#include <bits/stdc++.h>
using namespace std;
#define fi first
#define se second
#define BIT(n) (1ll << n)
#define GBIT(x, i) ((x >> i) & 1)
#define all(v) v.begin(), v.end()
#define eb emplace_back
#define pb push_back
#define endl '\n'
#define fu(i, l, r) for (int i = (int) (l); i <= (int) (r); i++)
#define fd(i, r, l) for (int i = (int) (r); i >= (int) (l); i--)
typedef pair <int, int> pii;
typedef pair <long long, long long> pll;
typedef unsigned long long ull;
typedef long long ll;
typedef double dl;
const int MAXN = 4e5 + 55;
const int MOD = 1e9 + 7;
const ll oo = 1ll * MOD * MOD;
int n;
int w[MAXN], h[MAXN];
void rf() {
cin >> n;
fu(i, 1, n) cin >> h[i];
fu(i, 1, n) cin >> w[i];
}
struct Line {
bool t;
ll m, b;
dl x;
bool operator < (const Line &a) const {
return (t || a.t) ? x < a.x : m > a.m;
}
};
struct Linecontainer {
set <Line> cht;
#define iterLine set <Line> :: iterator
bool has_prev(iterLine id) {return id != cht.begin();}
bool has_next(iterLine id) {return id != cht.end() && next(id) != cht.end();}
dl PointX(iterLine a, iterLine b) {
return (dl) (a -> b - b -> b) / (b -> m - a -> m);
}
bool bad(iterLine id) {
return has_prev(id) && has_next(id) && PointX(prev(id), next(id)) <= PointX(prev(id), id);
}
void calx(iterLine id) {
Line l = *id;
if (has_prev(id)) l.x = PointX(prev(id), id);
else l.x = -oo;
cht.insert(cht.erase(id), l);
}
void add(ll m, ll b) {
iterLine id = cht.lower_bound({0, m, b, 0});
if (id != cht.end() && id -> m == m) {
if (id -> b <= b) return;
cht.erase(id);
}
id = cht.insert({0, m, b, 0}).first;
if (bad(id)) return void(cht.erase(id));
while (has_prev(id) && bad(prev(id))) cht.erase(prev(id));
while (has_next(id) && bad(next(id))) cht.erase(next(id));
if (has_next(id)) calx(next(id));
calx(id);
}
ll query(ll x) {
Line l = *prev(cht.upper_bound({1, 0, 0, x}));
return l.m * x + l.b;
}
} cht;
ll p[MAXN];
ll _sqr(ll n) {
return n * n;
}
void solve() {
fu(i, 1, n) {
p[i] = p[i - 1] + w[i];
}
cht.add(h[1], p[n - 1] - p[1] + _sqr(h[1]));
ll res = _sqr(h[n] - h[1]) + p[n - 1] - p[1];
// cout << res << endl;
fu(i, 2, n - 1) {
ll cur = _sqr(h[n] - h[i]) - w[i] + _sqr(h[i]) + cht.query(-2 * h[i]);
res = min(res, cur);
// cout << res << " " << cur << endl;
cht.add(h[i], cur -_sqr(h[n] - h[i]) + _sqr(h[i]));
}
cout << res << endl;
}
int32_t main() {
ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0);
#define task "prob"
if (fopen(task".inp", "r")) {
freopen(task".inp", "r", stdin);
freopen(task".out", "w", stdout);
}
int ntest = 1;
// cin >> ntest;
fu(i, 1, ntest) rf(), solve();
}
