#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef pair<int, int> pii;
typedef long double ld;
#define fi first
#define se second
#define mp make_pair
#define fastIO ios::sync_with_stdio(false);cin.tie(0);cout.tie(0);
const int N = (int)1e5 + 10;
const ll inf = (ll)1e18;
const ld INF = (ld)4e18;
int h[N];
ll w[N];
ll dp[N];
ll sq(ll x){
return (x * 1ll * x);
}
bool Q;
struct Line{
ll ai;
ll bi;
mutable ld ri;
bool operator< (const Line &T) const {
if(Q) return ai < T.ai;
else return ri < T.ri;
}
};
struct Hull : multiset<Line>{
ld div(ld a, ld b){
return a/b;
}
ld inter(Line A, Line B){
return div((A.bi)-(B.bi),(B.ai)-(A.ai));
}
bool hasl(iterator it){
return (it != begin());
}
bool har(iterator it){
it++;
return (it != end());
}
bool bad(iterator it){
if(!hasl(it) || !har(it)) return false;
auto pv = it;
auto nx = it;
pv -- ;
nx ++ ;
return inter(*pv,*nx) <= inter(*pv,*it);
}
void upd(iterator &it){
auto ni = it;
ni ++ ;
if(ni == end()){
it->ri = INF;
}
else{
it->ri = inter(*it, *ni);
}
}
void add(ll ai, ll bi){
ai=-ai;
bi=-bi;
Q = true;
Line cur = {ai, bi, inf};
auto it = lower_bound(cur);
if(it != end()){
if(it->ai == ai){
if(it->bi >= bi){
return;
}
else{
it=erase(it); //
}
}
}
it=insert(cur);
if(bad(it)){
erase(it);
return;
}
auto nx = it;
nx++;
while(1){
if(nx==end()) break;
if(bad(nx))nx=erase(nx);
else break;
}
nx = it;
while(1){
if(it==begin()) break;
nx=it;
nx--;
if(bad(nx))erase(nx);
else break;
}
upd(it);
nx = it;
if(nx != begin()){
nx--;
upd(nx);
}
}
ll query(ld xi){
Q = false;
auto it = lower_bound({0,0,xi});
return -((it->ai) * xi + (it->bi));
}
};
ll ax[N];
ll bx[N];
int main(){
fastIO;
int n;
cin >> n;
for(int i = 1; i <= n; i ++ ){
cin >> h[i];
}
for(int i = 1; i <= n; i ++ ){
cin >> w[i];
w[i] += w[i - 1];
dp[i]=inf;
}
dp[1]=0;
Hull dpv;
for(int i = 1; i <= n; i ++ ){
if(i > 1){
dp[i]=dpv.query(h[i])+sq(h[i])+w[i-1];
}
ax[i]=-2ll*h[i];
bx[i]=sq(h[i])-w[i]+dp[i];
dpv.add(ax[i],bx[i]);
}
cout << dp[n];
return 0;
}
