#include <cmath>
#include <iostream>
#include <random>
#include <vector>

const std::vector<std::vector<double>> train_data = {
    {0.0, 0.0, 0.0, 1.0, 1.0, 1.0, 0.0, 1.0},
    {1.0, 0.0, 1.0, 0.0, 1.0, 0.0, 0.0, 1.0},
    {1.0, 1.0, 1.0, 1.0, 0.0, 0.0, 0.0, 0.0},
    {1.0, 1.0, 0.0, 1.0, 1.0, 1.0, 0.0, 1.0},
    {1.0, 0.0, 0.0, 0.0, 0.0, 1.0, 1.0, 0.0},
    {1.0, 1.0, 1.0, 0.0, 1.0, 0.0, 1.0, 0.0},
    {0.0, 0.0, 1.0, 0.0, 1.0, 0.0, 0.0, 0.0},
    {1.0, 0.0, 1.0, 1.0, 1.0, 0.0, 0.0, 0.0},
    {0.0, 1.0, 1.0, 0.0, 1.0, 0.0, 0.0, 1.0},
    {0.0, 1.0, 1.0, 0.0, 0.0, 1.0, 0.0, 1.0},
    {1.0, 1.0, 0.0, 0.0, 1.0, 1.0, 0.0, 0.0},
    {1.0, 1.0, 1.0, 1.0, 1.0, 0.0, 1.0, 0.0},
    {1.0, 0.0, 0.0, 1.0, 1.0, 0.0, 1.0, 0.0},
    {1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 0.0},
    {0.0, 0.0, 0.0, 1.0, 0.0, 1.0, 0.0, 0.0},
    {1.0, 1.0, 0.0, 0.0, 0.0, 1.0, 1.0, 0.0},
    {0.0, 1.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0},
    {1.0, 1.0, 0.0, 1.0, 0.0, 0.0, 1.0, 1.0},
    {0.0, 0.0, 1.0, 1.0, 1.0, 0.0, 1.0, 1.0},
    {1.0, 0.0, 1.0, 1.0, 0.0, 1.0, 0.0, 1.0},
    {1.0, 1.0, 0.0, 1.0, 0.0, 0.0, 1.0, 0.0},
    {1.0, 0.0, 0.0, 0.0, 1.0, 0.0, 1.0, 1.0},
    {1.0, 0.0, 1.0, 0.0, 1.0, 1.0, 0.0, 0.0},
    {0.0, 0.0, 1.0, 1.0, 0.0, 1.0, 1.0, 0.0},
    {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 1.0},
    {1.0, 0.0, 0.0, 1.0, 1.0, 0.0, 0.0, 1.0},
    {1.0, 0.0, 0.0, 1.0, 0.0, 0.0, 1.0, 1.0},
    {1.0, 1.0, 0.0, 0.0, 1.0, 0.0, 1.0, 1.0},
    {1.0, 0.0, 1.0, 1.0, 0.0, 0.0, 0.0, 0.0},
    {0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0},
    {0.0, 0.0, 1.0, 0.0, 0.0, 1.0, 0.0, 1.0},
    {1.0, 0.0, 1.0, 1.0, 1.0, 1.0, 0.0, 0.0},
    {0.0, 1.0, 0.0, 1.0, 1.0, 1.0, 0.0, 1.0},
    {0.0, 1.0, 0.0, 1.0, 1.0, 0.0, 0.0, 0.0},
    {1.0, 1.0, 1.0, 0.0, 1.0, 1.0, 0.0, 1.0},
    {1.0, 0.0, 0.0, 0.0, 0.0, 1.0, 1.0, 1.0},
    {1.0, 1.0, 1.0, 1.0, 0.0, 1.0, 0.0, 0.0},
    {0.0, 1.0, 0.0, 0.0, 1.0, 1.0, 0.0, 0.0},
    {1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 0.0, 0.0},
    {0.0, 1.0, 1.0, 0.0, 1.0, 1.0, 0.0, 0.0},
    {1.0, 0.0, 1.0, 1.0, 1.0, 0.0, 1.0, 0.0},
    {0.0, 0.0, 1.0, 0.0, 0.0, 1.0, 1.0, 1.0},
    {1.0, 0.0, 0.0, 1.0, 0.0, 0.0, 1.0, 0.0},
    {0.0, 1.0, 0.0, 0.0, 1.0, 0.0, 0.0, 1.0},
    {1.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0},
    {1.0, 1.0, 1.0, 0.0, 0.0, 0.0, 1.0, 0.0},
    {0.0, 1.0, 1.0, 1.0, 0.0, 1.0, 0.0, 1.0},
    {1.0, 0.0, 0.0, 0.0, 1.0, 1.0, 0.0, 1.0},
    {0.0, 0.0, 1.0, 1.0, 1.0, 0.0, 0.0, 1.0},
    {0.0, 1.0, 0.0, 1.0, 1.0, 1.0, 1.0, 0.0},
    {1.0, 1.0, 0.0, 0.0, 1.0, 0.0, 0.0, 1.0},
    {0.0, 1.0, 0.0, 0.0, 1.0, 0.0, 1.0, 1.0},
    {0.0, 0.0, 1.0, 0.0, 0.0, 1.0, 0.0, 0.0},
    {0.0, 0.0, 1.0, 0.0, 1.0, 0.0, 0.0, 1.0},
    {1.0, 0.0, 0.0, 0.0, 1.0, 0.0, 1.0, 0.0},
    {0.0, 0.0, 1.0, 1.0, 1.0, 1.0, 0.0, 0.0},
    {1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
    {0.0, 1.0, 1.0, 1.0, 1.0, 1.0, 0.0, 0.0},
    {1.0, 1.0, 1.0, 0.0, 0.0, 1.0, 1.0, 1.0},
    {1.0, 0.0, 1.0, 0.0, 0.0, 1.0, 0.0, 1.0},
    {0.0, 1.0, 0.0, 0.0, 0.0, 1.0, 0.0, 1.0},
    {0.0, 1.0, 0.0, 0.0, 0.0, 1.0, 1.0, 0.0},
    {1.0, 0.0, 0.0, 1.0, 1.0, 1.0, 1.0, 0.0},
    {0.0, 1.0, 1.0, 1.0, 1.0, 0.0, 1.0, 0.0},
    {0.0, 0.0, 1.0, 0.0, 1.0, 1.0, 0.0, 0.0},
