Convex Shell [unfinished]

#include <cstdio>

#include <algorithm>
#include <functional>
#include <set>

using namespace std;

typedef long long ll;

template <class Num>
struct Point {
    Num x, y;

    Point() {}

    Point(const Num& x, const Num& y) : x(x), y(y) {}

    bool operator<(const Point& p) const {
        if (x != p.x)
            return x < p.x;
        return y < p.y;
    }

    Point operator+(const Point& p) const {
        return Point(x + p.x, y + p.y);
    }

    Point operator-(const Point& p) const {
        return Point(x - p.x, y - p.y);
    }

    Point operator-() const {
        return Point(-x, -y);
    }

    Point operator*(const Num& a) const {
        return Point(x * a, y * a);
    }

    Point operator/(const Num& a) const {
        return Point(x / a, y / a);
    }

    Num operator^(const Point& p) const {
        return x * p.x + y * p.y;
    }

    Num operator*(const Point& p) const {
        return x * p.y - y * p.x;
    }

    friend Point operator*(const Num& a, const Point& p) {
        return Point(a * p.x, a * p.y);
    }
};

template <class Num>
struct ConvexShell {
    typedef Point<Num> PointT;

    set<PointT> shell;

    void insert(const PointT& p) {
        set<PointT>::iterator it = shell.insert(p).first;
        if (it != shell.begin() && next(it))
    }

    PointT bound(const PointT& slope) const;
};

ConvexShell<ll> slope;

int main() {
    return 0;
}