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)

(declaim (optimize (speed 3) (debug 0) (safety 0)))
(defun parse-data (text)
  (loop with x = 0
        for i from 0 below (- (length text) 2)
        do (loop for j from (1+ i) below (1- (length text))
                 do (loop for k from (1+ j) below (length text)
                          if (and (not (equal (aref text i)
                                              (aref text j)))
                                  (not (equal (aref text i)
                                              (aref text k)))
                                  (not (equal (aref text j)
                                              (aref text k)))
                                  (not (= (- j i)
                                          (- k j))))
                          do (incf x)))
        finally (format t "~A" x)))

(let ((n (read))
      (data (read-line)))
     (parse-data data))