#include <iostream>
#include <cmath>
#include <chrono>
#define sq 3

using namespace std;
typedef unsigned char byte;

template<class T>
inline T gcd(T a, T b) {
    while(b) {
        auto t = a % b;
        a = b;
        b = t;
    }
    return a;
}

int main() {
    auto start = chrono::system_clock::now();

    //triangles for which either (x1,y1) == (0,0)
    //or x1==0,y1!=0 or x1!=0,y1==0
    long count = 3*sq*sq;

    for (int vx = 1; vx <= sq; vx++)
    for (int vy = 1; vy <= sq; vy++) {
        int dx = -vy/gcd(vx,vy);
        int dy = vx/gcd(vx,vy);
        for (int d = 1; vx+dx*d >= 0 && vy+dy*d <= sq; d++)
            count++;
        for (int d = -1; vx+dx*d <= sq && vy+dy*d >= 0; d--)
            count++;
    }

    auto end = std::chrono::system_clock::now();

    std::chrono::duration<double> elapsed_seconds = end-start;
    cout << "solving took: " << elapsed_seconds.count() << endl;

    cout << "triangles: " << count;
    return 0;
}