#include <bits/stdc++.h>
using namespace std;
#define int long long
#define pt pair<int, int>
#define ft first
#define sc second
#define sz(a) int(a.size())
#define all(a) a.begin(), a.end()
struct Line{
bool type;
double x = 0;
int k = 0;
int b = 0;
};
set<Line> cht;
double intersect(set<Line>::iterator l1, set<Line>::iterator l2){
return double(l1->b - l2->b) / (l2->k - l1->k);
}
bool operator<(const Line& l1, const Line& l2){
if (l1.type || l2.type){
return l1.x < l2.x;
}
return l1.k > l2.k;
}
bool has_prev(set<Line>::iterator it){
return it != cht.begin();
}
bool has_next(set<Line>::iterator it){
return it != cht.end() && next(it) != cht.end();
}
bool bad(set<Line>::iterator it){
if (has_next(it) && next(it)->b <= it->b){
return true;
}
return has_prev(it) && has_next(it) && intersect(prev(it), next(it))
<= intersect(prev(it), it);
}
void calc_x(set<Line>::iterator it){
if (has_prev(it)){
Line l = *it;
l.x = intersect(prev(it), it);
cht.insert(cht.erase(it), l);
}
}
void add_line(int k, int b){
set<Line>::iterator it;
it = cht.lower_bound({0, 0, k, b});
if (it != cht.end() && it->k == k){
if (it->b <= b){
return;
}
cht.erase(it);
}
it = cht.insert({0, 0, k, b}).first;
if (bad(it)){
cht.erase(it);
}else{
while (has_prev(it) && bad(prev(it))){
cht.erase(prev(it));
}
while (has_next(it) && bad(next(it))){
cht.erase(next(it));
}
if (has_next(it)){
calc_x(next(it));
}
calc_x(it);
}
}
int get(int x){
auto it = prev(cht.upper_bound({1, double(x), 0, 0}));
return it->k * x + it->b;
}
void solve() {
int n;
cin >> n;
vector<int> h(n + 1), w(n + 1);
for (int i = 1; i <= n; ++i){
cin >> h[i];
}
int total = 0;
for (int i = 1; i <= n; ++i){
cin >> w[i];
total += w[i];
}
int ans = -w[1];
for (int i = 2; i <= n; ++i){
add_line(-2 * h[i - 1], ans + h[i - 1] * h[i - 1]);
ans = get(h[i]) + h[i] * h[i] - w[i];
}
cout << total + ans;
}
int32_t main() {
ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0);
int test = 1;
while (test--) {
solve();
}
}
