#include <bits/stdc++.h>
using namespace std;
#define rep(i,s,e) for (int i = s; i <= e; ++i)
#define rrep(i,s,e) for (int i = s; i >= e; --i)
#define pb push_back
#define pf push_front
#define fi first
#define se second
#define all(a) a.begin(), a.end()
#define len(a) (int)a.size()
typedef long long ll;
typedef pair<int, int> ii;
typedef pair<ll, ll> pll;
typedef vector<ii> vii;
typedef vector<int> vi;
typedef vector<double> vd;
typedef vector<string> vs;
typedef vector<ll> vll;
//let's implement cht then :)))))))))
const ll inf = 1e9;
ll cdiv (ll a, ll b) {
return a / b + !(((a < 0) != (b < 0)) || !(a % b));
}
int main() {
ios::sync_with_stdio(0);
cin.tie(0);
ll n, s = 0;
cin >> n;
ll h[n+1], w[n+1], x[n+1], dp[n+1];
set<pll,greater<pll>> stk;
set<pll> stx;
rep (i,1,n) cin >> h[i];
rep (i,1,n) {
cin >> w[i];
s += w[i];
}
dp[1] = h[1]*h[1] - w[1];
stk.insert({-2*h[1],1});
stx.insert({-inf,1});
x[1] = -inf;
rep (i,2,n) {
auto iti = stx.upper_bound({h[i], inf});
--iti;
ll u = (*iti).se;
dp[i] = dp[u] + -2*h[u]*h[i] + h[i] * h[i] - w[i];
if (i==n) cout << s+dp[n] << "\n";
else {
//add an element to the cht
dp[i] += h[i]*h[i];
auto it = stk.upper_bound({-2*h[i], -inf});
bool beg = 0;
if (it!=stk.begin()) {
--it;
while (true) {
if ((*it).fi==-2*h[i]) {
if (dp[i] >= dp[(*it).se]) break;
}
else {
ll nx = cdiv(dp[(*it).se]-dp[i],-2*h[i]-(*it).fi);
if (nx>x[(*it).se]) break;
}
stx.erase({x[(*it).se], (*it).se});
it = stk.erase(it);
if (it==stk.begin()) {
beg = 1;
break;
}
--it;
}
}
else beg = 1;
if (beg) {
stk.insert({-2*h[i], i});
x[i] = -inf;
stx.insert({-inf, i});
}
else {
if ((*it).fi==-2*h[i]) continue;
int X = cdiv(dp[(*it).se]-dp[i],-2*h[i]-(*it).fi);
++it;
if (it==stk.end() || X <= x[(*it).se]) {
if (it!=stk.end() && X==x[(*it).se]) {
if (cdiv(dp[(*it).se]-dp[i],-2*h[i]-(*it).fi)<=X) continue;
}
stx.insert({X, i});
stk.insert({-2*h[i],i});
x[i] = X;
}
else continue;
}
while (true) {
if (it==stk.end()) break;
int X = cdiv(dp[(*it).se]-dp[i],-2*h[i]-(*it).fi);
++it;
if (it==stk.end()) {
--it;
stx.erase({x[(*it).se], (*it).se});
stx.insert({X, (*it).se});
x[(*it).se] = X;
break;
}
if (X >= x[(*it).se]) {
--it;
stx.erase({x[(*it).se], (*it).se});
it = stk.erase(it);
}
else {
--it;
stx.erase({x[(*it).se], (*it).se});
stx.insert({X, (*it).se});
x[(*it).se] = X;
break;
}
}
}
}
return 0;
}
