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 sys
sys.setrecursionlimit(100000)

n = int(input())
s = input()
s_set = set(s)
S = []
for i in s_set:
    S.append(s.count(i))

def cal(n, S):
    if n == 1:
        return sum(S)
    if n == 2:
        ans = 0
        for i in range(len(S) - 1):
            for j in range(i+1, len(S)):
                ans += S[i] * S[j]
                ans %= 10 ** 9 + 7
        return ans
    else:
        ans = 0
        for i in range(len(S) - n + 1):
            ans += S[i] * cal(n-1, S[i+1:])
            ans %= 10 ** 9 +7
        return ans

ans = 0
for i in range(n):
    ans += cal(i+1, S)

ans %= 10 ** 9 + 7
print(ans)