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++ (GCC 9.2.1) (judge verdict: Time Limit Exceeded)

 #include<iostream>
 using namespace std;

 int main() {
     int N, count;
     string S;
     cin >> N;
     cin >> S;
     count = 0;

     for (int i=0; i<N; i++) {
         for (int j=i; j<N; j++) {
             for (int k=j; k<N; k++) {
                if (!(j-i==k-j or S[i]==S[j] or S[i]==S[k] or S[j]==S[k])) {
                    count++;
                }
             }
         }
     }
    cout << count << endl;

     return 0;
 }