#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 lim;
bool operator< (const Line &T) const {
if(Q) return ai < T.ai;
else return lim < T.lim;
}
};
struct Hull : multiset<Line>{
ld intersect(Line F1, Line F2){
return ld(F1.bi-F2.bi)/ld(F2.ai-F1.ai);
}
bool valid(iterator aq){
iterator pv = aq;
if(pv == begin()) return true;
pv -- ;
iterator nx = aq;
nx ++ ;
if(nx == end()) return true;
return intersect(*pv,*nx) > intersect(*pv,*aq);
}
void upd(iterator &it){
iterator nx = it;
nx ++ ;
if(nx == end()){
it->lim=INF;
}
else{
it->lim=intersect(*it,*nx);
}
}
void add(ll aa, ll bb){
aa=-aa;
bb=-bb;
Q=true;
Line cur = {aa,bb,INF};
auto it = lower_bound(cur);
if(it != end()){
if(it->ai == aa){
if(it->bi >= bb){
return;
}
else{
erase(it);
}
}
}
it = insert(cur);
if(!valid(it)){
erase(it);
return;
}
while(1){
auto nx = it;
nx++;
if(nx==end()) break;
if(valid(nx)) break;
erase(nx);
}
while(it!=begin()){
auto nx = it;
nx--;
if(valid(nx)) break;
erase(nx);
}
upd(it);
auto pv = it;
if(pv != begin()){
pv--;
upd(pv);
}
}
ll query(ld x){
Q = false;
auto it = lower_bound({0,0,x});
return -((it->ai)*x+(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;
}
