#include <set>
#include <algorithm>
#include <iostream>
#include <climits>
using namespace std;
using ll = long long;
const int MAXN = 1e5 + 5;
const ll INF = 1e18 + 5;
ll n, h[MAXN], w[MAXN];
ll dp[MAXN];
ll sp[MAXN];
void Read()
{
cin >> n;
for (int i = 1; i <= n; ++i)
cin >> h[i];
for (int i = 1; i <= n; ++i)
{
cin >> w[i];
sp[i] = sp[i - 1] + w[i];
}
}
struct Line {
ll m, k; // m*x + k
mutable ll x;
bool operator < (const Line &other) const { return m > other.m; } // aici < pt maxim
bool operator < (int x) const { return this->x < x; }
ll operator()(ll x) const {return m * x + k;}
};
struct CHT : multiset<Line, less<>> {
static const ll INF = LLONG_MAX;
ll div(ll a, ll b)
{
return a / b - ((a ^ b) < 0 && a % b);
}
bool isect(iterator a, iterator b)
{
if (b == end()) {a->x = INF; return false;}
if (a->m == b->m)
a->x = (a->k < b->k ? INF : -INF); // aici invers pt maxim
else
a->x = div(b->k - a->k, a->m - b->m);
return a->x >= b->x;
}
void add(ll m, ll k)
{
auto c = insert({m, k, 0}), b = c++, a = b;
while (isect(b, c))
c = erase(c);
if (a != begin() && isect(--a, b))
isect(a, b = erase(b));
while ((b = a) != begin() && (--a)->x >= b->x)
isect(a, erase(b));
}
ll query(ll x)
{
Line line = *lower_bound(x);
return line(x);
}
};
void Solve()
{
CHT hull;
fill(dp + 1, dp + n + 1, INF);
dp[1] = 0;
for (int i = 1; i <= n; ++i)
{
if (i > 1)
dp[i] = hull.query(h[i]) + h[i] * h[i] + sp[i - 1];
hull.add(-2 * h[i], dp[i] + h[i] * h[i] - sp[i]);
}
cout << dp[n];
}
int main()
{
ios_base::sync_with_stdio(false);
cin.tie(0); cout.tie(0);
Read();
Solve();
return 0;
}
