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 Python (3.4.3) (judge verdict: Time Limit Exceeded)

import itertools
def foo():
  N = int(input())
  S = input()

  count = N
  combination = [list(map(set, list(itertools.combinations(S, n + 1)))) for n in range(1, N)]
  for n in range(1, N):
    comb = combination[n - 1]  # list(itertools.combinations(S, n + 1))

    c = 0
    for sub_s in comb:
      if len(sub_s) == n + 1:
        c += 1

    count += c

  print(count % int(pow(10, 9) + 7))


if __name__ == "__main__":
  foo()