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: Accepted)

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

int main(){
    
    int N;
    string s;
    cin >> N >> s;
    
    long int r=0,g=0,b=0;
    
    for(int i=0; i<N; i++){
        if(s.at(i)=='R')
            r++;
        else if(s.at(i)=='G')
            g++;
        
    }
    b = N - r - g;
    
    long int ans =0;
    ans = r*g*b;
    
    for(int i=0; i<N; i++){
        for(int j=i+1; j<N && 2*j-i < N; j++){
            if(s.at(i)!=s.at(j) && s.at(i)!= s.at(2*j-i) && s.at(j)!= s.at(2*j-i))
                ans--;
        }
    }
    
    
    
    cout << ans << endl;
    
    
    
    
    
    return 0;
}