#include <bits/stdc++.h>
#pragma GCC optimize("O3")
#define int long long
using namespace std;
const int N = 1e5, INF = 1e12;
int n;
int dp[N], p[N], h[N];
struct segment{
mutable int l, r;
int m, a, mode;
bool operator<(const segment &o) const{
if(mode || o.mode) return m > o.m;
return l < o.l;
}
}; set<segment> s;
int qry(int x){
segment t = *--s.upper_bound({x, 0, 0, 0, 0});
return x*t.m + t.a;
}
double isect(int m1, int m2, int a1, int a2){
return (double)(a1-a2)/(double)(m2-m1);
}
void upd(int m, int a){
auto st = s.lower_bound({0, 0, m, 0, 1});
if(st != s.end() && st->m == m){
if(st->a < a) return;
st = s.erase(st);
}
if(st != s.begin()){
st--;
while(isect(m, st->m, a, st->a) < st->r){
double x = isect(m, st->m, a, st->a);
if(x <= st->l) st = --s.erase(st);
else st->r = floor(x);
}
}
else st = s.end();
auto en = s.upper_bound({0, 0, m, 0, 1});
while(en != s.end() && isect(m, en->m, a, en->a) > en->l){
double x = isect(m, en->m, a, en->a);
if(x >= en->r) en = s.erase(en);
else en->l = ceil(x);
}
if(st == s.end() || en == s.end() || en->l-st->r > 1)
s.insert({st == s.end()? -INF:st->r+1, en == s.end()? INF:en->l-1, m, a, 0});
}
signed main(){
cin.tie(0);
ios::sync_with_stdio(0);
cin >> n;
for(int i = 0; i < n; i++) cin >> h[i];
for(int i = 0; i < n; i++){
cin >> p[i];
if(i) p[i] += p[i-1];
}
upd(-2*h[0], h[0]*h[0]-p[0]);
for(int i = 1; i < n; i++){
dp[i] = qry(h[i]) + h[i]*h[i] + p[i-1];
upd(-2*h[i], dp[i] + h[i]*h[i] - p[i]);
}
cout << dp[n-1] << "\n";
}
