Convex Hull Dinamico

  struct upper {
	set<pt> se;
	set<pt>::iterator it;

	int is_under(pt p) { // 1 -> inside ; 2 -> border
		it = se.lower_bound(p);
		if (it == se.end()) return 0;
		if (it == se.begin()) return p == *it ? 2 : 0;
		if (ccw(p, *it, *prev(it))) return 1;
		return ccw(p, *prev(it), *it) ? 0 : 2;
	}
	void insert(pt p) {
		if (is_under(p)) return;

		if (it != se.end()) while (next(it) != se.end() and !ccw(*next(it), *it, p))
			it = se.erase(it);
		if (it != se.begin()) while (--it != se.begin() and !ccw(p, *it, *prev(it)))
			it = se.erase(it);

		se.insert(p);
	}
};

struct dyn_hull {
	upper U, L;

	int is_inside(pt p) {
		int u = U.is_under(p), l = L.is_under({-p.x, -p.y});
		if (!u or !l) return 0;
		return max(u, l);
	}
	void insert(pt p) {
		U.insert(p);
		L.insert({-p.x, -p.y});
	}
	int size() {
		int ans = U.se.size() + L.se.size();
		return ans <= 2 ? ans/2 : ans-2;
	}
};