/**
____ ____ ____ ____ ____
||a |||t |||o |||d |||o ||
||__|||__|||__|||__|||__||
|/__\|/__\|/__\|/__\|/__\|
**/
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
const int N_MAX = 100000;
const int H_MAX = 2000000;
const ll INF = LLONG_MAX;
int n;
int h[N_MAX + 2];
int w[N_MAX + 2];
ll dp[N_MAX + 2];
struct Line {
int a; ll b;
ll operator () (const int &x) const {
return (ll) a * x + b;
}
};
Line LiChao[H_MAX * 4 + 2];
void build (int node, int l, int r) {
LiChao[node] = Line{0, -INF};
if (l == r) {
return;
}
int mid = (l + r) / 2;
int lSon = node * 2, rSon = node * 2 + 1;
build(lSon, l, mid);
build(rSon, mid + 1, r);
}
void build () {
build(1, 1, H_MAX);
}
void update (int node, int l, int r, Line ln) {
if (l == r) {
if (LiChao[node](l) < ln(l)) {
swap(LiChao[node], ln);
}
return;
}
int mid = (l + r) / 2;
int lSon = node * 2, rSon = node * 2 + 1;
if (LiChao[node].a > ln.a) {
swap(LiChao[node], ln);
}
if (LiChao[node](mid) < ln(mid)) {
swap(LiChao[node], ln);
update(lSon, l, mid, ln);
} else {
update(rSon, mid + 1, r, ln);
}
}
void update (Line ln) {
update(1, 1, H_MAX, ln);
}
ll query (int node, int l, int r, int x) {
if (l == r) {
return LiChao[node](x);
}
int mid = (l + r) / 2;
int lSon = node * 2, rSon = node * 2 + 1;
if (x <= mid) {
return max(LiChao[node](x), query(lSon, l, mid, x));
} else {
return max(LiChao[node](x), query(rSon, mid + 1, r, x));
}
}
ll query (int x) {
return query(1, 1, H_MAX, x);
}
void insertDp (int i) {
update(Line{2 * h[i], -dp[i] - (ll) h[i] * h[i]});
}
ll getMin (int i) {
return w[i] + (ll) h[i] * h[i] - query(h[i]);
}
int main () {
ios_base::sync_with_stdio(false);
cin.tie(0);
cout.tie(0);
cin >> n;
for (int i = 1; i <= n; i++) {
cin >> h[i];
}
for (int i = 1; i <= n; i++) {
cin >> w[i];
}
ll sumw = 0;
for (int i = 1; i <= n; i++) {
sumw += w[i];
w[i] = -w[i];
}
build();
dp[1] = w[1]; insertDp(1);
for (int i = 2; i <= n; i++) {
dp[i] = getMin(i); insertDp(i);
}
cout << dp[n] + sumw << "\n";
return 0;
}
