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>
#include <vector>
using namespace std;

int main(){
    int n;
    string s;
    cin >> n >> s;
    int i, j, k, Ans = 0;
    vector<int> R, G, B;
    for(i=0;i<n;i++){
        if (s[i] == 'R'){
            R.push_back(i);
        }
        else if(s[i] == 'G'){
            G.push_back(i);
        }
        else{
            B.push_back(i);
        }
    }
    
    int r = R.size(), g = G.size(), b = B.size();
    for(i=0;i<r;i++){
        for(j=0;j<g;j++){
            if(G[j] < R[i]){
                continue;
            }
            for(k=0;k<b;k++){
                if(B[k] < G[j] || G[j]-R[i] == B[k]-G[j]){
                    continue;
                }
                Ans++;
            }
        }
        for(j=0;j<b;j++){
            if(B[j] < R[i]){
                continue;
            }
            for(k=0;k<g;k++){
                if(G[k] < B[j] || B[j]-R[i] == G[k]-B[j]){
                    continue;
                }
                Ans++;
            }
        }
    }
    for(i=0;i<g;i++){
        for(j=0;j<r;j++){
            if(R[j] < G[i]){
                continue;
            }
            for(k=0;k<b;k++){
                if(B[k] < R[j] || R[j]-G[i] == B[k]-R[j]){
                    continue;
                }
                Ans++;
            }
        }
        for(j=0;j<b;j++){
            if(B[j] < G[i]){
                continue;
            }
            for(k=0;k<r;k++){
                if(R[k] < B[j] || B[j]-G[i] == R[k]-B[j]){
                    continue;
                }
                Ans++;
            }
        }
    }
    for(i=0;i<b;i++){
        for(j=0;j<r;j++){
            if(R[j] < B[i]){
                continue;
            }
            for(k=0;k<g;k++){
                if(G[k] < R[j] || R[j]-B[i] == G[k]-R[j]){
                    continue;
                }
                Ans++;
            }
        }
        for(j=0;j<g;j++){
            if(G[j] < B[i]){
                continue;
            }
            for(k=0;k<r;k++){
                if(R[k] < G[j] || G[j]-B[i] == R[k]-G[j]){
                    continue;
                }
                Ans++;
            }
        }
    }

    cout << Ans << endl;
    return 0;
}