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.to_i
S = gets.chomp.split('')
n_r = S.count('R')
n_g = S.count('G')
n_b = S.count('B')
ans = 0
(0..n-1).each do |i|
  ((i + 1)..n-1).each do |j|
    next if S[i] == S[j]

    k = (j - i) + j
    next if k > n - 1
    next if S[i] == S[k] || S[j] == S[k]
    ans += 1
  end
end
puts n_r * n_g * n_b - ans