#include <bits/stdc++.h>
using namespace std;
//#define DEBUG
void setIO(const string &name) {
ios_base::sync_with_stdio(false);
cin.tie(nullptr);
cin.exceptions(istream::failbit);
#ifdef LOCAL
freopen((name + ".in").c_str(), "r", stdin);
freopen((name + ".out").c_str(), "w", stdout);
freopen((name + ".out").c_str(), "w", stderr);
#endif
}
const int inf = 0x3f3f3f3f, mod = 1e9 + 7;
const long long INFL = 0x3f3f3f3f3f3f3f3f;
const long long is_query = -(1LL << 62);
struct line {
long long m, b;
mutable function<const line *()> succ;
bool operator<(const line &rhs) const {
if (rhs.b != is_query) {
return m < rhs.m;
}
const line *s = succ();
if (!s) {
return false;
}
long long x = rhs.m;
return b - s->b < (s->m - m) * x;
}
};
struct dynamic_hull : public multiset<line> { // will maintain upper hull for maximum
const long long inf = LLONG_MAX;
bool bad(iterator y) {
auto z = next(y);
if (y == begin()) {
if (z == end()) {
return false;
}
return y->m == z->m && y->b <= z->b;
}
auto x = prev(y);
if (z == end()) {
return y->m == x->m && y->b <= x->b;
}
/* compare two lines by slope, make sure denominator is not 0 */
long long v1 = (x->b - y->b);
if (y->m == x->m) {
v1 = x->b > y->b ? inf : -inf;
} else {
v1 /= (y->m - x->m);
}
long long v2 = (y->b - z->b);
if (z->m == y->m) {
v2 = y->b > z->b ? inf : -inf;
} else {
v2 /= (z->m - y->m);
}
return v1 >= v2;
}
void insert_line(long long m, long long b) {
auto y = insert({m, b});
y->succ = [=] {
return next(y) == end() ? 0 : &*next(y);
};
if (bad(y)) {
erase(y);
return;
}
while (next(y) != end() && bad(next(y))) {
erase(next(y));
}
while (y != begin() && bad(prev(y))) {
erase(prev(y));
}
}
long long eval(long long x) {
auto l = *lower_bound((line) {x, is_query});
return l.m * x + l.b;
}
};
void solve() {
int n;
cin >> n;
vector<long long> h(n);
for (int i = 0; i < n; ++i) {
cin >> h[i];
}
vector<long long> w(n), pre(n);
for (int i = 0; i < n; ++i) {
cin >> w[i];
pre[i] = pre[max(0, i - 1)] + w[i];
}
dynamic_hull cht;
cht.insert_line(2 * h[0], -(h[0] * h[0] - pre[0]));
for (int i = 1; i < n - 1; ++i) {
long long cur = -cht.eval(h[i]) + h[i] * h[i] + pre[i - 1];
cht.insert_line(2 * h[i], -(cur + h[i] * h[i] - pre[i]));
}
cout << -cht.eval(h[n - 1]) + h[n - 1] * h[n - 1] + pre[n - 2] << "\n";
}
int main() {
setIO("1");
int test_case_number = 1;
while (test_case_number--) {
solve();
}
return 0;
}
