#include <bits/stdc++.h>
#define FOR(i, x, y) for (int i = x; i < y; i++)
typedef long long ll;
using namespace std;
struct Line {
bool type;
double x;
ll m, c;
};
bool operator<(Line l1, Line l2) {
if (l1.type || l2.type) return l1.x < l2.x;
return l1.m > l2.m;
}
set<Line> cht;
ll h[100001], w[100001], tot = 0;
ll dp[100001];
bool hasPrev(set<Line>::iterator it) { return it != cht.begin(); }
bool hasNext(set<Line>::iterator it) {
return it != cht.end() && next(it) != cht.end();
}
double intersect(set<Line>::iterator l1, set<Line>::iterator l2) {
return (double)(l1->c - l2->c) / (l2->m - l1->m);
}
void calcX(set<Line>::iterator it) {
if (hasPrev(it)) {
Line l = *it;
l.x = intersect(prev(it), it);
cht.insert(cht.erase(it), l);
}
}
bool bad(set<Line>::iterator it) {
if (hasNext(it) && next(it)->c <= it->c) return true;
return (hasPrev(it) && hasNext(it) &&
intersect(prev(it), next(it)) <= intersect(prev(it), it));
}
void add_line(ll m, ll c) {
set<Line>::iterator it;
it = cht.lower_bound({0, 0, m, c});
if (it != cht.end() && it->m == m) {
if (it->c <= c) return;
else cht.erase(it);
}
it = cht.insert({0, 0, m, c}).first;
if (bad(it)) cht.erase(it);
else {
while (hasPrev(it) && bad(prev(it))) cht.erase(prev(it));
while (hasNext(it) && bad(next(it))) cht.erase(next(it));
if (hasNext(it)) calcX(next(it));
calcX(it);
}
}
ll query(ll h) {
Line l = *prev(cht.upper_bound({1, (double)h, 0, 0}));
return l.m * h + l.c;
}
int main() {
ios_base::sync_with_stdio(0);
cin.tie(0);
int n;
cin >> n;
FOR(i, 1, n + 1) cin >> h[i];
FOR(i, 1, n + 1) {
cin >> w[i];
tot += w[i];
}
dp[1] = -w[1];
FOR(i, 2, n + 1) {
add_line(-2 * h[i - 1], dp[i - 1] + h[i - 1] * h[i - 1]);
dp[i] = query(h[i]) - w[i] + h[i] * h[i];
}
cout << tot + dp[n];
return 0;
}
