#include <bits/stdc++.h>
using namespace std;
#define int long long
#define pii pair<int,int>
#define fi first
#define se second
const int N = 1e5+5;
int n,h[N],w[N],dp[N],tot = 0;
struct Line{
bool type;
double x;
int m,c;
};
bool operator<(Line l1, Line l2){
if(l1.type || l2.type) return l1.x < l2.x;
return l1.m > l2.m;
}
set<Line>cht;
bool has_prev(set<Line>::iterator it) {return it != cht.begin();}
bool has_next(set<Line>::iterator it) {
return it != cht.end() && 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 l = *it;
l.x = intersect(prev(it),it);
cht.insert(cht.erase(it),l);
}
}
bool bad(set<Line>::iterator it){
if(has_next(it) && next(it)->c <= it->c) return true;
return(has_prev(it) && has_next(it) && intersect(prev(it),next(it)) <= intersect(prev(it),it));
}
void add_line(int m, int c){
set<Line>::iterator it;
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(has_prev(it) && bad(prev(it))) cht.erase(prev(it));
while(has_next(it) && bad(next(it))) cht.erase(next(it));
if(has_next(it)) calc_x(next(it));
calc_x(it);
}
}
int query(int h){
Line l = *prev(cht.upper_bound({1,(double)h,0,0}));
return l.m*h+l.c;
}
signed main(){
ios_base::sync_with_stdio(false);
cin.tie(NULL);
cin >> n;
int sum = 0;
for(int i = 1; i <= n; i++) cin >> h[i];
for(int i = 1; i <= n; i++){
cin >> w[i];
sum += w[i];
}
dp[1] = -w[1];
for(int i = 2; i <= n; i++){
add_line(-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;
}
