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 Java (OpenJDK 11.0.6) (judge verdict: Time Limit Exceeded)

import java.util.*;

public class Main {

    public static void main(String[] args) {

        Scanner sc = new Scanner(System.in);
        int N = sc.nextInt();
        String S = sc.next();

        List<Integer> R = new ArrayList<>();
        List<Integer> G = new ArrayList<>();
        List<Integer> B = new ArrayList<>();

        for (int i = 0; i < S.length(); i++) {
            char  c = S.charAt(i);
            if(c=='R'){
                R.add(i);
            }else if (c=='G'){
                G.add(i);
            }else{
                B.add(i);
            }
        }


        int ans = 0;
        for (int i :R) {
            for (int j :G) {
                for (int k :B) {
                    int[] aa= new int[3];
                    aa[0]=i;
                    aa[1]=j;
                    aa[2]=k;
                    Arrays.sort(aa);
                   if(aa[1]-aa[0] != aa[2]-aa[1])
                    ans ++;
                }
            }
        }
        System.out.println(ans);
    }

    static int gcd(int a, int b ){
        if (a == 0)
            return b;

        return gcd(b%a, a);
    }

}