#include "bits/stdc++.h"
using namespace std;
#pragma GCC optimize("O3")
#pragma GCC target("avx,avx2,tune=native")
typedef long long ll;
typedef vector<ll> vi;
typedef vector<vi> vvi;
#define sz(x) (int)(x).size()
#define all(x) (x).begin(), (x).end()
const ll INF = 1LL << 60;
int N;
vi H;
vi W;
ll ans;
vi dp;
struct segment
{
mutable ll l, r;
ll m, a;
int type = 0; // 0 - normal, 1 - compare by l, 2 - compare by m
bool operator<(const segment &o) const
{
if (type == 1 || o.type == 1)
return l < o.l;
if (type == 2 || o.type == 2)
return m > o.m;
return l < o.l;
}
};
double intersection(ll m1, ll a1, ll m2, ll a2)
{
return (a1 - a2) / (double)(m2 - m1);
// todo parallel???
}
struct convexHull
{
set<segment> H;
void insert(ll m, ll a)
{
auto it1 = H.lower_bound({0, 0, m, 0, 2});
if (it1 != H.end() && it1->m == m)
{
if (it1->a <= a)
return;
it1 = H.erase(it1);
}
if (it1 == H.begin())
it1 = H.end();
else
{
--it1; // the elements with o.m > m
while (intersection(it1->m, it1->a, m, a) < it1->r)
{
double inter = intersection(it1->m, it1->a, m, a);
if (inter < it1->l)
it1 = --H.erase(it1);
else
it1->r = (ll)floor(inter);
}
}
auto it2 = H.upper_bound({0, 0, m, 0, 2});
while (it2 != H.end() && intersection(it2->m, it2->a, m, a) > it2->l)
{
double inter = intersection(it2->m, it2->a, m, a);
if (inter > it2->r)
it2 = H.erase(it2);
else
it2->l = (ll)ceil(inter);
}
if (it1 == H.end() || it2 == H.end() || it1->r + 1 < it2->l)
{
H.insert({(it1 == H.end()) ? -INF : it1->r + 1, (it2 == H.end()) ? INF : it2->l - 1, m, a, 0});
}
}
ll query(ll x)
{
segment seg = *(--H.upper_bound({x, 0, 0, 0, 1}));
return seg.m * x + seg.a;
}
};
int main()
{
ios::sync_with_stdio(false);
cin.tie(0);
cin >> N;
H.resize(N), W.resize(N), dp.resize(N);
for (int i = 0; i < N; ++i)
cin >> H[i];
for (int i = 0; i < N; ++i)
cin >> W[i];
ans = accumulate(all(W), 0LL);
convexHull hull;
dp[0] = -W[0];
hull.insert(-2 * H[0], dp[0] + H[0] * H[0]); // first pillar
for (int i = 1; i < N; ++i)
{
dp[i] = hull.query(H[i]) - W[i] + H[i] * H[i];
hull.insert(-2 * H[i], dp[i] + H[i] * H[i]);
}
cout << dp.back() + ans << endl;
return 0;
}
