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 C# (.NET Core 3.1.201) (judge verdict: Time Limit Exceeded)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
class Program
{
    public static void Main()
    {
        int N = int.Parse(Console.ReadLine());
        string S = Console.ReadLine();
        List<int> R = new List<int>();
        List<int> G = new List<int>();
        List<int> B = new List<int>();
        for(int i=0; i < N; i++)
        {
            if (S[i] == 'R') { R.Add(i); }
            if (S[i] == 'G') { G.Add(i); }
            if (S[i] == 'B') { B.Add(i); }
        }
        int ans = R.Count*G.Count*B.Count;
        for(int i = 0; i < R.Count; i++)
        {
            for(int j = 0; j < G.Count; j++)
            {
                for (int k = 0; k < B.Count; k++)
                {
                    if (2 * G[j] - R[i] == B[k]||2*B[k]-G[j]==R[i]||2*G[j]-B[k]==R[i]||2*B[k]-R[i]==G[j]||2*R[i]-G[j]==B[k]||2*R[i]-B[k]==G[j]) { ans--; }
                }
            }
        }
        Console.WriteLine(ans);
    }
}