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 Fortran (gfortran v4.8.4) (judge verdict: Accepted)

program name
    use,intrinsic :: iso_fortran_env
    implicit none
    integer(int64):: i,j,n,cnt(ichar('a'):ichar('z')),ans
    integer(int64),parameter:: md=1000000007
    character(100000):: s
    
    read*, n
    read*, s
    cnt(:) = 1
    do i=1,n
        cnt(ichar(s(i:i)))=cnt(ichar(s(i:i)))+1
    end do

    ans = 1
    do i=ichar('a'),ichar('z')
        ans=mod(ans*cnt(i),md)
    end do
    print'(i0)', ans-1
end program name