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 Ruby (2.3.3) (judge verdict: Time Limit Exceeded)

class Integer
  def combination(k)
    return 1 if k.zero?

    (self - k + 1..self).inject(:*) / k.factorial
  end

  def factorial
    return 1 if self.zero?

    (1..self).inject(:*)
  end
end

N = gets.to_i
S = gets.chomp
MOD = 10 ** 9 + 7

counter = Hash.new(0)

ans = 0

S.each_char do |s|
  c = 1

  counter.each do |key, v|
    next if key == s

    t = v.combination(1) + 1

    c = (c * t) % MOD
  end

  ans = (ans + c) % MOD
  counter[s] += 1
end

puts ans