/*
Telebe of Adicto && Mamedov yani AzeTurk810
I see humans but no humanity
*/
#include <algorithm>
#include <deque>
#include <iostream>
#include <utility>
#include <vector>
// mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
using ll = long long;
using db = long double;
using i128 = __int128_t;
using namespace std;
#define ln '\n'
#define INFi 1e9
#define INFll 1e18
#ifdef ONPC
#include <algo.hpp>
#else
#define dbg(...)
#define dbg_out(...)
#endif
size_t _n;
vector<ll> W, H;
struct CHT {
struct line {
int k, b;
line(int k, int b) : k(k), b(b) {}
int f(int x) {
return x * k + b;
}
db col2(line a) { // NOTE: intersection point(x) of 2 lines
return db(a.b - b) / db(k - a.k);
}
int col(line a) {
return (a.b - b + k - a.k - 1) / k - a.k;
}
};
deque<pair<line, int>> dq;
void insert(int k, int b) {
line l(k, b);
while (dq.size() > 1 && dq.back().second >= dq.back().first.col(l)) {
dq.pop_back();
}
if (dq.empty()) {
dq.emplace_back(l, 0);
return;
}
dq.emplace_back(l, dq.back().first.col(l));
}
int query(int x) {
while (dq.size() > 1) {
if (dq[1].second <= x) {
dq.pop_back();
} else {
break;
}
}
return dq.front().first.f(x);
}
};
struct LiChaoTree {
struct Line {
ll k, c;
Line(ll k = 0, ll c = INFll) : k(k), c(c) {}
ll get(ll x) {
i128 prod = (i128)k * x + c;
if (prod > INFll)
return INFll;
if (prod < -INFll)
return -INFll;
return k * x + c;
}
};
struct Node {
Line L;
pair<int, int> interval;
Node *l, *r;
Node(Line V, ll l, ll r) : L(V), interval(make_pair(l, r)), l(nullptr), r(nullptr) {}
};
ll _L, _R;
Node *root;
LiChaoTree(ll l = -INFi, ll r = INFi) {
_L = l, _R = r;
root = new Node(Line(), l, r);
}
ll ask(Node *v, ll x) {
if (v == nullptr)
return INFll;
auto [l, r] = v->interval;
if (l == r)
return v->L.get(x);
ll mid = (l + r) >> 1LL;
if (x <= mid) {
return min(ask(v->l, x), v->L.get(x));
} else {
return min(ask(v->r, x), v->L.get(x));
}
}
Node *add(Node *v, Line L, ll _l, ll _r) {
if (v == nullptr) {
return new Node(L, _l, _r);
}
auto [l, r] = v->interval;
ll mid = (l + r) >> 1LL;
if (L.get(mid) < v->L.get(mid)) {
swap(v->L, L);
}
if (l == r) {
return v;
}
if (L.get(l) > v->L.get(l) && L.get(r) > v->L.get(r))
return v;
if (L.get(l) < v->L.get(l)) {
v->l = add(v->l, L, _l, mid);
} else {
v->r = add(v->r, L, mid + 1, _r);
}
return v;
}
ll query(ll x) {
return ask(root, x);
}
void add(ll k, ll b) {
root = add(root, Line(k, b), _L, _R);
}
};
vector<ll> pref, dp;
inline void systemd() {
H.resize(_n + 1);
W.resize(_n + 1);
pref.resize(_n + 1);
dp.resize(_n + 1);
}
char solve() {
if (!(cin >> _n))
return 1;
systemd();
for (size_t i = 1; i <= _n; i++) {
cin >> H[i];
}
for (size_t i = 1; i <= _n; i++) {
cin >> W[i];
}
for (size_t i = 1; i <= _n; i++) {
pref[i] = pref[i - 1] + W[i];
}
LiChaoTree t(-1e6 - 1, 1e6 + 1);
t.add(-2 * H[1], (ll)H[1] * H[1] - pref[1]);
for (size_t i = 2; i <= _n; i++) {
ll best = t.query(H[i]);
dp[i] = (ll)pref[i - 1] + best + (ll)H[i] * H[i];
t.add(-2LL * H[i], (ll)dp[i] + (ll)H[i] * H[i] - pref[i]);
}
cout << dp.back() << ln;
return 0;
}
// Attack on titan<3
signed main() {
ios::sync_with_stdio(0);
cin.tie(nullptr);
int t = 1e9;
// cin >> t;
for (int cases = 0; cases < t; cases++) {
if (solve())
break;
#ifdef ONPC
cerr << "__________\n";
#endif
}
}
// Just Imaginary
/*
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⢀⣴⣾⠀⠀⠀⡀⢀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣦⣾⣿⣿⣿⣿⣿⡆⠁⠀⢀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⡠⠂⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠔⠚⣿⣿⣿⣿⣿⣦⡄⠀⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⠠⠐⢂⠉⡀⣀⣤⣄⢻⣿⣿⡟⢈⡹⣿⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡀⠄⠂⠈⠀⣶⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⣷⡀⠀⡀⠐⠂⠐⢄
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣾⣷⠯⠀⠤⠤⠄⠈
⠀⠀⠀⠀⠀⠀⣼⣿⡟⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣰⣿⠋⠀⠀⢠⣾⣿⣿⣿⣿⣿⣭⠟⢻⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀
⠀⠀⠀⣀⣶⡟⠁⠀⢾⣶⣿⠟⠉⠈⢻⣿⣿⣿⣦⣜⠀⠛⠛⠿⠁⠀⠀⠀⠀⠀
⠚⠻⠿⠿⡿⠁⠀⢠⣿⣿⠁⠀⣠⠖⠋⠉⠻⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣰⣿⡿⠃⠠⠊⠁⠀⠀⠀⠀⠈⢿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣠⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣴⠾⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
*/
