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)

n = gets.chomp.to_i
s = gets.chomp.split('')

r, g, b = 0, 0, 0
reject_count = 0
s.each_with_index do |val_i, ind_i|
  if val_i == 'R'
    r += 1
  elsif val_i == 'G'
    g += 1
  else
    b += 1
  end
  
  s[ind_i+1..n-1].each.with_index(ind_i+1) do |val_j, ind_j|
    next if val_i == val_j
    
    ind_k = 2 * ind_j - ind_i
    reject_count += 1 if ind_k < n && s[ind_k] != val_i && s[ind_k] != val_j
  end
end

all = r * g * b

puts all - reject_count