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)

{-# OPTIONS_GHC -O2 #-}
{-# LANGUAGE BangPatterns          #-}
{-# LANGUAGE CPP                   #-}
{-# LANGUAGE MagicHash             #-}
{-# LANGUAGE MultiParamTypeClasses #-}
{-# LANGUAGE OverloadedStrings     #-}
{-# LANGUAGE TupleSections         #-}
{-# LANGUAGE TypeFamilies          #-}

import           Control.Applicative
import           Control.Monad
import           Control.Monad.Primitive
import           Control.Monad.ST
import           Control.Monad.State.Strict
import           Data.Bool
import qualified Data.ByteString             as B
import qualified Data.ByteString.Char8       as C
import qualified Data.ByteString.Unsafe      as B
import           Data.Char
import qualified Data.Foldable               as F
import           Data.Function
import qualified Data.IntMap.Strict          as IM
import qualified Data.IntSet                 as IS
import qualified Data.List                   as L
import qualified Data.Map.Strict             as M
import           Data.Monoid
import           Data.Ord
import           Data.Primitive.MutVar
import qualified Data.Set                    as S
import           Data.Tuple
import qualified Data.Vector                 as V
import qualified Data.Vector.Generic         as G
import qualified Data.Vector.Generic.Mutable as GM
import qualified Data.Vector.Unboxed         as U
import qualified Data.Vector.Unboxed.Mutable as UM
import           Debug.Trace
import           Foreign                     hiding (void)
import           GHC.Exts
import           Unsafe.Coerce

#define MOD 1000000007

main :: IO ()
main = do
    n <- readLn :: IO Int
    ws <- U.unfoldrN n B.uncons <$> B.getLine
    print $ solve ws

solve :: U.Vector Word8 -> Int
solve ws = (-% 1)
    . U.foldl' (*%) 1
    . U.unsafeAccumulate (+) (U.replicate 256 1)
    $ U.map (flip (,) 1 . fromIntegral) ws

infixr 8 ^%
infixl 7 *%, /%
infixl 6 +%, -%

type IntMod = Int

intMod :: Int -> IntMod
intMod x = mod x MOD

(+%) :: IntMod -> IntMod -> IntMod
(I# x#) +% (I# y#) = I# ((x# +# y#) `remInt#` MOD#)
{-# INLINE (+%) #-}

(-%) :: IntMod -> IntMod -> IntMod
(I# x#) -% (I# y#) = I# ((x# -# y# +# MOD#) `remInt#` MOD#)
{-# INLINE (-%) #-}

(*%) :: IntMod -> IntMod -> IntMod
(I# x#) *% (I# y#) = I# ((x# *# y#) `remInt#` MOD#)
{-# INLINE (*%) #-}

(/%) :: IntMod -> IntMod -> IntMod
(I# x#) /% (I# y#) = go# y# MOD# 1# 0#
  where
    go# a# b# u# v#
        | isTrue# (b# ># 0#) = case a# `quotInt#` b# of
            q# -> go# b# (a# -# (q# *# b#)) v# (u# -# (q# *# v#))
        | otherwise = I# ((x# *# (u# +# MOD#)) `remInt#` MOD#)
{-# INLINE (/%) #-}

(^%) :: IntMod -> Int -> IntMod
x ^% n
    | n > 0 = go 1 x n
    | n == 0 = 1
    | otherwise = go 1 (1 /% x) (-n)
  where
    go !acc !y !m
        | m .&. 1 == 0 = go acc (y *% y) (unsafeShiftR m 1)
        | m == 1 = acc *% y
        | otherwise = go (acc *% y) (y *% y) (unsafeShiftR (m - 1) 1)