void convex_hull(points &a, points &res) {
res.resize(2 * a.size() + 10);
sort(a.begin(), a.end(), cmpxy);
a.erase(unique(a.begin(), a.end()), a.end());
int m = 0;
for (int i = 0; i < (int)a.size(); i ++) {
while(m > 1 && dcmp(det(res[m - 1] - res[m - 2], a[i] - res[m - 2])) <= 0) --m;
res[m++] = a[i];
}
int k = m;
for (int i = (int)a.size() - 2; i >= 0; i --) {
while(m > k && dcmp(det(res[m - 1] - res[m - 2], a[i] - res[m - 2])) <= 0) --m;
res[m++] = a[i];
}
res.resize(m);
//if (a.size() > 1) res.resize(m - 1);
}
points convexHull (points a)
{
points up,dw;
sort (a.begin(), a.end());
for (int i=0;i<a.size();i++)
{
while (up.size()>=2 && ccw(*++up.rbegin(),*up.rbegin(),a[i])>=0) up.pop_back();
while (dw.size()>=2 && ccw(*++dw.rbegin(),*dw.rbegin(),a[i])<=0) dw.pop_back();
up.emplace_back(a[i]);
dw.emplace_back(a[i]);
}
up.insert (up.end(), ++dw.rbegin(), --dw.rend());
return up;
}