    {0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 1.0, 0.0},
    {0.0, 0.0, 1.0, 1.0, 0.0, 0.0, 0.0, 1.0},
    {1.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0},
    {0.0, 0.0, 1.0, 0.0, 1.0, 1.0, 0.0, 1.0},
    {1.0, 0.0, 0.0, 1.0, 0.0, 1.0, 1.0, 1.0},
    {1.0, 0.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0},
    {1.0, 1.0, 0.0, 1.0, 1.0, 0.0, 1.0, 1.0},
    {0.0, 1.0, 1.0, 1.0, 1.0, 0.0, 1.0, 1.0},
    {0.0, 1.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0},
    {1.0, 1.0, 1.0, 1.0, 0.0, 1.0, 0.0, 1.0},
    {1.0, 0.0, 1.0, 0.0, 0.0, 1.0, 1.0, 0.0},
    {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0},
    {0.0, 1.0, 0.0, 1.0, 0.0, 1.0, 1.0, 1.0},
    {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0},
    {0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 1.0, 0.0},
    {0.0, 0.0, 0.0, 1.0, 0.0, 1.0, 1.0, 0.0},
    {0.0, 0.0, 1.0, 1.0, 0.0, 0.0, 0.0, 0.0},
    {1.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 1.0},
    {1.0, 1.0, 0.0, 1.0, 1.0, 0.0, 0.0, 0.0},
    {0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 1.0, 1.0},
    {1.0, 0.0, 1.0, 1.0, 0.0, 1.0, 1.0, 0.0},
    {0.0, 1.0, 1.0, 1.0, 0.0, 1.0, 1.0, 1.0},
    {1.0, 1.0, 1.0, 0.0, 0.0, 1.0, 1.0, 0.0},
    {1.0, 0.0, 0.0, 1.0, 0.0, 1.0, 0.0, 0.0},
    {0.0, 1.0, 1.0, 0.0, 0.0, 1.0, 1.0, 0.0},
    {1.0, 1.0, 0.0, 0.0, 1.0, 1.0, 1.0, 1.0},
    {0.0, 1.0, 1.0, 0.0, 1.0, 1.0, 0.0, 1.0},
    {1.0, 0.0, 1.0, 0.0, 0.0, 0.0, 1.0, 1.0},
    {1.0, 1.0, 1.0, 0.0, 1.0, 0.0, 1.0, 1.0},
    {1.0, 1.0, 1.0, 0.0, 0.0, 1.0, 0.0, 1.0},
    {1.0, 1.0, 0.0, 1.0, 1.0, 1.0, 0.0, 0.0},
    {0.0, 0.0, 0.0, 1.0, 0.0, 1.0, 1.0, 1.0},
    {1.0, 1.0, 0.0, 0.0, 0.0, 1.0, 1.0, 1.0},
    {0.0, 1.0, 1.0, 0.0, 1.0, 1.0, 1.0, 1.0},
    {0.0, 1.0, 0.0, 1.0, 0.0, 0.0, 1.0, 0.0},
    {1.0, 0.0, 0.0, 1.0, 0.0, 1.0, 1.0, 0.0},
    {1.0, 1.0, 1.0, 0.0, 0.0, 0.0, 1.0, 1.0},
    {0.0, 1.0, 1.0, 0.0, 0.0, 0.0, 0.0, 1.0},
    {0.0, 0.0, 1.0, 1.0, 1.0, 0.0, 1.0, 0.0},
    {1.0, 0.0, 1.0, 1.0, 0.0, 0.0, 1.0, 0.0},
    {0.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 0.0},
    {0.0, 0.0, 1.0, 1.0, 0.0, 1.0, 0.0, 1.0},
    {0.0, 1.0, 0.0, 0.0, 1.0, 1.0, 1.0, 1.0},
    {1.0, 0.0, 0.0, 1.0, 1.0, 1.0, 0.0, 0.0},
    {0.0, 1.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0},
    {1.0, 1.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0},
    {0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 1.0, 1.0},
    {0.0, 0.0, 1.0, 1.0, 0.0, 1.0, 0.0, 0.0},
    {1.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 1.0},
    {0.0, 1.0, 0.0, 1.0, 1.0, 0.0, 1.0, 0.0},
    {0.0, 0.0, 1.0, 1.0, 0.0, 0.0, 1.0, 0.0},
    {0.0, 0.0, 1.0, 0.0, 0.0, 1.0, 1.0, 0.0},
    {0.0, 0.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0},
    {1.0, 1.0, 0.0, 1.0, 0.0, 0.0, 0.0, 1.0},
    {1.0, 1.0, 0.0, 0.0, 1.0, 1.0, 1.0, 0.0},
    {0.0, 1.0, 0.0, 0.0, 1.0, 0.0, 1.0, 0.0},
    {0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0},
    {0.0, 1.0, 0.0, 1.0, 0.0, 0.0, 1.0, 1.0},
    {0.0, 1.0, 1.0, 1.0, 0.0, 1.0, 0.0, 0.0},
    {1.0, 1.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0},
    {0.0, 1.0, 1.0, 1.0, 0.0, 0.0, 1.0, 1.0},
    {1.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
