#include"bits/stdc++.h"
using lint = int64_t;
using namespace std;
using ll = int64_t;
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<>> {
static const ll inf = LLONG_MAX; //for doubles 1/.0
ll div(ll a, ll b) { //for doubles a/b
return a / b - ((a ^ b) < 0 && a % b); }
bool isect(iterator x, iterator y) {
if (y == end()) { x->p = inf; return false; }
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;
}
};
int main(){
cin.tie(nullptr)->sync_with_stdio(false);
int n; cin>>n;
lint W = 0;
vector<lint> h(n+1), w(n+1);
for(int i=1; i<=n; i++) cin>>h[i];
for(int i=1; i<=n; i++) cin>>w[i], W += w[i];
vector<lint> dp(n+1);
/*
dp[i] = min(dp[j] + (hj - hi)^2 - wi)
dp[i] = min dp[j] + hj^2 -hi*hj + hi^2 - wi
dp[i] = (hi^2 - wi) -2hj * hi + (dp[j] + hj^2)
*/
dp[1] = -w[1];
LineContainer cht;
cht.add(2*h[1], -(dp[1] + h[1]*h[1]));
for(int i = 2; i <= n; i++){
dp[i] = h[i]*h[i] - w[i] - cht.query(h[i]);
cht.add(2*h[i], -(dp[i] + h[i]*h[i]));
}
cout<<W + dp[n]<<"\n";
return 0;
}
