#include<bits/stdc++.h>
#pragma GCC optimize("-Ofast")
//#pragma GCC optimize("trapv")
#pragma GCC target("sse,sse2,sse3,ssse3,sse4,sse4.2,popcnt,abm,mmx,avx2,tune=native")
#pragma GCC optimize("-ffast-math")
#pragma GCC optimize("-funroll-loops")
#define I inline void
#define S struct
#define vi vector<int>
#define vii vector<pair<int,int>>
#define pii pair<int,int>
#define pll pair<ll,ll>
using namespace std ;
using ll = long long ;
using ld = long double ;
const int N = 2e5 + 7 , mod = 1e9 + 7 ;
const ll inf = 2e18 ;
// How interesting!
int n ;
ll ans[N];
ll h[N], w[N] ;
ll pref[N] ;
vector<pair<ll,ll> > cht ;
#define MAXLC 1000000000
#define INF (1LL<<60)
inline ll f(ll m, ll b, int x) {
return m * x + b;
}
ll eval(int l, int r){
ll diff = h[r] - h[l] ;
return 1ll * diff * diff + pref[r - 1] - pref[l] ;
}
struct lc_node {
ll m = 0, b = INF;
lc_node *l = nullptr, *r = nullptr;
~lc_node() { delete l; delete r; }
void add_line(ll nm, ll nb, int lo=0, int hi=MAXLC) {
int mid = (lo + hi) / 2;
bool bl = f(nm, nb, lo) < f(m, b, lo);
bool bm = f(nm, nb, mid) < f(m, b, mid);
bool bh = f(nm, nb, hi) < f(m, b, hi);
if (bm) {
swap(nm, m);
swap(nb, b);
}
if (lo == hi || nb == INF)
return;
else if (bl != bm) {
if (!l) l = new lc_node;
l->add_line(nm, nb, lo, mid - 1);
}
else if (bh != bm) {
if (!r) r = new lc_node;
r->add_line(nm, nb, mid + 1, hi);
}
}
ll get(int x, int lo=0, int hi=MAXLC) {
int mid = (lo + hi) / 2;
ll ret = f(m, b, x);
if (l && x < mid)
ret = min(ret, l->get(x, lo, mid - 1));
if (r && x > mid)
ret = min(ret, r->get(x, mid + 1, hi));
return ret;
}
void clear() {
delete l; delete r;
m = 0, b = INF, l = nullptr, r = nullptr;
}
} lc;
int main(){
ios_base::sync_with_stdio(0) ;
cin.tie(0) ;
//freopen("in.in" , "r" , stdin) ;
cin >> n;
for(int i = 1 ;i <= n ; ++ i){
cin >> h[i] ;
}
for(int i = 1 ; i <= n ; ++ i){
cin >> w[i] ;
pref[i] += w[i] ;
pref[i+1]+=pref[i] ;
}
for(int i = 2 ; i <= n; ++ i){
ll ret = eval(1 , i) ;
ll cost = 1ll * h[i] * h[i] + pref[i - 1] ;
ret = min(ret , lc.get(h[i]) + cost ) ;
ans[i] = ret ;
lc.add_line( -2ll * h[i] , 1ll * h[i] * h[i] - pref[i] + ans[i] ) ;
}
cout<<ans[n] ;
return 0 ;
}
/*
- bounds sir (segtree = 4N, eulerTour = 2N, ...)
- a variable defined twice?
- will overflow?
- is it a good complexity?
- don't mess up indices (0-indexed vs 1-indexed)
- reset everything between testcases.
*/
