// #pragma GCC optimize("O3,unroll-loops")
// #pragma GCC target("avx2,bmi,bmi2,lzcnt,popcnt")
#include <iostream>
#include <cstring>
#include <algorithm>
#include <vector>
#include <utility>
#include <cmath>
#include <ctime>
#include <cassert>
#include <set>
#include <stack>
#include <map>
#include <queue>
#include <random>
#include <chrono>
#include <bitset>
#include <array>
using ll = long long;
#define debug(x) cout << #x << " = " << x << '\n'
#define separator "===============================================\n"
#define all(a) a.begin(), a.end()
#define SZ(a) (int)(a).size()
using namespace std;
const int mxn = 1e5 + 3;
const ll mod = 1e9 + 7;
const int inf32 = 2e9;
const ll inf64 = 3e18;
/*
dp[i] = min cost to reach i-th pillar
dp[i] = min_{j < i} dp[j] + (h[i] - h[j])^2 + (w[j + 1] + ... + w[i - 1])
= dp[j] + h[i]^2 + h[j]^2 - 2*h[i]*h[j] + pref[i - 1] - pref[j]
= (h[i]^2 + pref[i - 1]) - h[j]*2*h[i] + dp[j] + h[j]^2 - pref[j]
given n lines ax + b, given x, find line that minimizes ax+b
*/
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<>> {
ll div(ll a, ll b){
return a / b - ((a ^ b) < 0 && a % b); }
bool isect(iterator x, iterator y) {
if (y == end()) return x->p = inf64, 0;
if (x->k == y->k) x->p = x->m > y->m ? inf64 : -inf64;
else x->p = div(y->m - x->m, x->k - y->k);
return x->p >= y->p;
}
void add(ll k, ll m){
k = -k, m = -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);
}
};
void solve(){
int n; cin >> n;
vector<ll> h(n + 1), w(n + 1), pref(n + 1);
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];
vector<ll> dp(n + 1);
LineContainer cht;
cht.add(h[1], h[1] * h[1] - w[1]);
for (int i = 2; i <= n; ++i){
dp[i] = h[i] * h[i] + pref[i - 1] + cht.query(h[i] * -2);
cht.add(h[i], dp[i] + h[i] * h[i] - pref[i]);
}
cout << dp[n];
}
int main(){
auto start = chrono::steady_clock::now();
ios_base::sync_with_stdio(false);
cin.tie(NULL);
int t = 1;
// cin >> t;
while(t--) solve();
chrono::duration<double> elapsed {chrono::steady_clock::now() - start};
cerr << "\n>> Runtime: " << elapsed.count() << "s\n";
}
