#include <bits/stdc++.h>
using namespace std;
#define ff first
#define ss second
#define all(a) a.begin(), a.end()
#define int long long
const int inf = 1e9;
const int N = 1e5 + 5;
const int mod = 1e9 + 7;
struct Line{
int k, b;
int operator * (int x){
return k * x + b;
}
int operator ^ (Line x){
return ceil((b - x.b) / (x.k - k));
};
};
struct LiChao{
Line tree[N * 30];
int last, L[N * 30], R[N * 30];
LiChao(){
last = 0;
for(int i=0;i<(N*30);i++) tree[i] = {inf, inf * inf};
}
void add(Line v, int lx = 0, int rx = mod, int x = 0){
if(lx == rx){
if(tree[x] * lx > v * lx) swap(tree[x], v);
return;
}
if(v.k == tree[x].k){
tree[x].b = min(tree[x].b, v.b);
return;
}
int m = (lx + rx) >> 1;
int ix = tree[x] ^ v;
if(ix <= m){
if(tree[x] * (m + 1) > v * (m + 1)) swap(tree[x], v);
add(v, lx, m, (L[x] ? L[x] : L[x] = ++last));
} else {
if(tree[x] * m > v * m) swap(tree[x], v);
add(v, m + 1, rx, (R[x] ? R[x] : R[x] = ++last));
}
}
int get(int i, int lx = 0, int rx = mod, int x = 0){
if(lx == rx) return tree[x] * i;
int m = (lx + rx) >> 1;
if(i <= m && L[x]) return min(tree[x] * i, get(i, lx, m, L[x]));
if(m < i && R[x]) return min(tree[x] * i, get(i, m + 1, rx, R[x]));
return tree[x] * i;
}
}tree;
/*
6
3 8 7 1 6 6
0 -1 9 1 2 0
*/
signed main(){
int n; cin >> n;
vector<int> h(n+1);
for(int i = 1;i <= n; i++) cin >> h[i];
vector<int> w(n+1, 0);
for(int i = 1;i <= n; i++){
cin >> w[i];
w[i]+= w[i-1];
}
vector<int> dp(n+1);
dp[1] = 0;
tree.add({-2 * h[1], dp[1] - w[1] + h[1] * h[1]});
for(int i = 2;i <= n; i++){
// kx + b
/*
new_dp[i] = (h[i] - h[j])^2 + dp[j]
(h[i] - h[j]) * (h[i] - h[j]) = kx
h[i] * h[i] - h[i] * h[j] - h[j] * h[i] + h[j] * h[j]
dp[i] = min(dp[i], -2 * h[i] * h[j] + dp[j] - w[j] + h[j] * h[j] + w[i-1] + h[i] * h[i]);
*/
/*
for(int j = 1; j < i; j++){
//dp[i] = min(dp[i], -2 * h[i] * h[j] + dp[j] - w[j] + h[j] * h[j] + w[i-1] + h[i] * h[i]);
}
*/
int mn = tree.get(h[i]);
dp[i] = mn + h[i]*h[i] + w[i-1];
tree.add({-2 * h[i], dp[i] - w[i] + h[i] * h[i]});
}
cout << dp[n];
return 0;
}
