#include <bits/stdc++.h>
#define fr(i, n, m) for(int i = (n); i < (m); i ++)
#define pb push_back
#define st first
#define nd second
#define pq priority_queue
#define all(x) begin(x), end(x)
using namespace std;
typedef long long ll;
typedef long double ld;
typedef pair<int,int> pii;
const int i_inf = 1e9;
const ll mod = 1e9+7;
const ld eps = 1e-13;
const ld pi = 3.14159265359;
mt19937 _rand(time(NULL));
clock_t z;
const int mxn = 2e5+5;
int n;
ll h[mxn];
ll w[mxn];
ll dp[mxn];
ll pref[mxn];
ll p(ll a){
return a*a;
}
const ld inf = 1e18;
struct chtDynamic {
struct line {
ll m, b; ld x;
ll val; bool isQuery;
line(ll _m = 0, ll _b = 0) :
m(_m), b(_b), val(0), x(-inf), isQuery(false) {}
ll eval(ll x) const { return m * x + b; }
bool parallel(const line &l) const { return m == l.m; }
ld intersect(const line &l) const {
return parallel(l) ? inf : 1.0 * (l.b - b) / (m - l.m);
}
bool operator < (const line &l) const {
if(l.isQuery) return x < l.val;
else return m < l.m;
}
};
set<line> hull;
typedef set<line> :: iterator iter;
bool cPrev(iter it) { return it != hull.begin(); }
bool cNext(iter it) { return it != hull.end() && next(it) != hull.end(); }
bool bad(const line &l1, const line &l2, const line &l3) {
return l1.intersect(l3) <= l1.intersect(l2);
}
bool bad(iter it) {
return cPrev(it) && cNext(it) && bad(*prev(it), *it, *next(it));
}
iter update(iter it) {
if(!cPrev(it)) return it;
ld x = it -> intersect(*prev(it));
line tmp(*it); tmp.x = x;
it = hull.erase(it);
return hull.insert(it, tmp);
}
void addLine(ll m, ll b) {
line l(m, b);
iter it = hull.lower_bound(l);
if(it != hull.end() && l.parallel(*it)) {
if(it -> b < b) it = hull.erase(it);
else return;
}
it = hull.insert(it, l);
if(bad(it)) return (void) hull.erase(it);
while(cPrev(it) && bad(prev(it))) hull.erase(prev(it));
while(cNext(it) && bad(next(it))) hull.erase(next(it));
it = update(it);
if(cPrev(it)) update(prev(it));
if(cNext(it)) update(next(it));
}
ll query(ll x) const {
if(hull.empty()) return -inf;
line q; q.val = x, q.isQuery = 1;
iter it = --hull.lower_bound(q);
return it -> eval(x);
}
} ds;
void solve(){
cin >> n;
fr(i, 0, n){
cin >> h[i];
}
fr(i, 0, n){
cin >> w[i];
}
pref[0] = w[0];
fr(i, 1, n){
pref[i] = pref[i-1]+w[i];
}
dp[0] = 0;
ds.addLine(2*h[0], -(dp[0] + p(h[0])-pref[0]));
fr(i, 1, n){
dp[i] = -ds.query(h[i]) + p(h[i]) + pref[i] - w[i];
ds.addLine(2*h[i], -(dp[i] + p(h[i]) - pref[i]));
}
cout<<dp[n-1]<<endl;
}
int main(){
ios_base::sync_with_stdio(false);
cin.tie(NULL);
solve();
}
/*
6
3 8 7 1 6 6
0 -1 9 1 2 0
*/
