#include <bits/stdc++.h>
using ll = long long;
const int NMAX = 1e5;
const int VMAX = 1e6;
int n;
ll w[NMAX + 1];
ll h[NMAX + 1];
ll dp[NMAX + 1];
ll sp[NMAX + 1];
void read() {
std::cin >> n;
for (int i = 1; i <= n; i++)
std::cin >> h[i];
for (int i = 1; i <= n; i++) {
std::cin >> w[i];
sp[i] = sp[i - 1] + w[i];
}
}
ll get_sum(int l, int r) {
return sp[r] - sp[l - 1];
}
struct Line {
ll a, b;
Line() : a(0), b(LLONG_MAX) {}
Line(ll _a, ll _b) : a(_a), b(_b) {}
ll operator()(const int & x) {
return a * x + b;
}
};
namespace LiChao {
Line aint[4 * VMAX + 5];
void add(int node, int l, int r, Line nline) {
int m = (l + r) / 2;
bool lef = nline(l) < aint[node](l);
bool mid = nline(m) < aint[node](m);
if (mid)
std::swap(nline, aint[node]);
if (l == r) return;
if (lef != mid) add(node * 2, l, m, nline);
else add(node * 2 + 1, m + 1, r, nline);
}
ll query(int node, int l, int r, int x) {
int m = (l + r) / 2;
if (l == r)
return aint[node](x);
if (x < m)
return std::min(aint[node](x), query(node * 2, l, m, x));
return std::min(aint[node](x), query(node * 2 + 1, m + 1, r, x));
}
}
void solve() {
for (int i = 1; i <= n; i++) {
if (i > 1) {
dp[i] = h[i] * h[i] + sp[i - 1];
dp[i] += LiChao::query(1, 0, VMAX, h[i]);
}
LiChao::add(1, 0, VMAX, Line(-2 * h[i], h[i] * h[i] + dp[i] - sp[i]));
}
std::cout << dp[n] << '\n';
}
int main() {
std::ios_base::sync_with_stdio(false);
std::cin.tie(nullptr);
read();
solve();
return 0;
}
