#include <bits/stdc++.h>
using namespace std;
#define task "BUILD"
#define sz(x) (int)x.size()
const int N = 1e5 + 3;
const long long inf = 1e18;
long long dp[N];
long long pref[N];
int h[N], w[N];
int n;
long long sqr(int x) {
return 1ll * x * x;
}
namespace sub1 {
void sol() {
for (int i = 1; i <= n; i++) dp[i] = inf;
dp[1] = 0;
// dp[2] = sqr(h[2] - h[1]);
for (int i = 2; i <= n; i++) {
for (int j = i - 1; j >= 1; j--)
dp[i] = min(dp[i], dp[j] + sqr(h[i] - h[j]) + (pref[i] - pref[j] - w[i]));
}
cout << dp[n];
}
}
long long Res = inf;
namespace sub2 {
void sol() {
for (int i = 1; i <= n; i++) dp[i] = inf;
dp[1] = 0;
if (n != 1) Res = min(Res, sqr(h[n] - h[1]) + (pref[n] - pref[1] - w[n]));
for (int i = 2; i <= n; i++) {
if (i != n) {
Res = min(Res, sqr(h[i] - h[1]) + sqr(h[i] - h[n])
+ (pref[i] - pref[1] - w[i]) + (pref[n] - pref[i] - w[n]));
}
for (int j = i - 1; j >= max(1, i - 1001); j--)
dp[i] = min(dp[i], dp[j] + sqr(h[i] - h[j]) + (pref[i] - pref[j] - w[i]));
}
Res = min(Res, dp[n]);
}
}
namespace sub3 {
struct Line {
bool type;
double x;
long long 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(long long m, long long 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);
}
}
long long query(long long h) {
Line l = *prev(cht.upper_bound({1, (double)h, 0, 0}));
return l.m * h + l.c;
}
void sol() {
for (int i = 1; i <= n; i++) dp[i] = inf;
dp[1] = 0;
add_line(-2 * h[1], -pref[1] + sqr(h[1]));
for (int i = 2; i <= n; i++) {
dp[i] = query(h[i]) + sqr(h[i]) + pref[i] - w[i];
add_line(-2 * h[i], dp[i] - pref[i] + sqr(h[i]));
}
Res = min(Res, dp[n]);
}
}
void solve() {
cin >> n;
for (int i = 1; i <= n; i++) cin >> h[i];
for (int i = 1; i <= n; i++) {
cin >> w[i];
pref[i] = pref[i - 1] + w[i];
}
// if (n <= 1000) sub1::sol();
// else {
Res = inf;
// sub2::sol();
sub3::sol();
cout << Res;
// }
}
int main() {
// freopen(task".inp", "r", stdin);
// freopen(task".out", "w", stdout);
ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0);
int tc = 1;
// cin >> tc; cin.ignore();
while (tc--)
solve();
return 0;
}
