/* Author : Phan Thanh Nhan, ITK22, NBK High School for Gifted Student */
#include <bits/stdc++.h>
#define TASK "CEOI17_building"
#define ll long long
#define fi first
#define sc second
#define ii pair <int, int>
#define iii pair <int, ii>
#define int ll
using namespace std;
const int MAXN = 1e6;
const int INF = 2e9;
const ll LINF = 1e18;
struct line {
int a, b;
line () {
a = 0;
b = 0;
}
line(int valA, int valB) {
a = valA;
b = valB;
}
int cal(int x) {
return a * x + b;
}
int slope() {
return a;
}
};
vector <line> st;
int pref[MAXN + 5], n, h[MAXN + 5], w[MAXN + 5], dp[MAXN + 5];
void update(int l, int r, line newLine) {
// if (l > r) return;
int mid = (l + r) >> 1;
if (l == r) {
st[mid] = (st[mid].cal(l) < newLine.cal(l) ? st[mid] : newLine);
return;
}
if (newLine.cal(mid) < st[mid].cal(mid)) swap(newLine, st[mid]);
if (newLine.slope() > st[mid].slope()) update(l, mid - 1, newLine);
else update(mid + 1, r, newLine);
}
int get(int l, int r, int idx) {
int mid = (l + r) >> 1;
int ans = st[mid].cal(idx);
if (idx == mid) return ans;
if (idx > mid) return min(ans, get(mid + 1, r, idx));
return min(ans, get(l, mid - 1, idx));
}
int fiCost(int i) {
return -2 * h[i];
}
int scCost(int i) {
return dp[i] + h[i] * h[i] - pref[i];
}
void Bindu() {
cin >> n;
for (int i = 1; i <= n; i++) cin >> h[i];
for (int i = 1; i <= n; i++) {
cin >> w[i];
pref[i] = pref[i - 1] + w[i];
}
st.resize(MAXN + 2, line(0, LINF));
update(0, MAXN, line(fiCost(1), scCost(1)));
dp[1] = 0;
for (int i = 2; i <= n; i++) {
dp[i] = get(0, MAXN, h[i]) + h[i] * h[i] + pref[i - 1];
update(0, MAXN, line(fiCost(i), scCost(i)));
}
cout << dp[n];
}
signed main() {
#ifndef ONLINE_JUDGE
// freopen(TASK".inp", "r", stdin);
// freopen(TASK".out", "w", stdout);
#endif
cin.tie(0)->sync_with_stdio(false);
Bindu();
return 0;
}
/* Comment
Coming soon...
*/
