#include<bits/stdc++.h>
using namespace std;
#define int long long
#define nl '\n'
const int N = 1e5+1;
int dp[N];
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;
}
inline void solve(){
int n;
cin>>n;
int h[n+1], w[n+1], pre[n+1];
pre[0] = 0;
for(int i=1; i<=n; i++) cin>>h[i];
for(int i=1; i<=n; i++) cin>>pre[i], pre[i] += pre[i-1];
add_line(-h[1], h[1]*h[1] - pre[1]);
for(int i=2; i<=n; i++){
dp[i] = query(2*h[i]) + h[i]*h[i] + pre[i-1];
add_line(-h[i], dp[i] + h[i]*h[i] - pre[i]);
}
cout<<dp[n];
}
signed main(){
ios_base::sync_with_stdio(0);
cin.tie(NULL);cout.tie(NULL);
int t = 1;
//cin>>t;
while(t--) solve();
return 0;
}