    {0.0, 0.0, 1.0, 1.0, 1.0, 0.0, 0.0, 0.0},
    {1.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0},
    {1.0, 0.0, 1.0, 0.0, 0.0, 1.0, 1.0, 1.0},
    {0.0, 0.0, 0.0, 1.0, 1.0, 0.0, 0.0, 1.0},
    {1.0, 0.0, 1.0, 1.0, 0.0, 1.0, 0.0, 0.0},
    {1.0, 1.0, 0.0, 1.0, 1.0, 0.0, 1.0, 0.0},
    {0.0, 0.0, 0.0, 1.0, 0.0, 1.0, 0.0, 1.0},
    {1.0, 0.0, 0.0, 0.0, 1.0, 1.0, 1.0, 1.0},
    {0.0, 1.0, 1.0, 0.0, 0.0, 1.0, 1.0, 1.0},
    {0.0, 1.0, 0.0, 0.0, 1.0, 1.0, 0.0, 1.0},
    {0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 1.0, 1.0},
    {1.0, 0.0, 0.0, 1.0, 1.0, 1.0, 1.0, 1.0},
    {0.0, 1.0, 0.0, 1.0, 0.0, 0.0, 0.0, 1.0},
    {1.0, 1.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0},
    {1.0, 1.0, 0.0, 1.0, 0.0, 1.0, 1.0, 0.0},
    {0.0, 0.0, 1.0, 0.0, 1.0, 0.0, 1.0, 1.0},
    {0.0, 1.0, 1.0, 0.0, 1.0, 1.0, 1.0, 0.0},
    {0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 1.0},
    {1.0, 1.0, 1.0, 0.0, 0.0, 1.0, 0.0, 0.0},
    {0.0, 0.0, 0.0, 1.0, 1.0, 1.0, 1.0, 0.0},
    {1.0, 1.0, 1.0, 1.0, 1.0, 0.0, 1.0, 1.0},
    {1.0, 1.0, 1.0, 1.0, 1.0, 0.0, 0.0, 1.0},
    {1.0, 1.0, 0.0, 0.0, 1.0, 0.0, 1.0, 0.0},
    {0.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0},
    {0.0, 1.0, 0.0, 1.0, 1.0, 1.0, 0.0, 0.0},
    {0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0},
    {0.0, 1.0, 1.0, 0.0, 0.0, 1.0, 0.0, 0.0},
    {1.0, 0.0, 1.0, 1.0, 1.0, 1.0, 0.0, 1.0},
    {0.0, 0.0, 0.0, 1.0, 1.0, 0.0, 0.0, 0.0},
    {0.0, 0.0, 1.0, 0.0, 1.0, 0.0, 1.0, 0.0},
    {1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0},
    {1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0},
    {1.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0},
    {0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
    {0.0, 1.0, 1.0, 0.0, 0.0, 0.0, 1.0, 0.0},
    {0.0, 1.0, 1.0, 1.0, 0.0, 1.0, 1.0, 0.0},
    {0.0, 1.0, 0.0, 1.0, 1.0, 1.0, 1.0, 1.0},
    {0.0, 1.0, 1.0, 1.0, 1.0, 0.0, 0.0, 1.0},
    {1.0, 1.0, 0.0, 1.0, 0.0, 1.0, 0.0, 1.0},
    {1.0, 0.0, 1.0, 1.0, 1.0, 0.0, 0.0, 1.0},
    {1.0, 1.0, 1.0, 1.0, 0.0, 1.0, 1.0, 0.0},
    {1.0, 1.0, 1.0, 1.0, 0.0, 0.0, 0.0, 1.0},
    {1.0, 1.0, 1.0, 1.0, 1.0, 0.0, 0.0, 0.0},
    {0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0},
    {0.0, 1.0, 1.0, 0.0, 1.0, 0.0, 0.0, 0.0},
    {0.0, 0.0, 1.0, 1.0, 0.0, 1.0, 1.0, 1.0},
    {1.0, 0.0, 0.0, 1.0, 1.0, 1.0, 0.0, 1.0},
    {1.0, 0.0, 1.0, 1.0, 1.0, 0.0, 1.0, 1.0},
    {1.0, 1.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0},
    {0.0, 1.0, 0.0, 1.0, 0.0, 1.0, 1.0, 0.0},
    {0.0, 1.0, 1.0, 1.0, 1.0, 0.0, 0.0, 0.0},
    {1.0, 1.0, 1.0, 1.0, 0.0, 0.0, 1.0, 0.0},
    {1.0, 0.0, 1.0, 1.0, 0.0, 1.0, 1.0, 1.0},
    {1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 1.0},
    {1.0, 0.0, 1.0, 0.0, 1.0, 0.0, 1.0, 1.0},
    {1.0, 1.0, 0.0, 0.0, 1.0, 1.0, 0.0, 1.0},
    {1.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 1.0},
    {1.0, 0.0, 1.0, 0.0, 1.0, 1.0, 1.0, 1.0},
    {1.0, 1.0, 0.0, 1.0, 0.0, 1.0, 1.0, 1.0},
    {0.0, 1.0, 1.0, 1.0, 1.0, 1.0, 0.0, 1.0},
    {0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 1.0},
    {1.0, 0.0, 0.0, 1.0, 1.0, 0.0, 0.0, 0.0},
    {1.0, 1.0, 0.0, 0.0, 0.0, 0.0, 1.0, 1.0},
    {1.0, 1.0, 0.0, 1.0, 1.0, 1.0, 1.0, 0.0},
