//UNSTOPPABLE
#include "bits/stdc++.h"
#include <ext/pb_ds/assoc_container.hpp>
#define ll long long
#define pb push_back
#define pf push_front
#define ppb pop_back
#define ppf pop_front
#define int long long
#define F first
#define S second
#define all(x) (x).begin(), (x).end()
#define pii pair<int,int>
#define tpii pair <pair <int,int> , int>
#define bruh cout << "NO\n"
using namespace std;
using namespace __gnu_pbds;
const int N = 3e5 + 5;
int mod = 1e9 + 7;
const int INF = 1e18;
int n,a[N],b[N],dp[N],p[N];
int f(int x){
return x * x;
}
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;
}
};
void Gold(){
cin >> n;
for(int i = 1 ; i <= n ; i++){
cin >> a[i];
}
for(int i = 1 ; i <= n ; i++){
cin >> b[i];
p[i] = p[i - 1] + b[i];
}
LineContainer cht;
dp[1] = 0;
cht.add(a[1] , -(f(a[1]) + dp[1] - p[1]));
for(int i = 2 ; i <= n ; i++){
dp[i] = f(a[1] - a[i]) + (p[i - 1] - p[1]);
dp[i] = min(dp[i] , f(a[i]) - cht.query(2 * a[i]) + p[i - 1]);
cht.add(a[i] , -(f(a[i]) + dp[i] - p[i]));
}
cout << dp[n];
//6
//3 8 7 1 6 6
//0 -1 9 1 2 0
}
signed main(/*Zhunussov Temirlan*/){
//freopen("txt.in","r",stdin);
//freopen("txt.out","w",stdout);
ios_base::sync_with_stdio(0);
cin.tie(0);
srand(time(0));
int TT = 1;
// cin >> TT;
for(int i = 1 ; i <= TT ; i++){
//cout << "Case " << i << ": ";
Gold();
}
}
