#include <bits/stdc++.h>
#define int int64_t
const int M = 1e9;
const int inf = 1e18;
struct Line {
int k, n;
bool active = false;
int get(int x) {
return k * x + n;
}
};
const int N = 2e6 + 5;
Line t[N];
std::vector<int> ll(N);
std::vector<int> rr(N);
struct CHT {
int New = 2;
void add(int c, int tl, int tr, Line line) {
if(!t[c].active) {
t[c] = line;
return;
}
int mid = (tl + tr) / 2;
int oldtl = t[c].get(tl);
int oldmid = t[c].get(mid);
int oldtr = t[c].get(tr);
int newtl = line.get(tl);
int newmid = line.get(mid);
int newtr = line.get(tr);
if(oldtl <= newtl && oldtr <= newtr) {
return;
}
if(newtl <= oldtl && newtr <= oldtr) {
t[c] = line;
return;
}
if(newmid < oldmid) {
std::swap(t[c], line);
}
if(tl == tr) {
return;
}
if(!ll[c]) {
ll[c] = New++;
}
if(!rr[c]) {
rr[c] = New++;
}
if(t[c].get(tl) > line.get(tl)) {
add(ll[c], tl, mid, line);
}
else {
add(rr[c], mid + 1, tr, line);
}
}
int query(int c, int tl, int tr, int x) {
if(tl > x || tr < x || tl > tr || t[c].active == false) {
return inf;
}
int now = t[c].get(x);
if(tl == tr) {
return now;
}
if(!ll[c]) {
ll[c] = New++;
}
if(!rr[c]) {
rr[c] = New++;
}
int mid = (tl + tr) / 2;
return std::min({query(ll[c], tl, mid, x), query(rr[c], mid + 1, tr, x), now});
}
}cht;
void solve() {
int n;
std::cin >> n;
std::vector<int> h(n + 1);
for(int i = 1; i <= n; i++) {
std::cin >> h[i];
}
std::vector<int> w(n + 1);
for(int i = 1; i <= n; i++) {
std::cin >> w[i];
}
std::vector<int> pref(n + 1);
for(int i = 1; i <= n; i++) {
pref[i] = pref[i - 1] + w[i];
}
std::vector<int> dp(n + 1, inf);
dp[1] = 0;
Line uio;
uio.active = true;
uio.k = h[1];
uio.n = dp[1] + h[1] * h[1] - pref[1];
cht.add(1, -M, + M, uio);
for(int i = 2; i <= n; i++) {
dp[i] = h[i] * h[i] + pref[i - 1] + cht.query(1, -M, + M, - 2 * h[i]);
Line L;
L.active = true;
L.k = h[i];
L.n = dp[i] + h[i] * h[i] - pref[i];
cht.add(1, - M, M, L);
}
std::cout << dp[n];
}
signed main() {
std::ios::sync_with_stdio(false);
std::cin.tie(nullptr);
int t = 1;
//std::cin >> t;
while (t--) {
solve();
}
return 0;
}
