//https://atcoder.jp/contests/abc244/submissions/30254721 #include #include #include #include #include #include using namespace std; using ll = long long; using Point = pair; const ll INF = LLONG_MAX / 4; const double inv_phi = (sqrt(5) - 1) / 2; void chmax(ll& a, ll b){ if(a < b) a = b; } ll ccw(Point a, Point b, Point c){ ll cross = (b.first - a.first) * (c.second - b.second) - (b.second - a.second) * (c.first - b.first); if(cross > 0) return 1; else if(cross == 0) return 0; else return -1; } struct ConvexHull{ vector lower, upper; ConvexHull(Point p): lower{p}, upper{p}{} ConvexHull(const ConvexHull& a, const ConvexHull& b){ vector v; merge(a.lower.begin(), a.lower.end(), b.lower.begin(), b.lower.end(), back_inserter(v)); for(Point p : v){ while(lower.size() >= 2 && ccw(lower.rbegin()[1], lower.back(), p) <= 0){ lower.pop_back(); } lower.push_back(p); } v.clear(); merge(a.upper.begin(), a.upper.end(), b.upper.begin(), b.upper.end(), back_inserter(v)); for(Point p : v){ while(upper.size() >= 2 && ccw(upper.rbegin()[1], upper.back(), p) >= 0){ upper.pop_back(); } upper.push_back(p); } } ll get(ll A, ll B) const { auto& s = B < 0 ? lower : upper; // golden-section search auto f = [&](ll i){ return A * s[i].first + B * s[i].second; }; ll l = 0, r = s.size() - 1, r2 = round(r * inv_phi), f_r2 = f(r2); while(abs(l - r) >= 6){ ll l2 = r + llround((l - r) * inv_phi), f_l2 = f(l2); if(f_l2 < f_r2) tie(l, r) = tuple{r, l2}; else tie(r, r2, f_r2) = tuple{r2, l2, f_l2}; } ll ans = -INF; if(l > r) swap(l, r); for(ll i = l; i <= r; i++) chmax(ans, f(i)); return ans; } }; int main(){ cin.tie(nullptr); ios::sync_with_stdio(false); ll Q; cin >> Q; vector S; ll ans = -INF; for(ll i = 1; i <= Q; i++){ long long X, Y; cin >> X >> Y; S.emplace_back(pair{X, Y}); for(ll j = 1; (i & j) == 0; j <<= 1){ S.rbegin()[1] = ConvexHull(S.rbegin()[1], S.back()); S.pop_back(); } for(auto& s : S) chmax(ans, s.get(-Y, X)); for(auto& s : S) chmax(ans, s.get(Y, -X)); } cout << ans << '\n'; }