#include <bits/stdc++.h>
#define eb emplace_back
#define all(x) x.begin(), x.end()
#define compact(v) v.erase(unique(all(v)), v.end())
#define dbg(v) "[" #v " = " << (v) << "]"
#define el "\n"
using namespace std;
typedef long long ll;
typedef long double ld;
mt19937_64 rng(chrono::high_resolution_clock::now().time_since_epoch().count());
long long randRange(long long l, long long r){ return uniform_int_distribution<long long>(l,r)(rng); }
const int N = 1e6 + 5;
int n;
ll h[N], w[N], pref[N];
struct Line {
ll a, b;
Line (ll a = 0, ll b = 0) : a(a), b(b) {}
ll f(ll x) {
return a * x + b;
}
ld intersect(Line Other) {
return 1.0 * (Other.b - b) / (a - Other.a);
}
ll slope() {
return a;
}
};
struct Lichao {
vector <Line> st;
int n;
Lichao(int n) : n(n), st(4 * n + 5, LLONG_MAX) {}
void update(int id, int l, int r, Line val) {
if (l == r) {
st[id] = (val.f(l) < st[id].f(l) ? val : st[id]);
return;
}
int mid = (l + r) >> 1;
if (val.f(mid) < st[id].f(mid))
swap(st[id], val);
if (val.slope() > st[id].slope()) {
update(id << 1, l, mid, val);
}
else if (val.slope() < st[id].slope()) {
update(id << 1 | 1, mid + 1, r, val);
}
}
ll get(int id, int l, int r, ll x) {
if (l == r) {
return st[id].f(x);
}
int mid = (l + r) >> 1;
ll cur = st[id].f(x);
if (x <= mid) {
return min(cur, get(id << 1, l, mid, x));
}
else {
return min(cur, get(id << 1 | 1, mid + 1, r, x));
}
}
void upd(Line val) {
update(1, 1, n, val);
}
ll query(ll x) {
return get(1, 1, n, x);
}
};
ll dp[N];
void solve() {
cin >> n;
for(int i = 1; i <= n; ++i) cin >> h[i];
for(int i = 1; i <= n; ++i) {
cin >> w[i];
pref[i] = pref[i - 1] + w[i];
}
memset(dp, 0x3f, sizeof(dp));
dp[1] = 0;
// for(int i = 1; i <= n; ++i) {
// for(int j = 1; j < i; ++j) {
// dp[i] = min(dp[i], -2 * h[j] * h[i] + dp[j] + h[j] * h[j] - pref[j] + h[i] * h[i] + pref[i - 1]);
// }
// }
// cout << dp[n] << el;
Lichao lct(N);
lct.upd(Line(-2 * h[1], dp[1] + h[1] * h[1] - pref[1]));
for(int i = 1; i <= n; ++i) {
dp[i] = lct.query(h[i]) + h[i] * h[i] + pref[i - 1];
lct.upd(Line(-2 * h[i], dp[i] + h[i] * h[i] - pref[i]));
}
cout << dp[n] << el;
}
signed main() {
ios_base::sync_with_stdio(false);
cin.tie(0);
#define task "task"
if(fopen(task".inp", "r")) {
freopen(task".inp", "r", stdin);
freopen(task".out", "w", stdout);
}
solve();
return 0;
}
/*
*/
