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)

import Data.Int
import Data.Char
import qualified Data.Vector.Unboxed as V
import qualified Data.Vector.Unboxed.Mutable as VM
import Control.Monad

mulMod :: Int64 -> Int64 -> Int64
mulMod a b = a * b `rem` (10^9 + 7)

main :: IO ()
main = do
  n <- readLn :: IO Int -- 1 <= n <= 100000
  s <- getLine -- length s == n
  let vec = V.create $ do
        vec <- VM.replicate 26 1
        forM_ s $ \c -> do
          VM.modify vec (+ 1) (ord c - ord 'a')
        return vec
  print $ (V.foldl' mulMod 1 vec - 1) `mod` (10^9 + 7)