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: Wrong Answer)

{-# LANGUAGE BangPatterns #-}
{-# LANGUAGE ScopedTypeVariables #-}
{-# LANGUAGE TupleSections #-}
{-# LANGUAGE RankNTypes #-}
import qualified Data.ByteString.Lazy.Char8 as B
import Data.Maybe
import Data.Char
import Data.List
import qualified Data.Vector.Unboxed as VU
import qualified Data.Vector.Unboxed.Mutable as VUM
import Control.Monad
-- import Control.Monad.ST
-- import Debug.Trace
-- trace _ = id

solve :: Int -> String -> Int
solve n s = (VU.foldl' (*) 1 cnts) - 1
  where
  cnts = VU.create $ do
    vec <- VUM.replicate 26 1
    forM_ s $ \c -> do
      let i = ord c - ord 'a'
      VUM.modify vec (+ 1) i
    return vec



readBInt :: B.ByteString -> Int
readBInt = fst . fromJust . B.readInt

tmain :: B.ByteString -> Int
tmain cont =
  let remLines0 = map B.words (B.lines cont)
      [bs_n]:remLines1 = remLines0
      n = readBInt bs_n
      [bs_s]:remLines2 = remLines1
      s = B.unpack bs_s
  in solve n s

outAnswer :: Int -> IO ()
outAnswer = putStrLn . show

main :: IO ()
main = outAnswer . tmain =<< B.getContents


-------------------------------------------------------------------------------

inp1 = "4\nabcd\n"
inp2 = "3\nbaa\n"
inp3 = "5\nabcab\n"
tv1 = tmain $ B.pack inp1
tv2 = tmain $ B.pack inp2
tv3 = tmain $ B.pack inp3
test1 = tv1 == 15
test2 = tv2 == 5
test3 = tv3 == 17
alltest = test1 && test2 && test3