// TranThienPhuc2657
// 27 ngay truoc khi toi ki thi Hoc sinh gioi Quoc gia 2025 - 2026, 25/12/2025.
#include <bits/stdc++.h>
using namespace std;
#define file "BUILD"
#define TIME 1.0 * clock() / CLOCKS_PER_SEC
#define ll long long
#define pb push_back
#define fi first
#define se second
#define pii pair <int, int>
#define pll pair <ll, ll>
#define Sz(x) ((int) (x).size())
#define getBit(mask, i) (((mask) >> (i)) & 1)
template <typename T1, typename T2> bool mini(T1 &A, T2 B) {if (A > B) A = B; else return 0; return 1;}
template <typename T1, typename T2> bool maxi(T1 &A, T2 B) {if (A < B) A = B; else return 0; return 1;}
const int inf = 2e9 + 7;
const ll linf = 1e18l + 7;
const int mod = 1e9 + 7;
const int N = 1e5 + 5;
int n;
ll h[N], w[N];
ll sumW[N];
// inp
void inp() {
cin >> n;
for (int i = 1; i <= n; i++) cin >> h[i];
for (int i = 1; i <= n; i++) cin >> w[i];
}
// init
void init() {
for (int i = 1; i <= n; i++) sumW[i] = sumW[i - 1] + w[i];
}
// proc
namespace sub1 {
// check
bool check() {
return n <= 1000;
}
ll dp[N];
// init
void init() {
for (int i = 2; i <= n; i++) dp[i] = linf;
dp[1] = 0;
}
// solve
void solve() {
for (int i = 2; i <= n; i++) {
for (int j = 1; j < i; j++) {
mini(dp[i], - 2 * h[i] * h[j] + dp[j] + h[j] * h[j] - sumW[j] + h[i] * h[i] + sumW[i - 1]);
}
}
cout << dp[n];
}
// proc
void proc() {
init();
solve();
}
}
namespace sub3 {
const int MAX = 1e6;
// check
bool check() {
return true;
}
struct Li_chao_tree {
struct Line {
ll a, b;
Line() : a(0), b(linf) {}
Line(ll a, ll b) : a(a), b(b) {}
ll eval(ll x) {
return a * x + b;
}
};
Line d[MAX * 4];
void add(int id, int l, int r, Line cur) {
int mid = (l + r) / 2;
if (cur.eval(mid) < d[id].eval(mid)) swap(d[id], cur);
if (l == r) return;
if (cur.a == d[id].a) return;
if (cur.a > d[id].a) add(id * 2, l, mid, cur);
if (cur.a < d[id].a) add(id * 2 + 1, mid + 1, r, cur);
}
void add(ll a, ll b) {
add(1, 0, MAX, Line(a, b));
}
ll get(int id, int l, int r, int pos) {
ll cur = d[id].eval(pos);
if (l == r) return cur;
int mid = (l + r) / 2;
if (pos <= mid) return min(cur, get(id * 2, l, mid, pos));
return min(cur, get(id * 2 + 1, mid + 1, r, pos));
}
ll get(int pos) {
return get(1, 0, MAX, pos);
}
} lichao;
ll f = 0;
// init
void init() {
lichao.add(-2 * h[1], h[1] * h[1] - sumW[1]);
}
// solve
void solve() {
for(int i = 2; i <= n; i++) {
f = lichao.get(h[i]) + h[i] * h[i] + sumW[i - 1];
lichao.add(-2 * h[i], f + h[i] * h[i] - sumW[i]);
}
cout << f;
}
// proc
void proc() {
init();
solve();
}
}
void proc() {
if (sub1::check()) return sub1::proc();
if (sub3::check()) return sub3::proc();
}
signed main() {
ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0);
if (fopen(file".inp", "r")) {
freopen(file".inp", "r", stdin);
freopen(file".out", "w", stdout);
}
inp();
init();
proc();
cerr << "Time elapsed: " << TIME << "s.\n";
return 0;
}
