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 <bits/stdc++.h>
using namespace std;

int main(){
  int N,A=0;cin>>N;
  string S;cin>>S;
  vector<int> R(0),G(0),B(0);
  for(int i=0;i<N;i++){
    if (S.at(i)=='R'){
      R.push_back(i);
    }
    if (S.at(i)=='G'){
      G.push_back(i);
    }
    if (S.at(i)=='B'){
      B.push_back(i);
    }
  }
  for(int r=0;r<R.size();r++){
    for(int g=0;g<G.size();g++){
      for(int b=0;b<B.size();b++){
        if((R.at(r)+G.at(g)!=2*B.at(b)) && 
           (G.at(g)+B.at(b)!=2*R.at(r)) && 
           (B.at(b)+R.at(r)!=2*G.at(g)) ){
          A++;
        //  cout<<R.at(r)<<" "<<G.at(g)<<" "<<B.at(b)<<endl;
        }
      }
    }
  }
  cout << A <<endl;
}