#include <iostream>
#include <vector>
#include <queue>
#include <string>
#include <set>
#include <cassert>
#define rep(i, n) for (int i=0; i<(n); i++)
#define all(xs) xs.begin(), xs.end()
#define INF (1LL<<60)
#define _1 first
#define _2 second
using namespace std;
typedef pair<int, long long> P;
P operator -(const P &a, const P &b) { return P(a._1-b._1, a._2-b._2); }
inline long long det(P a, P b) { return 1LL*a._1*b._2 - 1LL*a._2*b._1; }
int N;
int H[100000], W[100000];
long long dp[1000001];
long long f[1000001];
set<int> ps;
inline P get(int x) { return P(x, f[x]); }
bool is_all_convex() {
vector<P> xs;
for (int x : ps) xs.push_back(P(x, f[x]));
rep(i, (int)xs.size()-2) {
if (det(xs[i+1]-xs[i], xs[i+2]-xs[i]) <= 0) return false;
}
return true;
}
inline auto lower(int x) { return ps.lower_bound(x); }
void update(int x, long long y) {
if (dp[x] <= y) return;
if (dp[x] < INF) {
auto it = ps.find(x);
if (it != ps.end()) ps.erase(it);
}
P p = P(x, y+1LL*x*x);
dp[x] = y;
f[x] = p._2;
//cout<<"cur: ";for (P p : ps) cout<<"("<<p._1<<","<<p._2<<"),"; cout<<"\n";
//cout<<"cur: ";for (P p : ps) cout<<"("<<p._1<<","<<p._2<<"),"; cout<<"\n";
while (true) {
auto right = lower(x);
if (right == ps.end()) break;
P r = get(*right);
if (p._2 >= r._2) return; // erase p
else {
right++;
if (right == ps.end()) break;
P k = get(*right);
if (det(r-p, k-r) > 0) break;
ps.erase(--right);
}
}
while (true) {
auto left = lower(x);
if (left == ps.begin()) break;
left--;
P l = get(*left);
if (l._2 >= p._2) ps.erase(left);
else {
if (left == ps.begin()) break;
left--;
P k = get(*left);
if (det(l-k, p-l) > 0) break;
ps.erase(++left);
}
}
auto right = lower(x);
if (right != ps.begin() && right != ps.end()) {
P r = get(*right);
P l = get(*(--right));
if (det(p-l, r-p) <= 0) return;
}
ps.insert(x);
}
signed main() {
cin >> N;
rep(i, N) cin >> H[i];
long long sum = 0;
rep(i, N) {
cin >> W[i];
sum += W[i];
W[i] = -W[i];
}
rep(h, 1000001) dp[h] = INF, f[h] = INF;
update(H[0], W[0]);
for (int i=1; i<N-1; i++) {
long long m = INF;
int h = H[i];
if (ps.size() <= 2) {
for (int x : ps) m = min(m, f[x] - 2LL*x*h);
}
else {
int lo = *ps.begin(), hi = *(--ps.end());
while (hi - lo > 1) {
int mid = (lo + hi) / 2;
auto l = lower(mid), r = ++lower(mid);
if (r == ps.end() || det(get(*r)-get(*l), P(1, 2LL*h)) <= 0) hi = mid;
else lo = mid;
}
auto it = lower(lo);
rep(_, 2) {
if (it == ps.end()) break;
int x = *it;
m = min(m, f[x] - 2LL*x*h);
it++;
}
}
update(H[i], m+1LL*H[i]*H[i]+W[i]);
}
long long m = INF;
rep(h, 1000001) m = min(m, dp[h] + 1LL*(h-H[N-1])*(h-H[N-1]));
cout << sum + m + W[N-1] << "\n";
return 0;
}
