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 Ruby (2.7.1) (judge verdict: Time Limit Exceeded)

n = gets.to_i
s = gets.chomp
r_cnt = 0
g_cnt = 0
b_cnt = 0

n.times do |i|
	if s[i] == "R"
		r_cnt += 1
	elsif	s[i] == "G"
		g_cnt += 1
	else
		b_cnt += 1
	end
end

ans = r_cnt * g_cnt * b_cnt


n.times do |i|
	n.times do |j|
		next if i >= j
		k = 2*j - i
		break if k >= n
		if s[i] != s[j] && s[j] != s[k] && s[k] != s[i]
			ans -= 1
		end
	end
end

puts ans