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 Lua (Lua 5.3.5) (judge verdict: Time Limit Exceeded)

N=io.read("*n", "*l")
S=io.read()

counter = 0

for i=1,N do
    for j=1,N do
        if i<j then
            for k=1,N do
                if j<k and j-i~=k-j then
                    if S:sub(i,i)~=S:sub(j,j) and S:sub(i,i)~=S:sub(k,k) and S:sub(j,j)~=S:sub(k,k) then
                        counter = counter + 1
                    end
                end
            end
        end
    end
end

print(counter)