#include <iostream>
#include <bits/stdc++.h>
#define ll long long
using namespace std;
const ll maxn = 2*1e5+5, INF = 4e18+9;
// line add min get, returns INF if no line added
template <class T>
struct LiChao {
const T INF = numeric_limits<T>::max() / 2;
int C;
vector<T> dom;
vector<array<T, 2>> first;
vector<int> label;
T f(array<T, 2> p, int x) {
return p[0] * dom[x] + p[1];
}
LiChao(vector<T> _dom) : dom(_dom) {
sort(dom.begin(), dom.end());
dom.resize(unique(dom.begin(), dom.end()) - dom.begin());
C = dom.size();
first.resize(4 * C, {0, INF});
label.resize(4 * C, -1);
}
void add(T a, T b, int lab) {
array<T, 2> p{a, b};
int idx = 0, l = 0, r = C;
while (l < r) {
int m = (l + r) >> 1;
bool doml = f(p, l) < f(first[idx], l);
bool domm = f(p, m) < f(first[idx], m);
if (domm) swap(p, first[idx]), swap(label[idx], lab);
if (l + 1 == r) break;
if (doml != domm) idx = 2 * idx + 1, r = m;
else idx = 2 * idx + 2, l = m;
}
}
pair<T, int> getMin(T x) {
// x -= 1e-9;
x = lower_bound(dom.begin(), dom.end(), x) - dom.begin();
T mn = INF;
int lab = -1;
int idx = 0, l = 0, r = C;
while (l < r) {
if (f(first[idx], x) < mn) mn = f(first[idx], x), lab = label[idx];
if (l + 1 == r) break;
int m = (l + r) >> 1;
if (x < m) idx = 2 * idx + 1, r = m;
else idx = 2 * idx + 2, l = m;
}
return make_pair(mn, lab);
}
};
void solve(){
int n;
cin >> n;
vector<ll> h(n+1), w(n+1);
for(int i = 1; i <= n; i++){
cin >> h[i];
}
ll tot = 0;
for(int i = 1; i <= n; i++){
cin >> w[i];
tot += w[i];
}
vector<ll> dom;
for(int i = 1; i <= n; i++){
dom.push_back(h[i]);
}
LiChao<ll> T(dom);
vector<ll> f(n+1, 0);
f[1] = -w[1];
T.add(-h[1]*2, f[1]+h[1]*h[1], 1);
for(int i = 2; i <= n; i++){
f[i] = T.getMin(h[i]).first + h[i]*h[i] - w[i];
T.add(-h[i]*2, f[i]+h[i]*h[i], i);
}
cout << f[n]+tot;
}
int main(){
ios_base::sync_with_stdio(false);
cin.tie(NULL);
//freopen("main.inp", "r", stdin);
//freopen("main.out", "w", stdout);
solve();
}
