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: Accepted)

# r * g * bを計算する
# その中からj-i = k-j を満たすものを引く
# 2j = i + k
n = gets.chomp.to_i
# s = gets.chomp.chars
s = gets.chomp

h = Hash.new(0)

c_map = {
    'R' => 0,
    'G' => 1,
    'B' => 2
}


s.each_char do |c|
  h[c_map[c]] += 1
end

ans = h[0] * h[1] * h[2]

0.upto(n-2) do |i|
  i.upto(n-1) do |j|
    k = 2 * j - i
    next if k >= n

    ans -= 1 if s[i] != s[j] && s[j] != s[k] && s[k] != s[i]
  end
end

p ans