#include <bits/stdc++.h>
#define lsb(x) (x & (-x))
#define ll long long
#define ull unsigned long long
#define ld long double
// 217
// 44
using namespace std;
const int MAXN = (int) 1e5;
int h[MAXN + 1], w[MAXN + 1];
ll dp[MAXN + 1];
class Batch { // min
private:
static const ll INF = 1e18;
struct Line {
ll a, b;
inline ll get(ll x) {
return 1LL * a * x + b;
}
};
struct LiChao {
LiChao *st, *dr;
Line l;
LiChao() {
st = dr = NULL;
l = {0, INF};
}
}*root;
public:
Batch() {
root = new LiChao;
}
inline void fix(LiChao *nod) {
if(nod -> st == NULL) nod -> st = new LiChao;
if(nod -> dr == NULL) nod -> dr = new LiChao;
}
void add(LiChao *nod, ll left, ll right, Line l) {
fix(nod);
Line &cur = nod -> l;
if(l.get(left) <= cur.get(left) && l.get(right) <= cur.get(right)) {
cur = l;
return ;
}
if(l.get(left) >= cur.get(left) && l.get(right) >= cur.get(right)) {
return ;
}
ll mid = (left + right) / 2;
if(cur.get(left) > l.get(left)) {
swap(l, cur);
}
if(cur.get(mid) > l.get(mid)) {
swap(l, cur);
add(nod -> st, left, mid, l);
}
else add(nod -> dr, mid + 1, right, l);
}
ll query(LiChao *nod, ll left, ll right, ll x) {
fix(nod);
ll cur = nod -> l.get(x);
if(left == right) {
return cur;
}
ll mid = (left + right) / 2;
if(x <= mid) return min(cur, query(nod -> st, left, mid, x));
return min(cur, query(nod -> dr, mid + 1, right, x));
}
void add(Line l) {
add(root, 0, 1e9, l);
}
ll query(ll x) { // x >= 0
return query(root, 0, 1e9, x);
}
};
int main() {
//ifstream cin("A.in");
//ofstream cout("A.out");
int i, n;
ios::sync_with_stdio(false);
cin.tie(0), cout.tie(0);
cin >> n;
for(i = 1; i <= n; i++) {
cin >> h[i];
}
ll sum = 0;
for(i = 1; i <= n; i++) {
cin >> w[i];
sum += w[i];
}
Batch hull;
hull.add({-2 * h[1], 1LL * h[1] * h[1] - w[1]});
for(i = 2; i <= n; i++) {
dp[i] = hull.query(h[i]) + 1LL * h[i] * h[i] - w[i];
hull.add({-2 * h[i], 1LL * h[i] * h[i] + dp[i]});
}
cout << dp[n] + sum;
//cin.close();
//cout.close();
return 0;
}
