/* Author : Mychecksdead */
#include<bits/stdc++.h>
using namespace std;
typedef long long int ll;
#define MOD (1000000000+7)
#define MOD1 (998244353)
#define PI 3.1415926535
#define pb push_back
#define all(x) x.begin(), x.end()
const int N = 1e6+100, M = 1e5+10, K = 20;
struct Line{
bool type;
double x;
ll m, c;
bool operator < (const Line &b) const{
if(type != b.type) return x < b.x;
return m > b.m;
}
};
set<Line> cht;
bool notbegin(const set<Line>::iterator &it){
return it != cht.begin();
}
bool notend(const set<Line>::iterator &it){
return it != cht.end() && next(it) != cht.end();
}
double intersection(const set<Line>::iterator &a, const set<Line>::iterator &b){
return (double) (a->c - b->c) / (b->m - a->m);
}
void calcX(const set<Line>::iterator &it){
if(notbegin(it)){
Line l = *it;
l.x = intersection(prev(it), it);
cht.insert(cht.erase(it), l);
}
}
bool bad(const set<Line>::iterator &it){
if(notend(it) && next(it)->c <= it->c) return true;
return notend(it) && notbegin(it) && intersection(prev(it), next(it)) <= intersection(prev(it), it);
}
void addLine(ll m, ll c){
auto it = cht.lower_bound({0, 0, m, c});
if(it != cht.end() && it->m == m){
if(it->c <= c) return;
cht.erase(it);
}
it = cht.insert({0, 0, m, c}).first;
if(bad(it)) cht.erase(it);
else{
while(notbegin(it) && bad(prev(it))) cht.erase(prev(it));
while(notend(it) && bad(next(it))) cht.erase(next(it));
if(notend(it)) calcX(next(it));
calcX(it);
}
}
ll query(ll h){
Line l = *prev(cht.upper_bound({1, double(h), 0, 0}));
return l.m * h + l.c;
}
int n;
ll h[N], w[N], dp[N], sum = 0;
void solve(){
cin >> n;
for(int i = 1; i <= n; ++i) cin >> h[i];
for(int i = 1; i <= n; ++i) cin >> w[i];
for(int i = 1; i <= n; ++i) sum += w[i];
dp[1] = -w[1];
set<pair<pair<ll, ll>, int>> s; // x end points, r - l - idx
for(int i = 2; i <= n; ++i){
addLine(-2*h[i - 1], dp[i - 1] + h[i - 1] * h[i - 1]);
dp[i] = query(h[i]) + h[i] * h[i] - w[i];
}
cout << dp[n] + sum;
}
int main(){
cin.tie(0); ios::sync_with_stdio(0);
int T = 1, aa;
// cin >> T;aa=T;
while(T--){
// cout << "Case #" << aa-T << ": ";
solve();
cout << '\n';
}
return 0;
}
