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
r = 0
g = 0
b = 0
a = []
for i in 0..(n-1)
  if @s[i] == "R"
    r += 1
  elsif @s[i] == "G"
    g += 1
  else
    b += 1
  end
end

def sp(a,b,c)
  if @s[a] != @s[b] && @s[b] != @s[c] && @s[c] != @s[a]
    true
  else
    false
  end
end



x = 0
if sp(0,1,2)
  x = 1
else
  x = 0
end

dp = Array.new(n)
dp[2] = x

for j in 3..(n-1)
  y = 0
  for k in 1..(j/2)
    if sp(j,j-k,j-(2*k))
      y += 1
    end
  end
  dp[j] = dp[j-1] + y
end

puts (r*g*b) - dp[n-1]