#include<bits/stdc++.h>
using namespace std;
#define ll long long
#define ii pair<int, int>
#define fi first
#define se second
#define pll pair<ll, ll>
#define vi vector<int>
#define db long double
const int maxn = 1e5+5;
const ll mod = 1e9+7;
const ll inf = 1e18+7;
const double eps = 1e-9;
const double pi = acos(-1);
const int block_size = 320;
int n, h[maxn], w[maxn];
ll s[maxn];
ll dp[maxn];
struct Line{
bool t;
db x;
ll a, b;
bool operator < (const Line &l) const{
if(t || l.t) return x < l.x;
return a > l.a;
}
};
struct linecontainer{
set<Line> cht;
bool has_prev(set<Line>::iterator it) {return it != cht.begin();}
bool has_next(set<Line>::iterator it) {return it != cht.end() && next(it) != cht.end();}
db intersect(set<Line>::iterator l1, set<Line>::iterator l2){
return (double) (l2->b - l1->b) / (l1->a - l2->a);
}
void cal_x(set<Line>::iterator it){
if(has_prev(it)){
Line l = *it;
l.x = intersect(prev(it), it);
cht.insert(cht.erase(it), l);
}
}
bool bad(set<Line>::iterator it){
return has_prev(it) && has_next(it) && (intersect(prev(it), next(it)) <= intersect(prev(it), it));
}
void add(ll a, ll b){
set<Line>::iterator it;
it = cht.lower_bound({0, 0, a, b});
if(it != cht.end() && it->a == a){
if(it->b >= b) cht.erase(it);
else return;
}
it = cht.insert({0, 0, a, b}).first;
if(bad(it)) cht.erase(it);
else{
while(has_prev(it) && bad(prev(it))) cht.erase(prev(it));
while(has_next(it) && bad(next(it))) cht.erase(next(it));
if(has_next(it)) cal_x(next(it));
cal_x(it);
}
}
ll query(ll x){
Line l = *prev(cht.upper_bound({1, (double)x, 0, 0}));
return l.a * x + l.b;
}
};
void solve(){
cin >> n;
for(int i=1; i<=n; i++){
cin >> h[i];
}
for(int i=1; i<=n; i++){
cin >> w[i];
s[i] = s[i-1] + w[i];
}
linecontainer cht;
ll a = -2*h[1];
ll b = 1ll*h[1]*h[1] - s[1];
cht.add(a, b);
for(int i=2; i<=n; i++){
dp[i] = cht.query(h[i]) + 1ll*h[i]*h[i] + s[i-1];
a = -2*h[i];
b = dp[i] + 1ll*h[i]*h[i] - s[i];
cht.add(a, b);
}
cout << dp[n] << "\n";
}
int main(){
ios_base::sync_with_stdio(0);
cin.tie(0); cout.tie(0);
int test = 1;
// cin >> test;
while(test--){
solve();
}
}
