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 C (GCC 5.4.1) (judge verdict: Time Limit Exceeded)

#include <stdio.h>
#include <stdint.h>

static int N;
static char S[100000];

uint64_t search(int i, uint32_t use) {
  if(i == N) return 0;

  int j;
  for(j = i+1; j < N; j++) {
    uint32_t mask = 0x1 << (S[j] - 'a');
    if((use & mask) == 0) break;
  }
  uint64_t retA = search(j, use);// not use

  uint32_t mask = 0x1 << (S[i] - 'a');
  if((use & mask) != 0) {// already used
    return retA;
  } else {// new value
    uint64_t retB = search(i+1, (use | mask)) + 1;// use
    return retA + retB;
  }
}

int main(void) {
  scanf("%d", &N);
  scanf("%s", S);

  uint64_t comb = search(0, 0x0);
  uint64_t mod = comb % (1000000000+7);
  printf("%ld\n", mod);

  return 0;
}