#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;
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 propagate(int i, set<pair<double,int>>::iterator it) {
double left = 0, right = 1000000;
auto it2 = it;
bool tried = false;
while (it2 != convex.end()) {
tried = true;
double inter = intersection(i, it2->se);
auto best = convex.lower_bound({inter, -1});
right = inter;
if (best->se == it2->se) break;
it2++;
}
while (it-- != convex.begin()) {
tried == true;
double inter = intersection(i, it->se);
auto best = convex.lower_bound({inter,-1});
left = inter;
if (best->se == it->se)break;
}
//if ((!left && right == 1000000 && tried) || right < 0 || left > 1e6) return;
auto it3 = convex.lower_bound({left, -1});
int index = -1;
if (it3->fi <= right) index = it3->se;
for (; it3 != convex.end() && it3->fi <= right;) {
auto it4 = it3; it4++;
convex.erase(it3);
it3 = it4;
}
if (index != -1 && left)convex.insert({left, index});
convex.insert({right, i});
}
void convexHull(int i) {
double l = 0.0, r = 1e6;
while (r - l > 0.0001) {
double mid = (l + r) / 2.0;
auto it = convex.lower_bound({mid,-1});
if (h[it->se] > h[i]) {
auto it2 = it; it2--;
if (it == convex.begin() || h[it2->se] <= h[i]) {
propagate(i, it);
break;
}
r = mid;
}
else {
auto it2 = it; it2++;
if (it2 == convex.end() || h[it2->se] > h[i]) {
propagate(i, it2);
break;
}
l = mid;
}
}
}
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]) {
convexHull(i);
}
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;
}
