Problem:
Score : 400 points

Problem Statement

We have a string S of length N consisting of R, G, and B.

Find the number of triples (i,~j,~k)~(1 \leq i < j < k \leq N) that satisfy both of the following conditions:

S_i \neq S_j, S_i \neq S_k, and S_j \neq S_k.

j - i \neq k - j.

Constraints

1 \leq N \leq 4000

S is a string of length N consisting of R, G, and B.

Input

Input is given from Standard Input in the following format:

N
S

Output

Print the number of triplets in question.

Sample Input 1

4
RRGB

Sample Output 1

1

Only the triplet (1,~3,~4) satisfies both conditions. The triplet (2,~3,~4) satisfies the first condition but not the second, so it does not count.

Sample Input 2

39
RBRBGRBGGBBRRGBBRRRBGGBRBGBRBGBRBBBGBBB

Sample Output 2

1800

Solution in Common Lisp (SBCL 2.0.3) (judge verdict: Time Limit Exceeded)

(defun solve ()
  (declare (optimize (speed 3) (debug 0) (safety 0)))
  (let ((n (read))
        (s (read-line))
        (count 0))
    (declare (type simple-string s))
    (flet ((check (i j k)
             (declare (type fixnum i j k))
             (and (/= (- j i) (- k j))
                  (char/= (char s i)
                          (char s j)
                          (char s k)))))
      (loop for i fixnum from 0 below n
            do (loop for j from (+ i 1) below n
                     when (char/= (char s i) (char s j))
                     do (loop for k from (+ j 1) below n
                              when (check i j k)
                              do (incf count))))
      (format t "~a~%" count))))

(solve)