#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using ld = long double;
using T = tuple<ll, ll, ll>;
#define int long long
#define Base 41
#define sz(a) (int)a.size()
#define FOR(i, a, b) for ( int i = a ; i <= b ; i++ )
#define FORD(i, a, b) for (int i = a; i >= b; i --)
#define all(x) x.begin() , x.end()
#define pii pair<int , int>
#define fi first
#define se second
#define Lg(x) 31 - __builtin_clz(x)
constexpr ll LINF = (1ll << 60);
constexpr int INF = (1ll << 30);
constexpr int MAX = 1e6 + 5;
constexpr int Mod = 1e9 + 7;
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
void setupIO(){
#define name "Whisper"
//Phu Trong from Nguyen Tat Thanh High School for gifted student
srand(time(NULL));
cin.tie(nullptr)->sync_with_stdio(false); cout.tie(nullptr);
// freopen(name".inp", "r", stdin);
// freopen(name".out", "w", stdout);
cout << fixed << setprecision(10);
}
bool minimize(int&a , int b){
if (a > b){
a = b; return 1;
}
return 0;
}
bool maximize(int&a, int b){
if (a < b){
a = b; return 1;
}
return 0;
}
int n;
int h[MAX], w[MAX];
int s[MAX];
int dp[MAX];
struct Line{
int a, b;
Line():a(0), b(LINF){};
Line(int _a, int _b){
a = _a;
b = _b;
}
int f(int x){
return a * x + b;
}
};
struct LichaoTree{
// query for min
int n;
vector<Line> f;
LichaoTree(int _n){
this -> n = _n;
f.resize(4 * n + 5);
}
void addLine(int id, int l, int r, Line line){
// nếu là max chỉ cần đổi dấu
if (l == r){
if (line.f(l) < f[id].f(l)) f[id] = line;
return;
}
int mid = (l + r) >> 1;
if (line.a > f[id].a) swap(line, f[id]);
if (line.f(mid) < f[id].f(mid)){
swap(line, f[id]);
addLine(id << 1, l, mid, line);
}
else{
addLine(id << 1 | 1, mid + 1, r, line);
}
}
int qry(int id, int l, int r, int x){
int ans = f[id].f(x);
if (l == r) return ans;
int mid = (l + r) >> 1;
if (x <= mid)
return min(ans, qry(id << 1, l, mid, x));
return min(ans, qry(id << 1 | 1, mid + 1, r, x));
}
void addLine(int a, int b){
addLine(1, 1, n, Line(a, b));
}
int qry(int x){
return qry(1, 1, n, x);
}
};
namespace SUB1{
void solve(){
auto cal = [&](int i, int j){
return (h[i] - h[j]) * (h[i] - h[j]) - w[j];
};
memset(dp, 0x3f, sizeof dp);
dp[1] = 0;
for (int i = 2; i <= n; ++i){
for (int j = 1; j < i; ++j){
dp[i] = min(dp[i], dp[j] + cal(j, i));
}
cout << dp[i] << " ";
}
cout << dp[n] + accumulate(w + 2, w + n + 1, 0ll) << " ";
}
}
void Whisper(){
cin >> n;
for (int i = 1; i <= n; ++i) cin >> h[i];
for (int i = 1; i <= n; ++i) cin >> w[i];
LichaoTree lichao(MAX);
lichao.addLine(-2 * h[1], h[1] * h[1]);
// SUB1 :: solve();
// cout << '\n';
for (int i = 2; i <= n; i++){
dp[i] = lichao.qry(h[i]) + h[i] * h[i] - w[i];
lichao.addLine(-2 * h[i], h[i] * h[i] + dp[i]);
// cout << dp[i] << " ";
}
cout << dp[n] + accumulate(w + 2, w + n + 1, 0ll);
}
signed main(){
setupIO();
int Test = 1;
// cin >> Test;
for ( int i = 1 ; i <= Test ; i++ ){
Whisper();
if (i < Test) cout << '\n';
}
}
