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", "*l")
local s = io.read()
local t = {}
for i = 1, n do
  t[i] = s:sub(i, i)
end

local r = 0
local g = 0
local b = 0
local rg, rb, gr, gb, br, bg = 0, 0, 0, 0, 0, 0

local ret = 0
for i = 1, n do
  if t[i] == "R" then
    ret = ret + gb + bg
    gr = gr + g
    br = br + b
    r = r + 1
  elseif t[i] == "G" then
    ret = ret + rb + br
    rg = rg + r
    bg = bg + b
    g = g + 1
  else
    ret = ret + rg + gr
    rb = rb + r
    gb = gb + g
    b = b + 1
  end
end
for mid = 1, n do
  if n < 1 + mid + mid then break end
  for left = 1, n do
    local center, right = left + mid, left + mid + mid
    if n < right then break end
    if t[left] ~= t[center] and t[center] ~= t[right] and t[left] ~= t[right] then
      ret = ret - 1
    end
  end
end
print(ret)