#include <bits/stdc++.h>
#define int long long
using namespace std;
const int MX = 1e6+5;
const int MN = -MX;
struct Line {
int m,b;
int operator()(int x){return m * x + b;}
Line(int x,int y) : m(x),b(y) {}
};
struct Node{
Line line;
Node *left, *right;
Node(Line ln) : line(ln),left(nullptr),right(nullptr) {}
void upd(Line nw,int l=MN,int r=MX) {
if(l+1==r){
if(nw(l) < line(l))swap(nw,line);
return;
}
int mid = (l+r)/2;
int ls = nw(l) < line(l);
int ms = nw(mid) < line(mid);
if(ms)swap(line,nw);
if(ls!=ms){
if(!left)left = new Node(nw);
else left->upd(nw,l,mid);
} else {
if(!right)right = new Node(nw);
else right->upd(nw,mid,r);
}
}
int qry(int x,int l=MN,int r=MX) {
if(l+1==r)return line(x);
int mid = (l+r)/2;
if(x<mid) {
if(left)return min(line(x),left->qry(x,l,mid));
} else if (right) return min(line(x),right->qry(x,mid,r));
return line(x);
}
};
int32_t main() {
cin.tie(0)->sync_with_stdio(0);
int n;
cin>>n;
vector<int> h(n+1),pref(n+1),dp(n+1);
for(int i = 1;i<=n;i++) cin >> h[i];
for(int i = 1;i<=n;i++) cin >> pref[i], pref[i]+=pref[i-1];
Line tmp = Line(-2*h[1], h[1] * h[1] - pref[1]);
Node t = Node(tmp);
for(int i = 2;i<=n;i++) {
dp[i] = h[i] * h[i] + pref[i-1] + t.qry(h[i]);
t.upd(Line(-2*h[i],dp[i] + h[i] * h[i] - pref[i]));
}
cout << dp[n];
}
