#include <bits/stdc++.h>
using namespace std;
#define FNAME "BRIDGEPOL"
#define int long long
const int N = 1e5 + 5;
const int C = 1e6 + 5;
const int oo = 1e18;
struct Line {
int a,b;
Line(int _a = 0, int _b = oo) : a(_a), b(_b) {}
int operator()(int x) {
return a * x + b;
}
};
int n, h[N], w[N], dp[N];
Line LCT[4 * C];
void Task() {
ios_base::sync_with_stdio(false);
cin.tie(0); cout.tie(0);
cout << fixed << setprecision(9);
if (fopen(FNAME".inp","r")) {
freopen(FNAME".inp","r",stdin);
freopen(FNAME".out","w",stdout);
}
}
void update(int id, int l, int r, Line d) {
int mid = (l + r) >> 1;
int idL = id * 2, idR = id * 2 + 1;
bool L = d(l) < LCT[id](l);
bool M = d(mid) < LCT[id](mid);
if (M) swap(LCT[id], d);
if (l == r) return;
if (L ^ M) update(idL, l, mid, d);
else update(idR, mid + 1, r, d);
}
int query(int id, int l, int r, int x) {
if (l == r) return LCT[id](x);
int mid = (l + r) >> 1;
int idL = id * 2, idR = id * 2 + 1;
if (x < mid) return min(LCT[id](x), query(idL, l, mid, x));
else return min(LCT[id](x), query(idR, mid + 1, r, x));
}
void Solve() {
//Your Code
cin >> n;
for (int i = 1; i <= n; i++) cin >> h[i];
w[0] = 0;
for (int i = 1; i <= n; i++) cin >> w[i], w[i] += w[i - 1];
dp[1] = 0;
update(1, 1, C, Line(-2 * h[1], h[1] * h[1] - w[1] + dp[1]));
for (int i = 2; i <= n; i++) {
dp[i] = h[i] * h[i] + w[i - 1] + query(1, 1, C, h[i]);
update(1, 1, C, Line(-2 * h[i], h[i] * h[i] - w[i] + dp[i]));
}
cout << dp[n] << '\n';
}
int32_t main() {
Task();
Solve();
cerr << "\nTime run: " << 1000*clock()/CLOCKS_PER_SEC << "ms";
return 37^37;
}
