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)

# frozen_string_literal: true

n = gets.to_i
s = gets.strip

count = 0

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

    if s[i] != s[j] && s[i] != s[k] && s[j] != s[k]
      count += 1
    end
  end
end

r = 0
g = 0
b = 0

cr = 'R'
cg = 'G'
s.chars.each do |c|
  if c == cr
    r += 1
  elsif c == cg
    g += 1
  else
    b += 1
  end
end

puts r * g * b - count