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 RGB-Triplets (n s)
    (let ((ans 0))
        (loop
            :for i :from 0 :to (- n 1)
            :do (loop
                    :for j :from i :to (- n 1)
                    :do (loop
                            :for k :from j :to (- n 1)
                            :do (cond
                                    ((> i j) ())
                                    ((> j k) ())
                                    ((= (- j i) (- k j))())
                                    ((char= (char s i) (char s j)) ())
                                    ((string= (char s j) (char s k)) ())
                                    ((string= (char s k) (char s i)) ())
                                    (t (incf ans))))))
        ans))

(princ (RGB-Triplets (read) (read-line)))