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: Runtime Error)

#include <stdio.h>
#include <string.h>
#include <math.h>

int fact(int n)
{
  int i, ans;
  ans = 1;
  for(i=1; i<=n; ++i) {
    ans = ans * i;
  };
  return (ans);
}

int main(void)
{
  int n, i, j;
  int m = 0;
  int num = 0;
  int ans = 0;
  char s[1000000];
  
  scanf("%d", &n);
  scanf("%s", s);
  
  for (i = 0; i < n; i++){
    for (j = i+1; j < n; j++){
      if ((i != j) && (s[i] == s[j])){
        num++;
        break;
      }
    }
  }
  
  for (i = 2; i <= n; i++){
    if (num == 0){
      ans += fact(n) / (fact(i) * fact(n-i));
    } else if (i > num){
      if (fact(n-num) / (fact(i) * fact(n-num-i)) > 0){
        ans += fact(n-num) / (fact(i) * fact(n-num-i))+1;
      }
    }
  }
  ans += n;
  
  printf("%d", ans);
  return 0;
}