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.Numerics;
using System.Linq;
using static System.Math;

class MainClass
{

    public static void Main(string[] args)
    {
        var N = LnInt();
        var S = LnStr();

        var r = CountChar(S, 'R');
        var g = CountChar(S, 'G');
        var v = CountChar(S, 'B');
        var result = r * g * v;

        int count = 0;
        int i = 0;
        int j = N - 2;
        int k = N - 1;
        var empty = new bool[N];
        for (int b = 0; k > 1; b++)
        {
            for (int m = 0; j > 0; m++)
            {
                for (int n = 0; i < j; n++)
                {
                    if (j - i == k - j) { if (S[j] != S[k] && S[i] != S[j] && S[i] != S[k]) { count++;} }
                    i++;
                }
                j--;
                i = 0;
            }
            k--;
            i = 0;
            j = k - 1;
        }
        Console.WriteLine(result - count);
    }

    public static int CountChar(string s, char c)
    {
        return s.Length - s.Replace(c.ToString(), "").Length;
    }


    public static int[] LnInts()
    {
        var vs = Console.ReadLine().Trim().Split(new[] { ' ' }, StringSplitOptions.RemoveEmptyEntries);
        var ins = new int[vs.Length];
        for (int i = 0; i < vs.Length; i++) ins[i] = int.Parse(vs[i]);
        return ins;
    }

    public static int LnInt()
    {
        var vs = Console.ReadLine().Trim();
        return int.Parse(vs);
    }

    public static string[] LnStrs()
    {
        var vs = Console.ReadLine().Trim().Split(new[] { ' ' }, StringSplitOptions.RemoveEmptyEntries);
        return vs;
    }
    public static string LnStr()
    {
        var vs = Console.ReadLine().Trim();
        return vs;
    }
}