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 <string>
#include <algorithm>
#include <math.h>
#include <vector>

using namespace std;

#define fori(x) for (int i = 0; i < x; ++i)
#define forj(x) for (int j = 0; j < x; ++j)
#define mini(a,b) ((a<b)?a:b)
#define mega(a,b) ((a>b)?a:b)

int main() {
    int n; char s; int ans = 0;
    vector<int> r, g, b;
    cin >> n;
    fori(n) {
        cin >> s;
        if (s == 'R') {
            r.push_back(i);
        }
        else if (s == 'G') {
            g.push_back(i);
        }
        else {
            b.push_back(i);
        }
    }
    for (int i = 0; i < r.size(); ++i) {
        for (int j = 0; j < g.size(); ++j) {
            for (int k = 0; k < b.size(); ++k) {
                int ar[3]; ar[0] = r[i]; ar[1] = g[j]; ar[2] = b[k];
                sort(ar, ar + 3);
                if (ar[1]-ar[0]!=ar[2]-ar[1]) {
                    ++ans;
                }
            }
        }
    }
    cout << ans;
    return 0;
}