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 Scala (2.11.7) (judge verdict: Time Limit Exceeded)

import scala.io.StdIn._

object Main extends App {
  val n = readLine.toInt
  val s = readLine.toList

  val MOD = 1000000007
  val values: List[Int] = s.groupBy(identity).mapValues(_.length).values.toList

  def combination(res: List[List[Int]], list: List[Int]): List[List[Int]] = list match {
    case Nil => res
    case h :: t => combination(res.map(l => h +: l) ++ res, t)
  }

  val res = combination(List(List()), values)
    .filter(!_.isEmpty)
    .map(l => l.foldLeft(1L)((acc, h) => acc * h % MOD))
    .foldLeft(0L)((acc, h) => (acc + h) % MOD)

  println(res)
}