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 0) (safety 3) (debug 3)))
#+sbcl (declaim (sb-ext:unmuffle-conditions sb-ext:compiler-note))
(declaim (optimize (speed 3) (safety 0) (debug 0)))

(declaim (type (integer 1 4000) *str-len*))
(defvar *str-len* (read))

(declaim (type simple-string *str*))
(defvar *str* (coerce (read-line) 'simple-string))

;; t_i = s[0..i]
;; cnt(t_n) = cnt(t_(n-1)) +

(declaim (type (simple-array fixnum (*)) *table*))
(defvar *table* (make-array (1+ *str-len*)
			    :element-type 'fixnum))
(setf (aref *table* 0) 0)
(setf (aref *table* 1) 0)

(loop for i of-type (integer 1 4000) from 2 to (1- *str-len*) do
      ;; calculate (aref *table i)
      (let ((sum (aref *table* (1- i))))
	(loop for j of-type (integer 0 4000) from (1- i) downto 1 do
	      (when (char/= (aref *str* i) (aref *str* j))
		(incf sum
		      (count-if #'(lambda (c) (and (char/= (aref *str* j)
							   (aref *str* i)
							   c)))
				*str*
				:start 0
				:end j))
		(when (and (>= (+ j j (- i)) 0)
			   (char/= (aref *str* j)
				   (aref *str* i)
				   (aref *str* (+ j j (- i)))))
		  (decf sum))))
	(setf (aref *table* i) sum)))
(princ (aref *table* (1- *str-len*)))