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 Ruby (2.7.1) (judge verdict: Accepted)

n = gets.to_i
s = gets.chomp

ss = s.split("")

rs = []
gs = []
bs = []
ss.each.with_index(1) do |rgb, i|
 if rgb == "R"
  rs << i
 elsif rgb == "G"
  gs << i
 else
  bs << i
 end
end

ans = 0
rs.each do |r|
  gs.each do |g|
    rg = (r - g).abs
    max = [r, g].max
    min = [r, g].min
    ans += bs.length
    if max + rg - 1 < ss.length && ss[max + rg - 1] == 'B'
      ans -= 1
    end
    if rg % 2 == 0 && ss[max - rg/2 - 1] == 'B'
      ans -= 1
    end
    if min - rg - 1 > 0 && ss[min - rg - 1] == 'B'
      ans -= 1
    end
  end
end
p ans