#include <bits/stdc++.h>
#define task "BriantheCrab"
#define int long long
#define pii pair <int, int>
#define fi first
#define se second
#define szf sizeof
#define sz(s) (int)((s).size())
#define all(v) (v).begin(), (v).end()
typedef long long ll;
typedef unsigned long long ull;
typedef long double ld;
using namespace std;
template <class T> void minimize (T &t, T f) {if (t > f) t = f;}
template <class T> void maximize (T &t, T f) {if (t < f) t = f;}
const int maxN = 1e6 + 5;
const int inf = 1e18 + 7;
const int mod = 1e9 + 7;
// khong tu code thi khong kha len duoc dau
// biet sol roi thi tu lam not di
struct Line {
int a, b;
Line () : a (0), b (inf) {}
Line (int a, int b) : a (a), b (b) {}
int calc (int x) {
return a * x + b;
}
};
struct LiChao {
vector <Line> lc;
void init (int n) {
lc.resize (n * 4, Line ());
}
void upd (int id, int l, int r, Line L) {
int mid = (l + r) >> 1;
bool left = L.calc (l) < lc[id].calc (l);
bool m = L.calc (mid) < lc[id].calc (mid);
if (m) {
swap (lc[id], L);
}
if (l == r) {
return;
}
if (left != m) {
upd (id * 2, l, mid, L);
}
else {
upd (id * 2 + 1, mid + 1, r, L);
}
}
int get (int id, int l, int r, int x) {
if (l == r) {
return lc[id].calc (x);
}
int mid = (l + r) >> 1;
if (x <= mid) {
return min (lc[id].calc (x), get (id * 2, l, mid, x));
}
return min (lc[id].calc (x), get (id * 2 + 1, mid + 1, r, x));
}
};
LiChao T;
int h[maxN], w[maxN];
int dp[maxN];
int pfs[maxN];
int p1 (int x) {
return - 2 * h[x];
}
int p2 (int x) {
return dp[x] + h[x] * h[x] - w[x];
}
int p3 (int x) {
return h[x] * h[x] + w[x - 1];
}
void solve () {
int n;
cin >> n;
for (int i = 1; i <= n; i ++) {
cin >> h[i];
}
for (int i = 1; i <= n; i ++) {
cin >> w[i];
w[i] += w[i - 1];
}
T.init (maxN + 1);
T.upd (1, 0, maxN, {p1 (1), p2 (1)});
for (int i = 1; i <= n; i ++) {
dp[i] = T.get (1, 0, maxN, h[i]) + p3 (i);
T.upd (1, 0, maxN, {p1 (i), p2 (i)});
}
cout << dp[n];
return;
}
signed main () {
cin.tie (nullptr) -> sync_with_stdio (false);
if (fopen (task".inp", "r")) {
freopen (task".inp", "r", stdin);
freopen (task".out", "w", stdout);
}
int t = 1;
//cin >> t;
while (t --) {
solve ();
}
return 0;
}
// thfv
