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: Time Limit Exceeded)

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

local S_byte = {S:byte(1, N)}
local count = 0
for i = 1, N - 2 do
    for j = i + 1, N - 1 do
        for k = j + 1, N do
            if j-i ~= k-j and S_byte[i] ~= S_byte[j] and S_byte[i] ~= S_byte[k] and S_byte[j] ~= S_byte[k] then
                count = count + 1
            end
        end
    end
end

print(count)