#include <bits/stdc++.h>
using namespace std;
#define int long long
#define ull unsigned long long
#define ld long double
#define pii pair<int, int>
#define fi first
#define se second
#define __builtin_popcount __builtin_popcountll
#define all(x) (x).begin(), (x).end()
#define BIT(x, i) (((x) >> (i)) & 1)
#define MASK(x) ((1ll << (x)))
#define debug(a, l, r) for (int _i = (l); _i <= (r); ++_i) cout << (a)[_i] << ' '; cout << '\n';
const int MAXN = 1e5 + 5;
const int INF = 1e18 + 5;
int n, h[MAXN], w[MAXN], dp[MAXN], pref[MAXN];
void init() {
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];
}
fill(dp + 1, dp + n + 1, INF);
dp[1] = 0;
}
namespace brute{
void solve() {
for (int i = 2; i <= n; ++i) {
for (int j = i - 1; j >= 1; --j) {
int cur = dp[j] + (h[i] - h[j]) * (h[i] - h[j]) + pref[i - 1] - pref[j];
dp[i] = min(dp[i], cur);
}
}
cout << dp[n];
}
}
template<bool isMin> // true for min, false for max
struct LineContainer{
static const long long INF = LLONG_MAX;
struct Line{
long long a, b; // ax + b
mutable long long p;
bool operator < (const Line &other) const {
if (other.a == INF && other.b == INF) return p < other.p;
return a < other.a;
}
long long calc(long long x) const {return a * x + b;}
};
multiset<Line> hull;
long long div(long long a, long long b) {
return a/b - ((a ^ b) < 0 && a % b);
}
bool isect(typename multiset<Line>::iterator x, typename multiset<Line>::iterator y) {
if (y == hull.end()) {x->p = INF; return 0;}
if (x->a == y->a) x->p = (x->b > y->b ? INF : -INF);
else x->p = div(y->b - x->b, x->a - y->a);
return x->p >= y->p;
}
// Add line y = ax + b
void add(long long a, long long b) {
if (isMin) {a = -a; b = -b;}
auto z = hull.insert({a, b, 0}), y = z++, x = y;
while (isect(y, z)) z = hull.erase(z);
if (x != hull.begin() && isect(--x, y)) isect(x, y = hull.erase(y));
while ((y = x) != hull.begin() && (--x)->p >= y->p)
isect(x, hull.erase(y));
}
// Query at x
long long query(long long x) {
assert(!hull.empty());
Line l = *hull.lower_bound({INF, INF, x});
long long res = l.calc(x);
return isMin ? -res : res;
}
};
namespace full{
void solve() {
LineContainer<true> cht;
for (int i = 2; i <= n; ++i) {
cht.add(h[i - 1], dp[i - 1] + h[i - 1] * h[i - 1] - pref[i - 1]);
int fixed = h[i] * h[i] + pref[i - 1];
int getmi = cht.query(-2*h[i]);
dp[i] = fixed + getmi;
}
cout << dp[n];
}
}
signed main() {
#ifdef NCTHANH
freopen("input.txt", "r", stdin);
freopen("output.txt", "w", stdout);
#endif
ios_base::sync_with_stdio(0);
cin.tie(nullptr); cout.tie(nullptr);
init();
full::solve();
return 0;
}
