#include<bits/stdc++.h>
#define taskname "A"
using namespace std;
typedef long long ll;
const ll INF = 1e18;
template<class T>void minimize(T& a, T b){
if(a > b){
a = b;
}
}
ll square(int x){
return 1LL * x * x;
}
int n;
namespace sub1{
void solve(){
vector<int>h(n + 1), w(n + 1);
for(int i = 1; i <= n; i++){
cin >> h[i];
}
for(int i = 1; i <= n; i++){
cin >> w[i];
}
vector<ll>dp(n + 1, INF);
dp[1] = 0;
for(int i = 2; i <= n; i++){
ll sum = 0;
for(int j = i - 1; j > 0; sum += w[j--]){
minimize(dp[i], dp[j] + square(h[i] - h[j]) + sum);
}
}
cout << dp[n];
}
}
namespace sub23{
const int lim = 1e5 + 5;
const int LIM = 1e6 + 5;
int h[lim];
ll w[lim];
pair<int, ll>lichao[LIM << 2];
ll f(int x, const pair<int, ll>& line){
return 1LL * line.first * x + line.second;
}
void update(int id, int l, int r, pair<int, ll>line){
if(l == r){
if(f(l, line) < f(l, lichao[id])){
lichao[id] = line;
}
return;
}
int m = (l + r) >> 1;
if(f(m, line) < f(m, lichao[id])){
swap(line, lichao[id]);
}
if(f(l, line) < f(l, lichao[id])){
update(id << 1, l, m, line);
}
else if(f(r, line) < f(r, lichao[id])){
update(id << 1 | 1, m + 1, r, line);
}
}
ll get(int id, int l, int r, int p){
if(l == r){
return f(l, lichao[id]);
}
int m = (l + r) >> 1;
return min(f(p, lichao[id]), m < p ? get(id << 1 | 1, m + 1, r, p) : get(id << 1, l, m, p));
}
void solve(){
fill(lichao, lichao + (LIM << 2), make_pair(0, INF));
for(int i = 1; i <= n; i++){
cin >> h[i];
}
w[0] = 0;
for(int i = 1; i <= n; i++){
cin >> w[i];
w[i] += w[i - 1];
}
update(1, 0, LIM - 1, make_pair(-(h[1] << 1), square(h[1]) - w[1]));
for(int i = 2; i < n; i++){
ll dp = get(1, 0, LIM - 1, h[i]) + w[i - 1] + square(h[i]);
update(1, 0, LIM - 1, make_pair(-(h[i] << 1), square(h[i]) + dp - w[i]));
}
cout << get(1, 0, LIM - 1, h[n]) + w[n - 1] + square(h[n]);
}
}
int main(){
ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0);
if(fopen(taskname".inp", "r")){
freopen(taskname".inp", "r", stdin);
}
cin >> n;
if(n <= 1000){
sub1::solve();
}
else{
sub23::solve();
}
}
