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]
  d = Dict{Int, typeof(Dict(3=>Int[], 5=>Int[], 6=>Int[]))}()
  for i1 in 1:length(S)-2
    s1 = S[i1]
    for i2 in i1+1:length(S)-1
      s2 = S[i2]
      d2 = get!(d, i2, Dict(3=>Int[], 5=>Int[], 6=>Int[]))
      if s1 != s2
        dval = push!(d2[s1+s2], i2-i1)
      end
    end
  end
  
  s = 0
  for i3 in 3:length(S)
    s3 = S[i3]
    for i2 in 2:i3-1
      dval = d[i2][7-s3]
      s += count(!isequal(i3-i2), dval)
    end
  end
  println(s)
end

isempty(ARGS) && main()