// find additional faces
vector<Polygon> bound_polygon(Polygon &points) {
    reorder_ccw(points);
    rotate(points.begin(), min_element(points.begin(), points.end(), PointCmp()), points.end());

    // find left bottom corner
    const int min_x = min_element(points.begin(), points.end(), PointCmpByX())->x - 1;
    const int min_y = min_element(points.begin(), points.end(), PointCmpByY())->y - 1;

    // find the farthest point
    auto farthest = *max_element(points.begin(), points.end(), [](const Point &a, const Point &b) {
        return a.x + a.y < b.x + b.y;
    });

    // find other coordinates
    const int max_x = farthest.x + (farthest.y - min_y) + 1;
    const int max_y = farthest.y + (farthest.x - min_x) + 1;

    const Polygon triangle = {Point(min_x, min_y, ++max_id),
                              Point(max_x, min_y, ++max_id),
                              Point(min_x, max_y, ++max_id)};

    int iter = 0;

    Polygon p1;
    p1.push_back(triangle[0]);
    while (points[iter].id != farthest.id) {
        p1.push_back(points[iter++]);
    }
    p1.push_back(points[iter]);
    p1.push_back(triangle[1]);

    Polygon p2;
    p2.push_back(triangle[1]);
    p2.push_back(farthest);
    p2.push_back(triangle[2]);

    Polygon p3;
    p3.push_back(triangle[2]);
    while (iter < points.size()) {
        p3.push_back(points[iter++]);
    }
    p3.push_back(points[0]);
    p3.push_back(triangle[0]);

    vector<Polygon> faces = {p1, p2, p3};

    return faces;
}