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
str = gets

def count(str, h = {})
  return 2 if str.length == 1
  return h[str] if h[str]
  
  str2 = str.chars.reject { |c| str[0] == c }.join('')
  h[str] = if str2.length > 0
             count(str[1..-1], h) + count(str2, h)
           else
             count(str[1..-1], h) + 1
           end
end

puts count(str.strip) - 1