#include <iostream>
#include <vector>
#include <algorithm>
#include <iomanip>
using namespace std;
long long inf = 1e18;
struct line {
long long k, b;
line(long long k = 0, long long b = inf) {
this->k = k;
this->b = b;
}
long long val(long long x) {
return k * x + b;
}
bool operator==(line a) {
return a.b == b && a.k == k;
}
};
line pust;
struct node {
line lin;
long long l, r;
node(line lin = pust, long long l = -1, long long r = -1) {
this->lin = lin;
this->l = l;
this->r = r;
}
};
vector<node> li_chao(1);
void add_line(long long i, long long l, long long r, line new_l) {
if (li_chao[i].lin == pust) {
li_chao[i].lin = new_l;
return;
}
long long mid = (l + r) / 2;
if (li_chao[i].lin.val(mid) > new_l.val(mid)) {
swap(new_l, li_chao[i].lin);
}
if (l + 1 == r) {
return;
}
if (new_l.k > li_chao[i].lin.k) {
if (li_chao[i].l == -1) {
li_chao[i].l = li_chao.size();
li_chao.push_back({});
}
add_line(li_chao[i].l, l, mid, new_l);
}
else {
if (li_chao[i].r == -1) {
li_chao[i].r = li_chao.size();
li_chao.push_back({});
}
add_line(li_chao[i].r, mid, r, new_l);
}
}
long long get_min(long long i, long long l, long long r, long long qx) {
if (l + 1 == r) {
return li_chao[i].lin.val(qx);
}
long long mid = (l + r) / 2;
if (qx < mid && li_chao[i].l != -1) {
return min(li_chao[i].lin.val(qx), get_min(li_chao[i].l, l, mid, qx));
}
if (mid <= qx && li_chao[i].r != -1) {
return min(li_chao[i].lin.val(qx), get_min(li_chao[i].r, mid, r, qx));
}
return li_chao[i].lin.val(qx);
}
int main() {
long long n;
long long R = 1e6 + 10;
cin >> n;
vector<long long> h(n), w(n);
for (long long i = 0; i < n; i++) {
cin >> h[i];
}
for (long long i = 0; i < n; i++) {
cin >> w[i];
}
vector<long long> dp(n);
dp[0] = 0;
vector<long long> pref(n);
pref[0] = w[0];
for (long long i = 1; i < n; i++) {
pref[i] = pref[i - 1] + w[i];
}
add_line(0, 0, R, line(-2 * h[0], dp[0] + h[0] * h[0] - pref[0]));
for (long long i = 1; i < n; i++) {
long long mni = get_min(0, 0, R, h[i]);
dp[i] = mni + pref[i] - w[i] + h[i] * h[i];
add_line(0, 0, R, line(-2 * h[i], dp[i] + h[i] * h[i] - pref[i]));
}
cout << dp[n - 1];
}
