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 (2.7.6) (judge verdict: Time Limit Exceeded)

import itertools

from operator import mul
from functools import reduce

def comb(r,n):
  r = min(n-r,r)
  if r == 0: return 1
  over = reduce(mul, range(n, n - r, -1))
  under = reduce(mul, range(1,r + 1))
  return over // under

mod = 10**9 + 7

n = int(raw_input())
s = raw_input()

ans = 0

q = []

for a in "abcdefghijklmnopqrstuvwxyz":
  q.append( s.count(a) )

for a in range(1,min(26+1,n+1)):
  #print a
  for x in itertools.combinations(q,a):
    ans += reduce(mul,x)
    ans %= mod

print ans % mod