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)

n=gets.chomp.to_i
s=gets.chomp.split("")

result = []
1.upto(2**n) do |i|
  tmp = []
  i.to_s(2).rjust(n, '0').split("").each_with_index do |o, idx|
    tmp << s[idx] if o == "1"
  end
  result << tmp.join() if tmp.size == tmp.uniq.size
end

p (result.size-1) % 1000000007