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 (LuaJIT 2.1.0) (judge verdict: Accepted)

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

local S_bytes = {S:byte(1, N)}
local R_count, G_count, B_count = 0LL, 0LL, 0LL
local R, G, B = string.byte("RGB", 1, 3)

for i = 1, N do
    if S_bytes[i] == R then
        R_count = R_count + 1
    elseif S_bytes[i] == G then
        G_count = G_count + 1
    else
        B_count = B_count + 1
    end
end

local minus_count = 0LL
for i = 1, math.modf(N/2) do
    for j = 1, N - i * 2 do
        if S_bytes[j] ~= S_bytes[j + i]
        and S_bytes[j + i] ~= S_bytes[j + 2 * i]
        and S_bytes[j] ~= S_bytes[j + 2 * i] then
            minus_count = minus_count + 1
        end
    end
end

print(tostring(R_count * G_count * B_count - minus_count):sub(1, -3))