#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef tuple<int, int> ii;
typedef tuple<int, int, int> iii;
typedef vector<int> vi;
#define FOR(i, a, b) for (int i = (a); i < (b); ++i)
const ll inf = LLONG_MAX;
void run();
signed main() {
ios_base::sync_with_stdio(false);
cin.tie(NULL);
run();
}
inline ll sqr(ll x) {
return x * x;
}
struct Line {
ll a, b;
mutable ll max_x;
bool operator<(const Line &o) const {
return a > o.a;
}
bool operator<(ll x) const {
return max_x < x;
}
};
struct LineContainer : multiset<Line, less<>> {
ll div(ll n, ll d) { // floor division for negative and positive lls
return n / d - ((n ^ d) < 0 && n % d);
}
bool isect(iterator l, iterator m) {
// assumption: l and m are neighbouring lines, with m > l
// do: adjust the max_x for l
// return: l covers x after or equal to last x of m
if (m == end()) { // handle case l is last line
l->max_x = inf;
return false;
}
if (l->a == m->a) { // prevent division by zero
l->max_x = l->b < m->b ? inf : -inf;
} else { // default case, intersection point of l and m floored
l->max_x = div(m->b - l->b, l->a - m->a);
}
return l->max_x >= m->max_x;
}
void add(ll a, ll b) {
auto cur = insert({a, b, 0}), pre = cur, nex = cur; // iterators
//cerr << "Adding line " << cur->a << ' ' << cur->b << ' ';
++nex;
while (isect(cur, nex)) nex = erase(nex); // keep erasing redundant lines after cur, note how this sets max_x of cur
//cerr << cur->max_x << '\n';
if (cur != begin() && isect(--pre, cur)) { // added line itself is redundant, erase and return
cur = erase(cur);
isect(pre, cur);
}
while ((cur = pre) != begin() && (--pre)->max_x >= cur->max_x) isect(pre, erase(cur)); // keep erasing redundant lines before cur, and adjust max_x of line left
}
ll min_y(ll x) {
auto l = lower_bound(x);
//cerr << "Minimal for x = " << x << " is line a = " << l->a << " b = " << l->b << " at y = " << l->y(x) << '\n';
return l->a * x + l->b;
}
};
int N;
ll h[100005];
ll W[100005];
ll dp[100005];
void run() {
cin >> N;
FOR(i, 0, N) cin >> h[i];
FOR(i, 0, N) {
ll w; cin >> w;
W[i+1] = W[i] + w;
}
LineContainer lc;
FOR(i, 1, N) {
lc.add(-2*h[i-1], dp[i-1] + h[i-1]*h[i-1] - W[i]);
dp[i] = h[i]*h[i] + W[i] + lc.min_y(h[i]);
}
// for (auto &l : lc) {
// cerr << l.a << ' ' << l.b << ' ' << l.max_x << '\n';
// }
cout << dp[N-1] << '\n';
}
