#include <bits/stdc++.h>
using namespace std;
#define all(x) x.begin(), x.end()
#define ar array
#define pb push_back
#define ln '\n'
#define int long long
using i64 = long long;
template <class F, class _S>
bool chmin(F &u, const _S &v){
bool flag = false;
if ( u > v ){
u = v; flag |= true;
}
return flag;
}
template <class F, class _S>
bool chmax(F &u, const _S &v){
bool flag = false;
if ( u < v ){
u = v; flag |= true;
}
return flag;
}
const int inf = 1e18;
const int C = 2e6;
struct Lichao{
struct Line{
int m, c;
Line(int m = 0, int c = inf) : m(m), c(c) {}
int operator ()(int x){ return m * x + c; }
};
struct Info{
Line sg;
Info *lf, *rg;
Info(Line sg) : sg(sg), lf(0), rg(0) {}
};
Info *root = new Info({0, inf});
void ins(Info *v, int l, int r, Line nw){
if ( l == r ){
if ( v->sg(l) > nw(l) ){
v->sg = nw;
} return;
}
int md = (l + r) >> 1;
if ( v->sg.m > nw.m ) swap(v->sg, nw);
if ( v->sg(md) <= nw(md) ){
if ( v->lf ){
ins(v->lf, l, md, nw);
} else v->lf = new Info(nw);
} else{
swap(v->sg, nw);
if ( v->rg ){
ins(v->rg, md + 1, r, nw);
} else v->rg = new Info(nw);
}
}
void ins(Line nw){
ins(root, -C, C, nw);
}
int get(Info *v, int l, int r, int x){
if ( l == r ){
return v->sg(x);
}
int md = (l + r) >> 1, ret = v->sg(x);
if ( x <= md ){
if ( v->lf ){
chmin(ret, get(v->lf, l, md, x));
}
} else{
if ( v->rg ){
chmin(ret, get(v->rg, md + 1, r, x));
}
} return ret;
}
int get(int x){
return get(root, -C, C, x);
}
void clear(){ root = new Info ({0, inf}); }
};
signed main(){
ios_base::sync_with_stdio(false);
cin.tie(nullptr);
int n; cin >> n;
vector <int> h(n), w(n);
for ( auto &u: h ) cin >> u;
for ( auto &u: w ) cin >> u;
vector <int> pf(n);
for ( int i = 0; i < n; i++ ){
pf[i] = (i ? pf[i - 1] : 0) + w[i];
}
Lichao lch;
vector <int> dp(n);
auto ins = [&](int j){
lch.ins({-2 * h[j], h[j] * h[j] - pf[j] + dp[j]});
};
ins(0);
for ( int i = 1; i < n; i++ ){
dp[i] = lch.get(h[i]) + h[i] * h[i] + pf[i - 1];
ins(i);
}
cout << dp.back();
cout << '\n';
}
/*
6
3 8 7 1 6 6
0 -1 9 1 2 0
*/
