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)

quit() = exit(0)
in_1(ch) = parse(Int, take!(ch))
in_a(ch) = parse.(Int, split(take!(ch)))

quit() = exit(0)
in_1() = parse(Int, readline())
in_a() = parse.(Int, split(readline()))

function main()
  N = in_1()
  S0 = readline()
  S = [(s=='R' ? 1 : s=='G' ? 2 : 4) for s in S0]
  ans = 0
  for (i, s1) in enumerate(S[1:end-2])
    for j in i+1:length(S)-1
      s2 = S[j]
      s1s2 = s1+s2
      for k in j+1:length(S)
        j-i != k-j || continue
        s3 = S[k]
        s1s2+s3==7 || continue
        ans += 1
      end
    end
  end
  println(ans)
end

isempty(ARGS) && main()