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)

function main()
    x = readlines()
    x1 = parse(Int, x[1])
    x2 = x[2]
    println(mysum(x1,x2))
end

function RGB(i::Char,j::Char,k::Char)
    if(i == j || i==k)
        return false
    elseif(j == k)
        return false
    else
        return true
    end
end

function mysum(x1::Int,x2::String)
    S = 0
    for j in [j for j = 2:x1-1]
        for i in [i for i = 1:j-1]
                for k in [k for k = j+1:x1]
                        if(j-i == k-j)
                            continue
                        elseif(RGB(x2[i],x2[j],x2[k]))
                            S +=1
                        else
                            continue
                        end
                end
        end
    end
    return S
end
main()