#include <bits/stdc++.h>
using namespace std;
using ll=long long;
struct Line{
bool type;
double x;
double m,c;
};
set<Line>cht;
bool operator<(Line l1,Line l2){
if(l1.type || l2.type) return l1.x<l2.x;
return l1.m>l2.m;
}
bool has_prev(set<Line>:: iterator it){
return it !=cht.begin();
}
bool has_next(set<Line>::iterator it){
if(it==cht.end()) return false;
return next(it)!=cht.end();
}
double intersect(set<Line>::iterator l1,set<Line>::iterator l2){
return (double)(l1->c-l2->c)/(l2->m-l1->m);
}
void calc_x(set<Line>::iterator it){
if(has_prev(it)){
Line newl=*it;
newl.x= intersect(prev(it),it);
cht.insert(cht.erase(it),newl);
}
}
bool bad(set<Line>::iterator it){
if(has_next(it) and next(it)->c<=it->c) return true;
return (has_prev(it) and has_next(it) and intersect(prev(it),next(it))<=intersect(prev(it),it));
}
void add_line(double m,double c){
set<Line>::iterator it;
it=cht.lower_bound({0,0,m,c});
if(it!=cht.end() and it->m==m){
if(it->c<=c) return;
cht.erase(it);
}
it=cht.insert({0,0,m,c}).first; // return iterator and second is boolean whether inserted or not
if(bad(it)) {
cht.erase(it);
}
else{
while(has_prev(it) and bad(prev(it))) cht.erase(prev(it));
while(has_next(it) and bad(next(it))) cht.erase(next(it));
if(has_next(it)) calc_x(next(it));
calc_x(it);
}
}
double query(ll h){
Line l=*prev(cht.upper_bound({1,(double)h,0,0}));
return l.m*h +l.c;
}
int main(){
ios::sync_with_stdio(false);
cin.tie(nullptr);
int n; cin>>n;
vector<long long>h(n),w(n);
for(int i=0;i<n;i++){
cin>>h[i];
}
long long total=0;
for(int i=0;i<n;i++){
cin>>w[i];
total+=w[i];
}
vector<double>dp(n);
dp[0]=-w[0];
add_line(-2*h[0],dp[0]+h[0]*h[0]);
for(int i=1;i<n;i++){
dp[i]=(query(h[i]) + 1.0*h[i]*h[i] -w[i]);
add_line(-2*h[i],dp[i]+h[i]*h[i]);
}
cout<<total+dp[n-1]<<endl;
return 0;
}
