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) {
                    if ( (i<j && j <k) ||(i>j && j >k)) {
                        if(i+k != 2 *j){
                             ans++;
                        }
                    }else if( (i <k &&  k <j) ||  (i >k &&  k >j)){
                        if(i+j != 2 *k){
                            ans++;
                        }
                    }else if( (j < i &&  i <k) ||  (j >i &&  i >k)){
                        if(j+k != 2 *i){
                            ans++;
                        }

                    }
                }
            }
        }
        System.out.println(ans);
    }

}