#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef long double ld;
ll INF = 1e18;
struct Line{
ll m,c;
Line(ll _m, ll _c){
m=_m;c=_c;
}
ll operator()(ll x){
return m*x+c;
}
};
struct Node{
ll s,e,m;
Line f = Line(0,INF);
Node *l, *r;
Node(ll _s, ll _e){
s=_s;e=_e;
if (s==e){return;}
m=(s+e)/2;
l = new Node(s,m);
r = new Node(m+1,e);
}
void insert(Line ins){
if (s==e){
if (ins(s)<f(s)){
f=ins;
}
return;
}
if (ins.m==f.m){
if (ins.c<f.c){
f=ins;
}
return;
}
//wlog insert line has higher gradient
if (ins.m<f.m){
swap(ins,f);
}
if (ins(m)<f(m)){
r->insert(f);
f=ins;
} else {
l->insert(ins);
}
}
ll query(ll x){
if (s==e){
return f(x);
}
if (x<=m){
return min(f(x),l->query(x));
} else {
return min(f(x),r->query(x));
}
}
};
int main(){
cin.tie(0);
ios_base::sync_with_stdio(0);
ll n;
cin>>n;
vector<ll> h(n);
vector<ll> pref(n+1);
for (ll i = 0; i<n; i++){
cin>>h[i];
}
for (ll i = 0; i<n; i++){
cin>>pref[i+1];
pref[i+1]+=pref[i];
}
vector<ll> dp(n);
Node *lichao = new Node(0,n-1);
lichao->insert(Line(-2*h[0],dp[0]-pref[1]+h[0]*h[0]));
for (ll x = 1; x<n; x++){
ll minval = lichao->query(h[x]);
dp[x]=h[x]*h[x]+pref[x]+minval;
lichao->insert(Line(-2*h[x],dp[x]-pref[x+1]+h[x]*h[x]));
}
cout<<dp[n-1]<<'\n';
}