    {1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0},
    {0.0, 1.0, 1.0, 0.0, 1.0, 0.0, 1.0, 0.0},
    {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
    {0.0, 0.0, 0.0, 0.0, 1.0, 1.0, 1.0, 1.0},
    {1.0, 1.0, 1.0, 0.0, 1.0, 1.0, 1.0, 1.0},
    {1.0, 1.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0},
    {0.0, 1.0, 1.0, 1.0, 0.0, 0.0, 0.0, 1.0},
    {1.0, 0.0, 1.0, 1.0, 0.0, 0.0, 0.0, 1.0},
    {1.0, 1.0, 1.0, 0.0, 1.0, 0.0, 0.0, 1.0},
    {0.0, 0.0, 0.0, 0.0, 1.0, 1.0, 1.0, 0.0},
    {1.0, 0.0, 0.0, 0.0, 1.0, 1.0, 1.0, 0.0},
    {0.0, 0.0, 0.0, 1.0, 1.0, 1.0, 0.0, 0.0},
    {0.0, 1.0, 0.0, 0.0, 1.0, 1.0, 1.0, 0.0}};
const std::vector<std::vector<double>> train_label = {
    {0.0, 1.0, 1.0, 1.0, 0.0}, {1.0, 0.0, 0.0, 1.0, 1.0},
    {0.0, 1.0, 1.0, 1.0, 1.0}, {1.0, 1.0, 0.0, 1.0, 0.0},
    {0.0, 1.0, 1.0, 1.0, 0.0}, {1.0, 1.0, 0.0, 0.0, 0.0},
    {0.0, 1.0, 0.0, 1.0, 0.0}, {1.0, 0.0, 0.0, 1.0, 1.0},
    {0.0, 1.0, 1.0, 1.0, 1.0}, {0.0, 1.0, 0.0, 1.0, 1.0},
    {1.0, 1.0, 0.0, 0.0, 0.0}, {1.0, 1.0, 0.0, 0.0, 1.0},
    {1.0, 0.0, 0.0, 1.0, 1.0}, {1.0, 1.0, 1.0, 0.0, 1.0},
    {0.0, 0.0, 1.0, 0.0, 1.0}, {1.0, 0.0, 0.0, 1.0, 0.0},
    {0.0, 1.0, 0.0, 0.0, 0.0}, {1.0, 0.0, 0.0, 0.0, 0.0},
    {0.0, 1.0, 1.0, 1.0, 0.0}, {1.0, 0.0, 0.0, 0.0, 0.0},
    {0.0, 1.0, 1.0, 1.0, 1.0}, {1.0, 0.0, 0.0, 1.0, 1.0},
    {1.0, 0.0, 1.0, 1.0, 0.0}, {0.0, 1.0, 0.0, 0.0, 1.0},
    {0.0, 0.0, 0.0, 1.0, 1.0}, {1.0, 0.0, 0.0, 1.0, 0.0},
    {0.0, 1.0, 1.0, 0.0, 0.0}, {1.0, 0.0, 1.0, 1.0, 1.0},
    {0.0, 1.0, 0.0, 1.0, 1.0}, {0.0, 0.0, 1.0, 1.0, 0.0},
    {0.0, 0.0, 1.0, 1.0, 1.0}, {1.0, 0.0, 1.0, 1.0, 1.0},
    {1.0, 0.0, 0.0, 1.0, 0.0}, {0.0, 1.0, 1.0, 0.0, 1.0},
    {1.0, 1.0, 0.0, 1.0, 1.0}, {0.0, 1.0, 1.0, 1.0, 1.0},
    {1.0, 0.0, 0.0, 1.0, 1.0}, {1.0, 0.0, 0.0, 0.0, 0.0},
    {1.0, 1.0, 0.0, 1.0, 1.0}, {1.0, 0.0, 0.0, 1.0, 0.0},
    {1.0, 0.0, 1.0, 0.0, 1.0}, {0.0, 1.0, 0.0, 0.0, 1.0},
    {0.0, 1.0, 0.0, 1.0, 1.0}, {0.0, 1.0, 1.0, 0.0, 1.0},
    {0.0, 1.0, 0.0, 0.0, 1.0}, {1.0, 0.0, 0.0, 0.0, 0.0},
    {0.0, 1.0, 1.0, 0.0, 0.0}, {1.0, 0.0, 1.0, 0.0, 1.0},
    {0.0, 1.0, 1.0, 0.0, 0.0}, {1.0, 0.0, 0.0, 1.0, 1.0},
    {1.0, 0.0, 1.0, 0.0, 1.0}, {0.0, 1.0, 1.0, 1.0, 1.0},
    {0.0, 0.0, 1.0, 1.0, 0.0}, {0.0, 1.0, 0.0, 1.0, 1.0},
    {1.0, 0.0, 0.0, 1.0, 0.0}, {0.0, 1.0, 1.0, 1.0, 1.0},
    {0.0, 1.0, 0.0, 0.0, 0.0}, {1.0, 0.0, 0.0, 1.0, 1.0},
    {1.0, 0.0, 1.0, 0.0, 1.0}, {0.0, 1.0, 1.0, 1.0, 1.0},
    {0.0, 1.0, 0.0, 0.0, 1.0}, {0.0, 1.0, 0.0, 1.0, 0.0},
    {1.0, 0.0, 1.0, 1.0, 1.0}, {1.0, 0.0, 0.0, 0.0, 1.0},
    {0.0, 1.0, 1.0, 1.0, 0.0}, {0.0, 1.0, 0.0, 1.0, 0.0},
    {0.0, 0.0, 1.0, 0.0, 0.0}, {0.0, 1.0, 0.0, 1.0, 0.0},
    {0.0, 1.0, 1.0, 1.0, 1.0}, {1.0, 0.0, 0.0, 0.0, 0.0},
    {1.0, 1.0, 0.0, 1.0, 0.0}, {1.0, 1.0, 0.0, 0.0, 0.0},
    {1.0, 0.0, 0.0, 1.0, 0.0}, {0.0, 1.0, 1.0, 0.0, 0.0},
    {1.0, 0.0, 1.0, 0.0, 0.0}, {1.0, 0.0, 0.0, 0.0, 0.0},
    {0.0, 0.0, 0.0, 0.0, 1.0}, {0.0, 1.0, 1.0, 0.0, 0.0},
    {0.0, 0.0, 0.0, 1.0, 0.0}, {0.0, 0.0, 0.0, 1.0, 1.0},
    {0.0, 0.0, 1.0, 1.0, 1.0}, {0.0, 0.0, 0.0, 1.0, 1.0},
    {0.0, 1.0, 0.0, 1.0, 1.0}, {1.0, 0.0, 1.0, 0.0, 1.0},
    {0.0, 0.0, 1.0, 0.0, 1.0}, {1.0, 0.0, 0.0, 0.0, 1.0},
    {0.0, 1.0, 1.0, 1.0, 0.0}, {1.0, 0.0, 1.0, 0.0, 0.0},
