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())
S = input()
D = 10**9+7

d = {}
for i,n in enumerate(S):
    if n in d.keys():
        d[n] += 1
    else:
        d[n] = 1

count = 0
for i in range(1,len(d.keys())+1):
    for p in list(itertools.combinations(d.keys(),i)):
        tmp = 1
        for c in p:
            tmp *= d[c]
        count += tmp
print(count%D)