Convex hull

#include<bits/stdc++.h>

using namespace std;

using ll = long long;
using ii = pair <int, int>;
#define all(v) begin(v), end(v)
#define sz(v) (int)(v).size()

template <class T> int sgn(T x) { return (x > 0) - (x < 0); }
template<class T>
struct Point {
	typedef Point P;
	T x, y;
	explicit Point(T x=0, T y=0) : x(x), y(y) {}
	bool operator<(P p) const { return tie(x,y) < tie(p.x,p.y); }
	bool operator==(P p) const { return tie(x,y)==tie(p.x,p.y); }
	P operator+(P p) const { return P(x+p.x, y+p.y); }
	P operator-(P p) const { return P(x-p.x, y-p.y); }
	P operator*(T d) const { return P(x*d, y*d); }
	P operator/(T d) const { return P(x/d, y/d); }
	T dot(P p) const { return x*p.x + y*p.y; }
	T cross(P p) const { return x*p.y - y*p.x; }
	T cross(P a, P b) const { return (a-*this).cross(b-*this); }
	T dist2() const { return x*x + y*y; }
	double dist() const { return sqrt((double)dist2()); }
	// angle to x-axis in interval [-pi, pi]
	double angle() const { return atan2(y, x); }
	P unit() const { return *this/dist(); } // makes dist()=1
	P perp() const { return P(-y, x); } // rotates +90 degrees
	P normal() const { return perp().unit(); }
	// returns point rotated 'a' radians ccw around the origin
	P rotate(double a) const {
		return P(x*cos(a)-y*sin(a),x*sin(a)+y*cos(a)); }
	friend ostream& operator<<(ostream& os, P p) {
		return os << "(" << p.x << "," << p.y << ")"; }
};

typedef Point<ll> P;
vector<P> convexHull(vector<P> pts) {
	if (sz(pts) <= 1) return pts;
	sort(all(pts));
	vector<P> h(sz(pts)+1);
	int s = 0, t = 0;
	for (int it = 2; it--; s = --t, reverse(all(pts)))
		for (P p : pts) {
			while (t >= s + 2 && h[t-2].cross(h[t-1], p) <= 0) t--;
			h[t++] = p;
		}
	return {h.begin(), h.begin() + t - (t == 2 && h[0] == h[1])};
}

int main () {
  ios::sync_with_stdio(0); cin.tie(0);
#ifdef LOCAL
  freopen("in.txt", "r", stdin);
#endif
  int n;
  while (cin >> n) {
    if (n == 0) break;
    vector <P> points;
    for (int i = 0; i < n; ++i) {
      int x, y; cin >> x >> y;
      points.emplace_back(x, y);
    }
    ll ans = 0;
    for (int i = 0; i < n; ++i) {
      for (int j = i + 1; j < n; ++j) {
        for (int k = j + 1; k < n; ++k) {
          for (int l = k + 1; l < n; ++l) {
            auto CH = convexHull({points[i], points[j], points[k], points[l]});
            ans += 1LL * ((int) CH.size() == 4);
          }
        }
      }
    }
    cout << ans << "\n";
  }
}
/*
array bound?
overflow?
print newline after every cases
idea correct?
*/