//#pragma GCC optimize("O3,unroll-loops")
//#pragma GCC target("avx2,bmi,bmi2,lzcnt,popcnt")
#include<bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#define ll long long
#define F first
#define S second
#define ull unsigned long long
#define db double
#define ldb long double
#define pb push_back
#define pf push_front
#define ppb pop_back
#define ppf pop_front
#define yes cout << "YES\n"
#define no cout << "NO\n"
#define ordered_set tree < ll, null_type, less < ll > , rb_tree_tag, tree_order_statistics_node_update >
#define all(x) x.begin(), x.end()
const int mod = 1e9 + 7;
const int N = 500001;
using namespace std;
using namespace __gnu_pbds;
ll n, m, a, b, c, p[N], f[N], dp[N], pr[N];
struct Line {
mutable ll k, m, p;
bool operator<(const Line& o) const { return k < o.k; }
bool operator<(ll x) const { return p < x; }
};
struct LineContainer : multiset<Line, less<>> {
// (for doubles, use inf = 1/.0, div(a,b) = a/b)
static const ll inf = LLONG_MAX;
ll div(ll a, ll b) { // floored division
return a / b - ((a ^ b) < 0 && a % b); }
bool isect(iterator x, iterator y) {
if (y == end()) return x->p = inf, 0;
if (x->k == y->k) x->p = x->m > y->m ? inf : -inf;
else x->p = div(y->m - x->m, x->k - y->k);
return x->p >= y->p;
}
void add(ll k, ll m) {
auto z = insert({k, m, 0}), y = z++, x = y;
while (isect(y, z)) z = erase(z);
if (x != begin() && isect(--x, y)) isect(x, y = erase(y));
while ((y = x) != begin() && (--x)->p >= y->p)
isect(x, erase(y));
}
ll query(ll x) {
assert(!empty());
auto l = *lower_bound(x);
return l.k * x + l.m;
}
};
signed main() {
ios_base::sync_with_stdio(0);
cin.tie(0);
cin >> n;
for (int i = 1; i <= n; i++){
cin >> p[i];
}
for (int i = 1; i <= n; i++){
cin >> f[i];
pr[i] = f[i] + pr[i - 1];
}
LineContainer cht;
dp[1] = 0;
cht.add(p[1], -(p[1] * p[1] + dp[1] - pr[1]));
// cout << -(dp[1] - pr[1] + p[1] * p[1]) << '\n';
for (int i = 2; i <= n; i++){
dp[i] = (p[1] - p[i]) * (p[1] - p[i]) + (pr[i - 1] - pr[1]);
dp[i] = min(p[i] * p[i] - cht.query(2 * p[i]) + pr[i - 1] , dp[i]);
cht.add (p[i], -(p[i] * p[i] + dp[i] - pr[i]));
// cout << dp[i] << ' ';
}
cout << dp[n];
}