    {0.0, 1.0, 1.0, 0.0, 1.0}, {0.0, 1.0, 1.0, 0.0, 0.0},
    {1.0, 1.0, 0.0, 1.0, 1.0}, {1.0, 0.0, 0.0, 1.0, 1.0},
    {0.0, 1.0, 1.0, 0.0, 1.0}, {1.0, 1.0, 0.0, 0.0, 1.0},
    {1.0, 0.0, 0.0, 1.0, 1.0}, {1.0, 1.0, 0.0, 0.0, 1.0},
    {0.0, 1.0, 0.0, 0.0, 0.0}, {1.0, 0.0, 0.0, 1.0, 1.0},
    {1.0, 0.0, 1.0, 0.0, 1.0}, {0.0, 0.0, 1.0, 1.0, 1.0},
    {0.0, 1.0, 1.0, 1.0, 1.0}, {1.0, 0.0, 0.0, 0.0, 1.0},
    {0.0, 0.0, 1.0, 1.0, 1.0}, {0.0, 1.0, 1.0, 0.0, 1.0},
    {0.0, 1.0, 1.0, 0.0, 1.0}, {1.0, 0.0, 1.0, 0.0, 1.0},
    {0.0, 1.0, 0.0, 0.0, 0.0}, {1.0, 0.0, 0.0, 1.0, 1.0},
    {1.0, 0.0, 1.0, 0.0, 1.0}, {0.0, 0.0, 1.0, 1.0, 0.0},
    {0.0, 1.0, 1.0, 0.0, 1.0}, {0.0, 0.0, 1.0, 1.0, 1.0},
    {0.0, 0.0, 1.0, 1.0, 1.0}, {0.0, 1.0, 0.0, 1.0, 0.0},
    {0.0, 1.0, 1.0, 1.0, 1.0}, {0.0, 0.0, 1.0, 0.0, 1.0},
    {0.0, 1.0, 0.0, 0.0, 0.0}, {1.0, 0.0, 0.0, 1.0, 0.0},
    {0.0, 1.0, 1.0, 1.0, 0.0}, {1.0, 1.0, 0.0, 1.0, 0.0},
    {0.0, 1.0, 1.0, 1.0, 0.0}, {0.0, 1.0, 0.0, 0.0, 0.0},
    {0.0, 1.0, 0.0, 0.0, 0.0}, {0.0, 1.0, 0.0, 1.0, 1.0},
    {0.0, 1.0, 1.0, 1.0, 0.0}, {0.0, 1.0, 0.0, 1.0, 0.0},
    {0.0, 1.0, 1.0, 0.0, 0.0}, {0.0, 1.0, 0.0, 1.0, 1.0},
    {1.0, 0.0, 0.0, 0.0, 0.0}, {1.0, 0.0, 0.0, 0.0, 1.0},
    {0.0, 1.0, 0.0, 1.0, 0.0}, {0.0, 1.0, 1.0, 1.0, 1.0},
    {1.0, 0.0, 1.0, 1.0, 1.0}, {0.0, 0.0, 1.0, 1.0, 0.0},
    {1.0, 0.0, 1.0, 1.0, 1.0}, {0.0, 1.0, 1.0, 0.0, 1.0},
    {1.0, 0.0, 0.0, 0.0, 1.0}, {0.0, 1.0, 0.0, 1.0, 1.0},
    {1.0, 1.0, 0.0, 0.0, 0.0}, {0.0, 0.0, 1.0, 1.0, 0.0},
    {0.0, 1.0, 1.0, 1.0, 0.0}, {1.0, 0.0, 0.0, 1.0, 1.0},
    {0.0, 1.0, 1.0, 0.0, 1.0}, {1.0, 0.0, 1.0, 0.0, 0.0},
    {0.0, 0.0, 0.0, 1.0, 0.0}, {1.0, 0.0, 0.0, 1.0, 0.0},
    {0.0, 1.0, 1.0, 1.0, 1.0}, {1.0, 1.0, 0.0, 1.0, 0.0},
    {1.0, 1.0, 0.0, 0.0, 0.0}, {1.0, 0.0, 1.0, 1.0, 0.0},
    {1.0, 0.0, 1.0, 1.0, 0.0}, {1.0, 0.0, 0.0, 0.0, 1.0},
    {0.0, 0.0, 0.0, 0.0, 1.0}, {0.0, 1.0, 0.0, 1.0, 0.0},
    {1.0, 1.0, 0.0, 0.0, 0.0}, {0.0, 1.0, 0.0, 0.0, 1.0},
    {0.0, 1.0, 1.0, 0.0, 0.0}, {1.0, 1.0, 1.0, 1.0, 0.0},
    {0.0, 1.0, 0.0, 0.0, 1.0}, {0.0, 1.0, 1.0, 0.0, 0.0},
    {0.0, 0.0, 1.0, 0.0, 0.0}, {0.0, 1.0, 0.0, 0.0, 0.0},
    {0.0, 1.0, 1.0, 0.0, 1.0}, {1.0, 0.0, 1.0, 0.0, 0.0},
    {1.0, 0.0, 0.0, 0.0, 0.0}, {1.0, 0.0, 0.0, 1.0, 0.0},
    {1.0, 0.0, 1.0, 0.0, 0.0}, {1.0, 0.0, 1.0, 0.0, 1.0},
    {1.0, 0.0, 0.0, 0.0, 0.0}, {1.0, 0.0, 1.0, 1.0, 1.0},
    {0.0, 0.0, 0.0, 1.0, 0.0}, {0.0, 1.0, 1.0, 1.0, 0.0},
    {0.0, 1.0, 0.0, 1.0, 0.0}, {1.0, 0.0, 1.0, 1.0, 0.0},
    {1.0, 0.0, 1.0, 1.0, 0.0}, {1.0, 0.0, 0.0, 0.0, 0.0},
    {0.0, 1.0, 0.0, 1.0, 1.0}, {0.0, 1.0, 1.0, 1.0, 1.0},
    {1.0, 0.0, 0.0, 0.0, 1.0}, {1.0, 0.0, 0.0, 1.0, 0.0},
    {0.0, 1.0, 0.0, 1.0, 1.0}, {1.0, 0.0, 1.0, 0.0, 1.0},
    {1.0, 1.0, 0.0, 0.0, 1.0}, {0.0, 1.0, 1.0, 0.0, 1.0},
    {1.0, 1.0, 0.0, 0.0, 1.0}, {1.0, 0.0, 1.0, 0.0, 0.0},
    {1.0, 0.0, 1.0, 0.0, 0.0}, {0.0, 0.0, 0.0, 1.0, 1.0},
    {1.0, 0.0, 0.0, 0.0, 1.0}, {0.0, 1.0, 1.0, 1.0, 1.0},
    {1.0, 1.0, 0.0, 1.0, 1.0}, {0.0, 1.0, 0.0, 1.0, 0.0},
    {1.0, 0.0, 0.0, 0.0, 0.0}, {0.0, 0.0, 0.0, 0.0, 0.0},
    {0.0, 1.0, 1.0, 1.0, 1.0}, {1.0, 1.0, 1.0, 0.0, 1.0},
    {1.0, 0.0, 1.0, 0.0, 0.0}, {0.0, 1.0, 0.0, 0.0, 0.0},
    {0.0, 1.0, 1.0, 0.0, 0.0}, {1.0, 0.0, 1.0, 1.0, 1.0},
