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

n = int(input())

dic = {}
for a in input():
    if not a in dic:
        dic[a] = 0
    dic[a] += 1
s = []
for k, v in dic.items():
    s.append([k, v])


def combinations(ls, r):
    if 1 == r:
        ans = []
        for l in ls:
            ans.append([l])
        return ans
    
    ans = []
    for i, l in enumerate(ls):
        left = [l]
        unused = ls[i + 1:len(ls)]
        for right in combinations(unused, r - 1):
            ans.append(left + right)
    return ans


total = 0
for i in range(1, len(s) + 1):
    ls = combinations(s, i)
    sub_total = 0
    for cmb in ls:
        num = 1
        for elm in cmb:
            num *= elm[1]
        sub_total += num
    total += sub_total

modulo = 10 ** 9 + 7
print(total % modulo)