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 Julia (1.4.0) (judge verdict: Time Limit Exceeded)

(() -> begin
  n = readline() |> x->parse.(Int,x)
  s = readline()

  ans = 0
  for i in 1:(n-2)
    s_i = s[i]
    for j in i+1:(n-1)
      s_j = s[j]
      if s_i == s_j
        continue
      end
      for k in j+1:n
        s_k = s[k]
        if s_i != s_k && s_j != s_k && j - i != k - j
          ans += 1
        end
      end
    end
  end
  println(ans)
end)()