    {0.0, 1.0, 1.0, 1.0, 0.0}, {1.0, 0.0, 1.0, 1.0, 0.0},
    {0.0, 1.0, 1.0, 0.0, 1.0}, {1.0, 0.0, 0.0, 1.0, 0.0}};
const std::vector<std::vector<double>> val_data = {
    {1.0, 1.0, 0.0, 0.0, 0.0, 1.0, 0.0, 1.0},
    {0.0, 1.0, 1.0, 0.0, 0.0, 0.0, 1.0, 1.0},
    {1.0, 0.0, 0.0, 0.0, 1.0, 1.0, 0.0, 0.0},
    {0.0, 0.0, 0.0, 0.0, 1.0, 1.0, 0.0, 0.0},
    {0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0},
    {1.0, 1.0, 1.0, 0.0, 1.0, 1.0, 1.0, 0.0},
    {0.0, 0.0, 0.0, 0.0, 1.0, 1.0, 0.0, 1.0},
    {1.0, 1.0, 1.0, 0.0, 1.0, 1.0, 0.0, 0.0},
    {1.0, 1.0, 1.0, 0.0, 1.0, 0.0, 0.0, 0.0},
    {0.0, 0.0, 1.0, 1.0, 1.0, 1.0, 0.0, 1.0},
    {0.0, 0.0, 0.0, 1.0, 1.0, 0.0, 1.0, 1.0},
    {0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 1.0},
    {0.0, 1.0, 0.0, 0.0, 0.0, 1.0, 1.0, 1.0},
    {1.0, 1.0, 1.0, 1.0, 0.0, 0.0, 1.0, 1.0},
    {0.0, 1.0, 1.0, 1.0, 0.0, 0.0, 0.0, 0.0},
    {1.0, 0.0, 0.0, 1.0, 1.0, 0.0, 1.0, 1.0},
    {1.0, 1.0, 0.0, 1.0, 0.0, 1.0, 0.0, 0.0},
    {1.0, 1.0, 1.0, 0.0, 0.0, 0.0, 0.0, 1.0},
    {1.0, 0.0, 1.0, 0.0, 1.0, 1.0, 0.0, 1.0},
    {0.0, 0.0, 0.0, 1.0, 1.0, 0.0, 1.0, 0.0},
    {0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0},
    {1.0, 0.0, 1.0, 1.0, 1.0, 1.0, 1.0, 0.0},
    {1.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0},
    {0.0, 1.0, 1.0, 1.0, 0.0, 0.0, 1.0, 0.0},
    {0.0, 1.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0},
    {0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 1.0, 0.0},
    {0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 1.0, 1.0},
    {0.0, 1.0, 0.0, 1.0, 1.0, 0.0, 0.0, 1.0},
    {0.0, 0.0, 0.0, 1.0, 1.0, 1.0, 1.0, 1.0},
    {0.0, 0.0, 1.0, 0.0, 1.0, 1.0, 1.0, 1.0},
    {1.0, 0.0, 1.0, 1.0, 0.0, 0.0, 1.0, 1.0},
    {0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 1.0, 0.0},
    {0.0, 1.0, 0.0, 1.0, 1.0, 0.0, 1.0, 1.0},
    {0.0, 0.0, 1.0, 0.0, 1.0, 1.0, 1.0, 0.0},
    {0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 1.0},
    {0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 1.0, 1.0},
    {1.0, 1.0, 0.0, 1.0, 1.0, 0.0, 0.0, 1.0},
    {1.0, 0.0, 0.0, 1.0, 0.0, 1.0, 0.0, 1.0},
    {1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 0.0, 1.0},
    {1.0, 0.0, 1.0, 0.0, 0.0, 1.0, 0.0, 0.0},
    {1.0, 0.0, 1.0, 0.0, 1.0, 1.0, 1.0, 0.0},
    {0.0, 0.0, 1.0, 1.0, 1.0, 1.0, 1.0, 0.0},
    {1.0, 1.0, 1.0, 1.0, 0.0, 1.0, 1.0, 1.0},
    {1.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 1.0},
    {0.0, 0.0, 1.0, 1.0, 0.0, 0.0, 1.0, 1.0},
    {1.0, 0.0, 1.0, 0.0, 0.0, 0.0, 1.0, 0.0},
    {0.0, 1.0, 0.0, 1.0, 0.0, 1.0, 0.0, 0.0},
    {0.0, 1.0, 1.0, 0.0, 1.0, 0.0, 1.0, 1.0},
    {0.0, 1.0, 0.0, 1.0, 0.0, 1.0, 0.0, 1.0},
    {1.0, 0.0, 1.0, 0.0, 1.0, 0.0, 0.0, 0.0},
    {1.0, 1.0, 0.0, 1.0, 1.0, 1.0, 1.0, 1.0},
    {1.0, 0.0, 1.0, 0.0, 1.0, 0.0, 1.0, 0.0}};
const std::vector<std::vector<double>> val_label = {
    {1.0, 0.0, 0.0, 0.0, 1.0}, {0.0, 1.0, 0.0, 0.0, 1.0},
    {1.0, 0.0, 1.0, 0.0, 0.0}, {0.0, 1.0, 1.0, 0.0, 0.0},
    {0.0, 0.0, 1.0, 0.0, 0.0}, {1.0, 1.0, 1.0, 0.0, 0.0},
    {0.0, 1.0, 1.0, 0.0, 1.0}, {1.0, 1.0, 0.0, 1.0, 0.0},
    {1.0, 0.0, 1.0, 1.0, 0.0}, {1.0, 0.0, 0.0, 0.0, 0.0},
    {0.0, 1.0, 1.0, 0.0, 0.0}, {0.0, 1.0, 0.0, 0.0, 1.0},
