#include <bits/stdc++.h> #include <ext/pb_ds/assoc_container.hpp> #include <ext/pb_ds/tree_policy.hpp> #define ll long long #define ld long double #define ull unsigned long long #define ff first #define ss second #define pii pair<int,int> #define pll pair<long long, long long> #define vi vector<int> #define vl vector<long long> #define pb push_back #define rep(i, b) for(int i = 0; i < (b); ++i) #define rep2(i,a,b) for(int i = a; i <= (b); ++i) #define rep3(i,a,b,c) for(int i = a; i <= (b); i+=c) #define count_bits(x) __builtin_popcountll((x)) #define all(x) (x).begin(),(x).end() #define siz(x) (int)(x).size() #define forall(it,x) for(auto& it:(x)) using namespace __gnu_pbds; using namespace std; typedef tree<int, null_type, less<int>, rb_tree_tag,tree_order_statistics_node_update> ordered_set; //mt19937 mt;void random_start(){mt.seed(chrono::time_point_cast<chrono::milliseconds>(chrono::high_resolution_clock::now()).time_since_epoch().count());} //ll los(ll a, ll b) {return a + (mt() % (b-a+1));} const int INF = 1e9+50; const ll INF_L = 1e18+40; const ll MOD = 1e9+7; struct line { ll a,b; ll operator()(ll x) { return a*x+b; } }; struct lichao { ll l = 0; ll r = 1e6; line f = {(ll)1e9,(ll)1e17}; lichao* left = NULL; lichao* right = NULL; void add_line(line f2) { if(l > r) return; if(f.a == 1e9 && f.b == 1e17) { f = f2; return; } ll mid = (l+r)/2; if(f2(mid) < f(mid)) swap(f,f2); ll p1 = f2.b-f.b; ll p2 = f.a-f2.a; if(p2 == 0) return; if(p2 < 0) { p1 *= -1; p2 *= -1; } if(mid*p2 > p1 || (mid*p2 == p1 && f2.a > f.a)) { if(left == NULL) { left = new lichao; left -> l = l; left -> r = mid-1; } left->add_line(f2); } else { if(right == NULL) { right = new lichao; right -> l = mid+1; right -> r = r; } right->add_line(f2); } } ll query(ll x) { ll ans = f(x); if(x < (l+r)/2) { if(left != NULL) ans = min(ans,left->query(x)); } else { if(right != NULL) ans = min(ans,right->query(x)); } return ans; } }; lichao tree_; ll pref[100001]; ll H[100001]; ll dp[100001]; int main() { ios_base::sync_with_stdio(0);cin.tie(0);cout.tie(0); //random_start(); int n; cin >> n; rep2(i,1,n) cin >> H[i]; rep2(i,1,n) { cin >> pref[i]; pref[i] += pref[i-1]; } tree_.add_line({-2*H[1],-pref[1]+H[1]*H[1]}); rep2(i,2,n) { dp[i] = tree_.query(H[i])+pref[i-1]+H[i]*H[i]; tree_.add_line({-2*H[i],-pref[i]+H[i]*H[i]+dp[i]}); } cout << dp[n] << "\n"; }