vector<PII> chull(vector<PII>& v) {
    int n = v.size();
    vector<PII> lower(n);
    int k = 0;
    for (int i = 0; i < n; ++i) {
        while (k>=2 and esc(lower[k-2],lower[k-1],v[i])<0) --k;
        lower[k++]=v[i];
    }
    lower.resize(k);
    return lower;
}