    {0.0, 1.0, 0.0, 1.0, 1.0}, {1.0, 0.0, 0.0, 1.0, 0.0},
    {0.0, 0.0, 1.0, 1.0, 1.0}, {1.0, 0.0, 1.0, 0.0, 0.0},
    {1.0, 0.0, 0.0, 0.0, 1.0}, {0.0, 1.0, 1.0, 1.0, 1.0},
    {1.0, 0.0, 1.0, 1.0, 1.0}, {0.0, 1.0, 0.0, 1.0, 1.0},
    {0.0, 0.0, 1.0, 0.0, 1.0}, {1.0, 1.0, 0.0, 0.0, 1.0},
    {0.0, 1.0, 1.0, 0.0, 1.0}, {0.0, 1.0, 0.0, 0.0, 1.0},
    {0.0, 0.0, 1.0, 0.0, 1.0}, {0.0, 0.0, 1.0, 1.0, 0.0},
    {0.0, 0.0, 1.0, 0.0, 0.0}, {0.0, 1.0, 1.0, 1.0, 0.0},
    {1.0, 0.0, 0.0, 0.0, 0.0}, {1.0, 0.0, 0.0, 0.0, 1.0},
    {0.0, 1.0, 1.0, 1.0, 0.0}, {0.0, 0.0, 1.0, 0.0, 0.0},
    {1.0, 0.0, 0.0, 0.0, 0.0}, {1.0, 0.0, 0.0, 0.0, 0.0},
    {0.0, 0.0, 1.0, 0.0, 1.0}, {0.0, 0.0, 1.0, 1.0, 1.0},
    {1.0, 0.0, 1.0, 1.0, 0.0}, {0.0, 1.0, 1.0, 1.0, 0.0},
    {1.0, 1.0, 1.0, 0.0, 0.0}, {0.0, 1.0, 1.0, 1.0, 0.0},
    {1.0, 1.0, 0.0, 0.0, 0.0}, {1.0, 0.0, 0.0, 0.0, 1.0},
    {1.0, 0.0, 1.0, 1.0, 0.0}, {1.0, 0.0, 0.0, 0.0, 1.0},
    {0.0, 0.0, 1.0, 1.0, 0.0}, {0.0, 1.0, 1.0, 0.0, 0.0},
    {0.0, 1.0, 0.0, 0.0, 1.0}, {1.0, 0.0, 0.0, 0.0, 1.0},
    {0.0, 1.0, 0.0, 1.0, 0.0}, {1.0, 0.0, 0.0, 1.0, 0.0},
    {1.0, 1.0, 1.0, 0.0, 0.0}, {1.0, 0.0, 1.0, 0.0, 0.0}};

const double learning_rate = 0.5f;
const int training_epochs = 500;

const int n_hidden_1 = 17;
const int n_hidden_2 = 9;
const int n_input = 8;
const int n_output = 5;

// weights
std::vector<std::vector<double>> w1(n_hidden_1, std::vector<double>(n_input));
std::vector<std::vector<double>> w2(n_hidden_2,
                                    std::vector<double>(n_hidden_1));
std::vector<std::vector<double>> w3(n_output, std::vector<double>(n_hidden_2));
// biases
std::vector<double> b1(n_hidden_1);
std::vector<double> b2(n_hidden_2);
std::vector<double> b3(n_output);

inline double inner_prod(const std::vector<double> &lhs,
                         const std::vector<double> &rhs) {
  double ret = 0.0f;
  for (int i = 0; i < lhs.size(); ++i) {
    ret += lhs[i] * rhs[i];
  }
  return ret;
}

inline double sigmoid(double x) { return 1.0f / (1.0f + std::exp(-x)); }

std::vector<double> mlp_forward(const std::vector<double> &input) {
  std::vector<double> z1(n_hidden_1);
  for (int i = 0; i < n_hidden_1; ++i) {
    z1[i] = sigmoid(inner_prod(input, w1[i]) + b1[i]);
  }
  std::vector<double> z2(n_hidden_2);
  for (int i = 0; i < n_hidden_2; ++i) {
    z2[i] = sigmoid(inner_prod(z1, w2[i]) + b2[i]);
  }
  std::vector<double> out(n_output);
  for (int i = 0; i < n_output; ++i) {
    out[i] = sigmoid(inner_prod(z2, w3[i]) + b3[i]);
  }
  return out;
}

double loss(const std::vector<double> &h, const std::vector<double> &y) {
  double ret = 0.0f;
  for (int i = 0; i < h.size(); ++i) {
    ret += (h[i] - y[i]) * (h[i] - y[i]);
  }
  return ret * 0.5f;
}

double accuracy(const std::vector<double> &h, const std::vector<double> &y) {
  double ret;
  int count = 0;
  for (int i = 0; i < h.size(); ++i) {
    double t = h[i] < 0.5f ? 0.0f : 1.0f;
    if (abs(t - y[i]) < 1e-9) {
      count++;
    }
  }
  return count / (double)h.size();
}

void mlp_backward(const std::vector<double> &input,
                  const std::vector<double> &label) {
  // weights
  std::vector<std::vector<double>> d_w1(n_hidden_1,
                                        std::vector<double>(n_input));
