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# (Mono-mcs 6.8.0.105) (judge verdict: Time Limit Exceeded)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace _20200412_ABC162D
{
    class Program
    {
        static void Main(string[] args)
        {
            var input = ReadStringList(2);

            int N = int.Parse(input[0]);
            string S = input[1];
            char[] c = S.ToCharArray();

            long output = 0;

            for(int i = 0; i < N; i++)
            {
                for(int j = i + 1; j < N; j++)
                {
                    if (c[i] == c[j])
                    {
                        continue;
                    }
                    for(int k = j + 1; k < N; k++)
                    {
                        if ((c[i] == c[k]) || (c[j] == c[k]))
                        {
                            continue;
                        }
                        if (j - i == k - j)
                        {
                            continue;
                        }
                        output++;
                    }
                }
            }

            Console.WriteLine(output);
        }

        private static List<string> ReadStringList(int numberOfLines)
        {
            var stringList = new List<string>();

            for (int lineIndex = 0; lineIndex < numberOfLines; lineIndex++)
            {
                stringList.Add(Console.ReadLine().Trim());
            }

            return stringList;
        }

    }
}