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: Runtime Error)

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

T={}
for i=1,N do
    if T[S:sub(i,i)] == nil then
        T[S:sub(i,i)] = 1
    else
        T[S:sub(i,i)] = T[S:sub(i,i)] + 1
    end
end

M=T["R"]*T["G"]*T["B"]

for i=1,N do
    x=S:sub(i,i)
    for j=1,(N-i)//2 do
        y=S:sub(i+j,i+j)
        z=S:sub(i+2*j,i+2*j)
        if x~=y and y~=z and z~=x then
            M = M-1
        end
    end
end

print(M)