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: Accepted)

(defun calc (n text)
  (loop with r = 0
        with g = 0
        with b = 0
        for i below n
        do (case (schar text i)
             (#\R (incf r))
             (#\G (incf g))
             (#\B (incf b)))
        finally (return (* r g b))))

(defun minus (n text)
  (loop with x = 0
        for i below n
        do (loop for j from (1+ i) below n
                 if (< (- (* 2 j) i) 
                       n)
                 do (if (and (not (equal (schar text i)
                                         (schar text j)))
                             (not (equal (schar text j)
                                         (schar text (- (* 2 j) i))))
                             (not (equal (schar text i)
                                         (schar text (- (* 2 j) i)))))
                        (incf x)))
        finally (return x)))

(let ((n (read))
      (text (read-line)))
     (format t "~A" (- (calc n text)
                       (minus n text))))