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: Wrong Answer)

#include <stdio.h>
#include <string.h>
// long combi(int, int);
long combi(int n, int r) {
    if (r == 0) {
        return 1;
    }
    
    return (n - r + 1) * combi(n, r - 1) / r;
}

int main(){
  int n;
  char s[100001];
  char cmp[100001];
  int num;
  int ans = 0;
  
  scanf("%d%s", &n, s);

  for(int cnt = 0; cnt < strlen(s); cnt++){
    if(cnt == 0){
      cmp[0] = s[0];
    }
    for(int n = 0; n < strlen(cmp); n++){
      if(cmp[n] == s[cnt]){
	break;
      }
      else if(n == strlen(cmp) - 1){
	cmp[n + 1] = s[cnt];
	break;
      }
    }
  }

  //  printf("%ld %ld\n", strlen(s), strlen(cmp));
  for(int cnt = 1; cnt <= strlen(s); cnt++){
    ans += combi(n, cnt);
  }

  for(int cnt = 1; cnt <= n - strlen(cmp); cnt++){
    ans -= combi(strlen(cmp), cnt);
  }

  printf("%d", ans);

  printf("\n");
  
}