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 Common Lisp (SBCL 1.1.14) (judge verdict: Runtime Error)

(defun string->duplicates-removed-list (string)
  (declare (optimize (speed 3) (safety 0) (debug 0)))
  (labels ((rec (n acc)
             (if (= n -1)
                 acc
                 (let ((c (char string n)))
                   (if (member c acc)
                       (rec (1- n) acc)
                       (rec (1- n) (cons c acc)))))))
    (rec (1- (length string)) nil)))

(defun f (str)
  (declare (optimize (speed 3) (safety 0) (debug 0)))
  (labels ((rec (lst acc)
             (if (null lst)
                 acc
                 (rec (cdr lst) (* (1+ (count (car lst) str)) acc)))))
    (1- (rec (string->duplicates-removed-list str) 1))))

(defparameter *n* (read))
(defparameter *s* (read))

(print (mod (f *s*) (+ 1e9 7)))