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))
      (s (read-line))
      (count 0))
  (flet ((check (i j k)
           (and (/= (- j i) (- k j))
                (char/= (char s i)
                        (char s j)
                        (char s k)))))
    (loop for i from 0 below n
          do (loop for j from (+ i 1) below n
                   do (loop for k from (+ j 1) below n
                            when (check i j k)
                            do (incf count))))
    (format t "~a~%" count)))