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: Wrong Answer)

n = gets.to_i
str = gets.chomp.split('').map(&:to_s)
r_lsit = []
g_list = []
b_list = []
str.each_with_index do |s, idx|
  if s == "R"
    r_lsit << idx
  elsif s == "G"
    g_list << idx
  else
    b_list << idx
  end
end
ans = 0
r_lsit.each do |r|
  g_list.each do |g|
    b_list.each do |b|
      ans += 1 if (r - g).abs != (b - g).abs
    end
  end
end
puts ans