#include <bits/stdc++.h>
#define fi first
#define se second
#define int long long
#define double long double
using namespace std;
vector<int> memo, cost, h, pref;
set<pair<double,int>> convex;
queue<pair<double,int>> change;
int N;
int prefix(int l, int r) {
if (l > r) return 0;
l--;
if (l <= 0) return pref[r];
else return pref[r] - pref[l];
}
double intersection(int a, int b) {
return (h[b] * h[b] + memo[b] - prefix(b, N-1) + prefix(a, N-1) - memo[a] - h[a] * h[a]) / ((double)(2*(h[b] - h[a])));
}
void forward(int i, set<pair<double,int>>::iterator it) {
do {
double inter = intersection(i, it->se);
auto it2 = convex.upper_bound({inter, -1});
if (it2->se == it->se) {
if (h[it->se] < h[i]) {
change.push({inter,it->se});
change.push({it2->fi,i});
}
else change.push({inter, i});
}
else break;
} while (++it != convex.end());
}
void backward(int i, set<pair<double,int>>::iterator it) {
while (it-- != convex.begin()) {
double inter = intersection(i, it->se);
auto it2 = convex.upper_bound({inter, -1});
if (it2->se == it->se) {
if (h[it->se] < h[i]) {
change.push({inter,it->se});
change.push({it2->fi,i});
}
else change.push({inter, i});
}
else break;
}
}
signed main() {
ios::sync_with_stdio(false);
cin.tie(0);
cin >> N;
memo.resize(N, -1); cost.resize(N); h.resize(N); pref.resize(N, 0);
for (int i = 0; i < N; i++) cin >> h[i];
for (int i = 0; i < N; i++) {
if (i) pref[i] = pref[i-1];
cin >> cost[i];
pref[i] += cost[i];
}
memo[N-1] = 0;
convex.insert({1e6, N-1});
for (int i = N - 2; i >= 0; i--) {
auto it = convex.lower_bound({h[i], -1});
memo[i] = memo[it->se] + (h[i] - h[it->se]) * (h[i] - h[it->se]) + pref[it->se-1] - pref[i];
if (h[i] != h[it->se]) {
backward(i, it);
forward(i, it);
while (!change.empty()) {
auto x = change.front(); change.pop();
for (set<pair<double,int>>::iterator it = convex.lower_bound({x.fi, -1}); it != convex.end() && abs(it->fi- x.fi) < 0.01;) {
auto it2 = it; it2++;
convex.erase(it);
it = it2;
}
convex.insert({x.fi, x.se});
}
}
else if (memo[i] - prefix(i, N-1) < memo[it->se] - prefix(it->se, N-1)) {
convex.insert({it->fi, i});
convex.erase(it);
}
}
cout << memo[0] << '\n';
return 0;
}
