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: Time Limit Exceeded)

def main
    n = gets.to_i
    s = gets.chomp.split("")
    rs = []
    gs = []
    bs = []
    s.each_with_index do |c, i|
        rs.push i if c == "R"
        gs.push i if c == "G"
        bs.push i if c == "B"
    end
    ans = 0
    rs.each do |r|
        gs.each do |g|
            min = [r,g].min
            max = [r,g].max
            b1 = min - (max - min)
            if (max + min) % 2 == 0
                b2 = (max + min) / 2
            else
                b2 = n + 100
            end
            b3 = max + (max - min)

            ng = 0
            ng += 1 if bs.include? b1
            ng += 1 if bs.include? b2
            ng += 1 if bs.include? b3

            ans += bs.size - ng
        end
    end
    puts ans
end

main