#include <bits/stdc++.h>
//#include <bits/debug.hpp>
#define ll long long
#define all(x) x.begin(), x.end()
#define Neco "xay cau"
#define resp(x) sort(all(x)), x.resize(unique(all(x)) - x.begin())
#define getbit(x,i) ((x >> i)&1)
#define _left id * 2, l, mid
#define _right id * 2 + 1, mid + 1, r
#define cntbit(x) __builtin_popcountll(x)
#define fi(i, a, b) for(int i = a; i <= b; i++)
#define fid(i, a, b) for(int i = a; i >= b; i--)
#define maxn (int) 2e5 + 7
using namespace std;
const ll mod = 1e9 + 7; //972663749
const ll base = 911382323;
int n;
ll h[maxn], s[maxn];
ll dp[maxn];
struct CHT {
vector<pair<ll, ll>> P;
vector<long double> X;
void init() { P.clear(), X.clear(); }
bool empty() { return P.empty(); }
long double inter(pair<ll, ll> x, pair<ll, ll> y) {
return 1. * (y.second - x.second) / (x.first - y.first);
}
void Add(pair<ll, ll> p) {
long double Nw = -1e18;
while(!P.empty()) {
assert(P.back().first <= p.first);
if(P.back().first == p.first && P.back().second >= p.second) return;
Nw = inter(p, P.back());
if(Nw < X.back()) P.pop_back(), X.pop_back();
else break;
}
P.push_back(p), X.push_back(Nw);
}
ll get(ll x) {
if(P.empty()) return -1e18;
int it = upper_bound(all(X), x) - X.begin() - 1;
return P[it].first * x + P[it].second;
}
} Cht[18];
void Add(pair<ll, ll> p) {
vector<pair<ll, ll>> P = {p};
fi(i, 0, 17) {
if(Cht[i].empty()) {
sort(all(P), greater<pair<ll, ll>>());
for(auto [x, y] : P) Cht[i].Add({-x, -y});
break;
}
else {
for(auto [x, y] : Cht[i].P) P.push_back({-x, -y});
Cht[i].init();
}
}
}
ll get(ll x, ll ans = 1e18) {
fi(i, 0, 17) ans = min(ans, -Cht[i].get(x));
return ans;
}
void solve()
{
cin >> n;
fi(i, 1, n) cin >> h[i];
fi(i, 1, n) {
ll x; cin >> x;
s[i] = s[i - 1] + x;
}
Add({ -2 * h[1], h[1] * h[1] - s[1] + dp[1] });
fi(i, 2, n) {
dp[i] = get(h[i]) + s[i - 1] + h[i] * h[i];
Add({ -2 * h[i], h[i] * h[i] - s[i] + dp[i] });
}
cout << dp[n];
}
int main()
{
ios_base::sync_with_stdio(0);
cin.tie(0);
cout.tie(0);
if(fopen(Neco".inp", "r")) {
freopen(Neco".inp", "r", stdin);
freopen(Neco".out", "w", stdout);
}
int nTest = 1;
// cin >> nTest;
while(nTest--)
{
solve();
}
return 0;
}
