#include <iostream>
#include <cmath>
#include <tuple>
#include <chrono>

using namespace std;

// Calculates the divisors of an integer by determining its prime factorisation.

int get_divisors(long long n)
{
    int divisors_count = 1;

    for(long long i = 2;
        i <= sqrt(n);
        /* empty */)
    {
        int divisions = 0;
        while(n % i == 0)
        {
            n /= i;
            divisions++;
        }

        divisors_count *= (divisions + 1);

        //here, we try to iterate more efficiently by skipping
        //obvious non-primes like 4, 6, etc
        if(i == 2)
            i++;
        else
            i += 2;
    }

    if(n != 1) //n is a prime
        return divisors_count * 2;
    else
        return divisors_count;
}

long long euler12()
{
    //n and n + 1
    long long n, n_p_1;

    n = 1; n_p_1 = 2;

    // divisors_x will store either the divisors of x or x/2
    // (the later iff x is divisible by two)
    long long divisors_n = 1;
    long long divisors_n_p_1 = 2;

    for(;;)
    {
        /* This loop has been unwound, so two iterations are completed at a time
         * n and n + 1 have no prime factors in common and therefore we can
         * calculate their divisors separately
         */

        long long total_divisors;                 //the divisors of the triangle number
                                                  // n(n+1)/2

        //the first (unwound) iteration

        divisors_n_p_1 = get_divisors(n_p_1 / 2); //here n+1 is even and we

        total_divisors =
                  divisors_n
                * divisors_n_p_1;

        if(total_divisors > 1000)
            break;

        //move n and n+1 forward
        n = n_p_1;
        n_p_1 = n + 1;

        //fix the divisors
        divisors_n = divisors_n_p_1;
        divisors_n_p_1 = get_divisors(n_p_1);   //n_p_1 is now odd!

        //now the second (unwound) iteration

        total_divisors =
                  divisors_n
                * divisors_n_p_1;

        if(total_divisors > 1000)
            break;

        //move n and n+1 forward
        n = n_p_1;
        n_p_1 = n + 1;

        //fix the divisors
        divisors_n = divisors_n_p_1;
        divisors_n_p_1 = get_divisors(n_p_1 / 2);   //n_p_1 is now even!
    }

    return (n * n_p_1) / 2;
}

int main()
{
    for(int i = 0; i < 5; i++)
    {
        using namespace std::chrono;
        auto start = high_resolution_clock::now();
        auto result = euler12();
        auto end = high_resolution_clock::now();

        double time_elapsed = duration_cast<milliseconds>(end - start).count();

        cout << result << " " << time_elapsed << '\n';
    }
    return 0;
}