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: Time Limit Exceeded)

import Control.Monad
import Data.List

main = do
    _ <- getLine
    s <- getLine :: IO String
    print $ solve s (nub s)

comb :: Int -> [a] -> [[a]]
comb 0 xs = [[]]
comb _ [] = []
comb n (x:xs) = [x:y | y <- comb (n-1) xs] ++ comb n xs

solve :: String -> String -> Int 
solve s s'= sum $ [ (length . filter (\x -> length (nub x) == length x) $ comb i s ) `mod` (10^9 + 7) | i <- [1..length s']]