/**
* Problem: CEOI17_building
* Link: https://oj.uz/problem/view/CEOI17_building
* Tags: DP, Lichao Tree
*
* Solution: DP State: dp[i][j] là xét i cột đầu, end tại j
* DP Transition: dp[i][i] = dp[i - 1][k] + (h[i] - h[k])^2 + (prf[i - 1] - prf[k])
* = dp[i - 1][k] + h[k]^2 + h[i]^2 - 2 * h[i] * h[k] + prf[i - 1] - prf[k]
* = (dp[i - 1][k] + h[k]^2 - prf[k]) -2 * h[i] * h[k] + (h[i]^2 + prf[i - 1])
**/
#include<iostream>
#include<algorithm>
using namespace std;
typedef long long ll;
const ll inf = 1e18;
const int N = 1e5 + 9, H = 1e6;
int n;
ll h[N], w[N], prf[N];
struct Line {
ll a, b;
Line(ll a = 0, ll b = inf) : a(a), b(b) {}
ll operator()(ll x) { return a * x + b; }
} seg[1 << 21];
void upd(int u, int l, int r, Line line) {
if (l == r) {
if (seg[u](l) > line(l)) seg[u] = line;
return;
}
int m = (l + r) >> 1;
if (seg[u].a < line.a) swap(seg[u], line);
if (seg[u](m) > line(m)) {
swap(seg[u], line);
upd(u << 1, l, m, line);
}
else upd(u << 1 | 1, m + 1, r, line);
}
ll qry(int u, int l, int r, int x) {
if (l == r) return seg[u](x);
int m = (l + r) >> 1;
if (x <= m)
return min(seg[u](x), qry(u << 1, l, m, x));
else return min(seg[u](x), qry(u << 1 | 1, m + 1, r, x));
}
ll dp[N];
int main() {
cin.tie(NULL)->sync_with_stdio(false);
cin >> n;
for (int i = 1; i <= n; ++i) cin >> h[i];
for (int i = 1; i <= n; ++i) cin >> w[i], prf[i] = prf[i - 1] + w[i];
upd(1, 0, H, Line(-2 * h[1], h[1] * h[1] - prf[1]));
for (int i = 2; i < n; ++i) {
// dp[i][i] = dp[i - 1][k] + (h[i] - h[k])^2 + (prf[i - 1] - prf[k])
// = dp[i - 1][k] + h[k]^2 + h[i]^2 - 2 * h[i] * h[k] + prf[i - 1] - prf[k]
// = (dp[i - 1][k] + h[k]^2 - prf[k]) -2 * h[i] * h[k] + (h[i]^2 + prf[i - 1])
dp[i] = qry(1, 0, H, h[i]) + h[i] * h[i] + prf[i - 1];
upd(1, 0, H, Line(-2 * h[i], dp[i] + h[i] * h[i] - prf[i]));
}
cout << qry(1, 0, H, h[n]) + h[n] * h[n] + prf[n - 1] << '\n';
}
/** /\_/\
* (= ._.)
* / >0 \>1
**/
/*
==================================================+
INPUT: |
--------------------------------------------------|
6
3 8 7 1 6 6
0 -1 9 1 2 0
--------------------------------------------------|
==================================================+
OUTPUT: |
--------------------------------------------------|
17
--------------------------------------------------|
==================================================+
*/