  std::vector<std::vector<double>> d_w2(n_hidden_2,
                                        std::vector<double>(n_hidden_1));
  std::vector<std::vector<double>> d_w3(n_output,
                                        std::vector<double>(n_hidden_2));
  // biases
  std::vector<double> d_b1(n_hidden_1);
  std::vector<double> d_b2(n_hidden_2);
  std::vector<double> d_b3(n_output);
  for (int i = 0; i < n_hidden_1; ++i) {
    double l0 = loss(mlp_forward(input), label);
    b1[i] += 1e-9;
    double l = loss(mlp_forward(input), label);
    b1[i] -= 1e-9;
    d_b1[i] = (l - l0) / 1e-9 * learning_rate;
    for (int j = 0; j < n_input; ++j) {
      w1[i][j] += 1e-9;
      double l = loss(mlp_forward(input), label);
      w1[i][j] -= 1e-9;
      d_w1[i][j] = (l - l0) / 1e-9 * learning_rate;
    }
  }
  for (int i = 0; i < n_hidden_2; ++i) {
    double l0 = loss(mlp_forward(input), label);
    b2[i] += 1e-9;
    double l = loss(mlp_forward(input), label);
    b2[i] -= 1e-9;
    d_b2[i] = (l - l0) / 1e-9 * learning_rate;
    for (int j = 0; j < n_hidden_1; ++j) {
      w2[i][j] += 1e-9;
      double l = loss(mlp_forward(input), label);
      w2[i][j] -= 1e-9;
      d_w2[i][j] = (l - l0) / 1e-9 * learning_rate;
    }
  }
  for (int i = 0; i < n_output; ++i) {
    double l0 = loss(mlp_forward(input), label);
    b3[i] += 1e-9;
    double l = loss(mlp_forward(input), label);
    b3[i] -= 1e-9;
    d_b3[i] = (l - l0) / 1e-9 * learning_rate;
    for (int j = 0; j < n_hidden_2; ++j) {
      w3[i][j] += 1e-9;
      double l = loss(mlp_forward(input), label);
      w3[i][j] -= 1e-9;
      d_w3[i][j] = (l - l0) / 1e-9 * learning_rate;
    }
  }
  for (int i = 0; i < n_hidden_1; ++i) {
    b1[i] -= d_b1[i];
    for (int j = 0; j < n_input; ++j) {
      w1[i][j] -= d_w1[i][j];
    }
  }
  for (int i = 0; i < n_hidden_2; ++i) {
    b2[i] -= d_b2[i];
    for (int j = 0; j < n_hidden_1; ++j) {
      w2[i][j] -= d_w2[i][j];
    }
  }
  for (int i = 0; i < n_output; ++i) {
    b3[i] -= d_b3[i];
    for (int j = 0; j < n_hidden_2; ++j) {
      w3[i][j] -= d_w3[i][j];
    }
  }
}
int main() {
  // init
  std::random_device rd;
  std::mt19937 gen(rd());
  std::uniform_real_distribution<> dis(-1.0, 1.0);
  for (int i = 0; i < n_hidden_1; ++i) {
    b1[i] = dis(gen);
    for (int j = 0; j < n_input; ++j) {
      w1[i][j] = dis(gen);
    }
  }
  for (int i = 0; i < n_hidden_2; ++i) {
    b2[i] = dis(gen);
    for (int j = 0; j < n_hidden_1; ++j) {
      w2[i][j] = dis(gen);
    }
  }
  for (int i = 0; i < n_output; ++i) {
    b3[i] = dis(gen);
    for (int j = 0; j < n_hidden_2; ++j) {
      w3[i][j] = dis(gen);
    }
  }
  // train
  int n = train_label.size();
  int m = val_label.size();
  for (int i = 0; i < training_epochs; ++i) {
    for (int j = 0; j < n; ++j) {
      mlp_backward(train_data[j], train_label[j]);
    }
    double acc = 0.0f;
    for (int j = 0; j < n; ++j) {
      acc += accuracy(mlp_forward(train_data[j]), train_label[j]);
    }
    std::cout << "Train Accuracy:" << acc / n << " ";
    acc = 0.0f;
    for (int j = 0; j < m; ++j) {
      acc += accuracy(mlp_forward(val_data[j]), val_label[j]);
    }
    std::cout << "Val Accuracy:" << acc / m << std::endl;
  }
}