// Born_To_Laugh - Hughie Do
#include <bits/stdc++.h>
#define alle(AC) AC.begin(), AC.end()
#define fi first
#define se second
using namespace std;
typedef long long ll;
[[maybe_unused]] const ll MOD = 998244353, INF = 1e18 + 7;
#define int ll
struct linecontainer
{
struct line{
ll a, b;
mutable ll p;
bool operator < (const line& o) const {
if(o.a == INF && o.b == INF) return p < o.p;
return a > o.a;
}
};
multiset<line> lc;
ll div(ll a, ll b){
return (a / b) - ((a ^ b) < 0 && a % b);
}
bool phe(multiset<line>::iterator x, multiset<line>::iterator y){
if(y == lc.end()){
x->p = INF;
return 0;
}
if(x->a == y->a){
if(x->b <= y->b) x->p = INF;
else x->p = -INF;
return x->p >= y->p;
}
x->p = div(x->b - y->b, y->a - x->a);
return x->p >= y->p;
}
void add(ll a, ll b){
auto x = lc.insert({a, b, 0});
auto y = next(x);
while(phe(x, y)) y = lc.erase(y);
if((y = x) != lc.begin() && phe(--x, y))
phe(x, y = lc.erase(y));
while((y = x) != lc.begin() && (--x)->p >= y->p)
phe(x, y = lc.erase(y));
}
ll qr(ll x){
assert(!lc.empty());
line l = *lc.lower_bound({INF, INF, x});
return l.a * x + l.b;
}
};
const int maxn = 1e6 + 10;
int n, h[maxn];
ll p[maxn], dp[maxn];
linecontainer lc;
void solve(){
cin >> n;
for(int i=1; i<=n; ++i) cin >> h[i];
for(int i=1; i<=n; ++i){
ll x;cin >> x;
p[i] = p[i - 1] + x;
}
lc.add(h[1] * -2, h[1] * h[1] - p[1]);
for(int i=2; i<=n; ++i){
dp[i] = (h[i] * h[i] + p[i - 1]) + lc.qr(h[i]);
lc.add(h[i] * -2, h[i] * h[i] - p[i] + dp[i]);
}
cout << dp[n] << '\n';
}
signed main(){
// freopen("inp.txt", "r", stdin);
// freopen("out.txt", "w", stdout);
ios_base::sync_with_stdio(false);
cin.tie(nullptr);
solve();
}
