#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#define pb push_back
#define F first
#define S second
#define all(x) x.begin(), x.end()
#define debug(x) cerr << #x << " : " << x << '\n'
using namespace std;
using namespace __gnu_pbds;
typedef long long ll;
typedef long double ld;
typedef string str;
typedef pair<ll, ll> pll;
typedef tree<ll, null_type, less<ll>, rb_tree_tag, tree_order_statistics_node_update> ordered_set;
const ll Mod = 998244353;
const ll Inf = LONG_LONG_MAX;
const ll Log = 20;
const ll N = 1ll << Log;
const int Maxn = 1e5 + 10;
const int Maxk = 101;
const int Base = 101;
typedef pair < ll , ll > Line;
struct CHT{
set < pair < Line , ll > > S;
set < pair < ll , Line > > I;
ll INF = 4e18;
inline void Add(Line X)
{
X.F *= -1;
X.S *= -1;
ll t = -INF;
auto it = S.lower_bound({X, -INF});
while ((int)S.size())
{
if (it == S.begin())
{t = -INF; break;}
it --; ll r = Intersection(it->first, X);
if (r <= it->second)
I.erase({it->second, it->first}), it = S.erase(it);
else
{t = r; break;}
}
it = S.lower_bound({X, -INF});
while ((int)S.size())
{
if (it == S.end())
break;
ll r = Intersection(X, it->first);
Line Y = it->first;
I.erase({it->second, it->first});
it = S.erase(it);
if (r <= t)
{
r = -INF;
if (it != S.begin())
it --, r = Intersection(it->first, Y);
S.insert({Y, r}); I.insert({r, Y}); return ;
}
if (it != S.end() && it->second <= r)
continue;
S.insert({Y, r}); I.insert({r, Y}); break;
}
S.insert({X, t}); I.insert({t, X});
}
inline ll GetMin(ll X)
{
auto it = I.upper_bound({X, {INF, INF}}); it --;
return -(X * it->second.first + it->second.second);
}
inline ll Intersection(Line X, Line Y)
{
if (X.first == Y.first && X.second <= Y.second)
return (-INF);
if (X.first == Y.first)
return (INF);
return ((X.second - Y.second) / (Y.first - X.first)) + ((X.second - Y.second) % (Y.first - X.first) > 0);
}
};
CHT cht;
ll h[Maxn], w[Maxn], dp[Maxn], ps[Maxn];
int main(){
ios::sync_with_stdio(0); cin.tie(0); cout.tie(0);
ll n;
cin >> n;
for(int i = 1; i <= n; i++) cin >> h[i];
for(int i = 1; i <= n; i++) cin >> w[i];
for(int i = 1; i <= n; i++) ps[i] = ps[i - 1] + w[i];
dp[1] = 0;
cht.Add({-2LL * h[1], h[1] * h[1] + dp[1] - ps[1]});
for(int i = 2; i <= n; i++){
dp[i] = cht.GetMin(h[i]) + h[i] * h[i] + ps[i - 1];
cht.Add({-2LL * h[i], h[i] * h[i] + dp[i] - ps[i]});
}
cout << dp[n];
return 0;
}
/*
6
3 8 7 1 6 6
0 -1 9 1 2 0
*/
