#include <iostream>
#include <vector>
#include <queue>
#include <algorithm>
#define f first
#define s second
using namespace std;
long long n, h[100010], ps[100010], dp[100010];
vector<pair<long long,long long>> slope;
vector<pair<long double,pair<long long,long long>>> pt;
long double findx(long double m1, long double c1, long double m2, long double c2) {
if (m1-m2 == 0) return -1e18;
return (c2-c1)/(m1-m2);
}
void solve(int l, int r) {
if (l == r) return;
int mid = (l+r)/2;
solve(l,mid);
slope.clear(); pt.clear();
for (int i = l; i <= mid; i++) slope.push_back({-2*h[i],h[i]*h[i]-ps[i]+dp[i]});
sort(slope.begin(),slope.end(),greater<pair<long long,long long>>());
pt.push_back({-1e18,slope[0]});
for (int i = 1; i < slope.size(); i++) {
while ((pt.size()) && (pt.back().f >= findx(slope[i].f,slope[i].s,pt.back().s.f,pt.back().s.s))) pt.pop_back();
if (pt.empty()) pt.push_back({-1e18,slope[i]});
else pt.push_back({findx(slope[i].f,slope[i].s,pt.back().s.f,pt.back().s.s),slope[i]});
}
for (int i = mid+1; i <= r; i++) {
int ll = 0, rr = pt.size()-1;
while (ll <= rr) {
int midd = (ll+rr)/2;
if (pt[midd].f >= h[i]) rr = midd-1;
else ll = midd+1;
}
dp[i] = min(dp[i],pt[rr].s.f*h[i]+pt[rr].s.s+h[i]*h[i]+ps[i-1]);
}
solve(mid+1,r);
}
int main() {
cin >> n;
for (int i = 1; i <= n; i++) cin >> h[i];
for (int i = 1; i <= n; i++) {
cin >> ps[i];
ps[i] += ps[i-1];
}
for (int i = 2; i <= n; i++) dp[i] = 1e18;
solve(1,n);
cout << dp[n] << endl;
}
