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 8.8.3) (judge verdict: Time Limit Exceeded)

import qualified Data.ByteString.Char8 as BS
import Data.List
import Data.Maybe

readInt = fromIntegral . fst . fromJust . BS.readInteger

readString = map BS.unpack . BS.words

getInt = readInt <$> BS.getLine

getString = readString <$> BS.getLine

powerset :: [a] -> [[a]]
powerset [] = [[]]
powerset (x:xs) = [x:ps | ps <- powerset xs] ++ powerset xs

product' :: [Int] -> Int -> Int
product' [] p = p
product' (x : xs) p = product' xs (x * p `mod` (10 ^ 9 + 7))

calc :: [[Int]] -> Int -> Int
calc [] n = n
calc (p : ps) n = calc ps (((product' p 1) + n) `mod` (10 ^ 9 + 7))

main = do
  n <- getInt
  [s] <- getString
  let s' = map length (group (sort s))
  let ps = powerset s'
  print $ calc (init ps) 0