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: Accepted)

(() -> begin
  n = readline() |> x->parse.(Int,x)
  s = readline()
  dict = Dict([['R',0],['G',0],['B',0]])
  for i in 1:n
    dict[s[i]] += 1
  end
  ans = dict['R'] * dict['G'] * dict['B']
  for i in 1:n-2
    for j in i+1:n-1
      k = 2 * j - i
      if k <= n && s[i] != s[j] && s[j] != s[k] && s[k] != s[i]
        ans -= 1
      end
    end
  end
  println(ans)
end)()