		
		for(char c:m.keySet()) {
			if(m.get(c)==1)
				l.add(c);
				
		}
		for(char c:l)
			m.remove(c);
		long count2=1;
		long sum1=0;
		for(char c:m.keySet()) {
			sum1+=m.get(c);
			count2=count2*(1+m.get(c));
		}
		long number3=helper(sum1)-count2+1;
		long number4=helper(str.length()-sum1)+1;
		 number3=number3*number4;
		 System.out.println(count-number3);

	}



	public static void out(String str) {

		if (dbg)
			System.out.println(str);
	}

	public static void out(int str) {

		if (dbg)
			System.out.println(str);
	}

	public static int ni() {

		return sc.nextInt();

	}

	public static String ns() {

		return sc.nextLine();
	}

	public static int[] ni(int k) {
		int[] res = new int[k];
		for (int i = 0; i < k; i++)
			res[i] = sc.nextInt();
		sc.nextLine();
		return res;
	}

	public static String[] ns(int k) {
		String[] res = new String[k];
		for (int i = 0; i < k; i++)
			res[i] = sc.nextLine();
		return res;
	}

	public static int[][] ni(int a, int b) {
		int[][] res = new int[a][b];
		for (int i = 0; i < a; i++)
			for (int j = 0; j < b; j++)
				res[i][j] = sc.nextInt();
		sc.nextLine();
		return res;
	}
}