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)

(let* ((n (read))
       (r nil)
       (g nil)
       (b nil))
  (loop :for k :in (concatenate 'list (read-line))
        :for j :from 1
        :do(cond ((char= #\R k) (push j r))
                 ((char= #\G k) (push j g))
                 ((char= #\B k) (push j b))))
  (defun f (xx yy zz)
    (loop :for x :in xx
          :sum (loop :for y :in yy
                     :sum (loop :for z :in zz
                                  :if (and (not (cond ((< x y z) (= (- x y) (- y z)))
                                                      ((< x z y) (= (- x z) (- z y)))
                                                      ((< y x z) (= (- y x) (- x z)))
                                                      ((< y z x) (= (- y z) (- z x)))
                                                      ((< z x y) (= (- z x) (- x y)))
                                                      ((< z y x) (= (- z y) (- y x))))))
                                 :count t))))
  (print (f r g b)))