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 Haskell (GHC 7.10.3) (judge verdict: Accepted)

{-# LANGUAGE BangPatterns      #-} --引数に!
{-# LANGUAGE MultiWayIf        #-}
{-# LANGUAGE TupleSections     #-}

import Data.List

main :: IO ()
main = do
  _ <- getLine
  s <- getLine
  putStrLn $ show $ (foldl1' (\x y -> (mod0 $ x*y)) $ map (mod0.(+1).length) $ group $ sort s)-1

mod0 :: Int -> Int
mod0 n = if n < 1000000007 then n else mod n 1000000007