#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
const int N = (int)1e5 + 10;
int h[N];
ll s[N], f[N];
struct line_t {
ll k, m;
ll operator() (ll x) {
return k * x + m;
}
bool operator< (const line_t& rhs) const {
if(k != rhs.k) return k > rhs.k;
return m < rhs.m;
}
bool operator== (const line_t& rhs) const {
return k == rhs.k;
}
};
struct cht {
deque<line_t> dq;
ll div(ll a, ll b) { // floored division
return a / b - ((a ^ b) < 0 && a % b); }
bool check(const line_t& a, const line_t& b, const line_t& c) {
return div(b.m - a.m, a.k - b.k) >= div(c.m - b.m, b.k - c.k);
}
void add(const line_t& l) {
while((int)dq.size() > 1 && check(dq[(int)dq.size() - 2], dq.back(), l))
dq.pop_back();
dq.push_back(l);
}
ll query(int x) {
while((int)dq.size() > 1 && dq[0](x) >= dq[1](x))
dq.pop_front();
return dq.front()(x);
}
};
line_t lf[N];
int rt[N];
void dq(int l, int r) {
if(l == r)
return;
int m = (l + r) >> 1;
dq(l, m);
for(int i = l; i <= m; ++i)
lf[i] = { -2LL * h[i], f[i] + (ll)h[i] * h[i] - s[i] };
sort(lf + l, lf + m + 1);
int ptr = unique(lf + l, lf + m + 1) - lf;
cht c;
for(int i = l; i < ptr; ++i)
c.add(lf[i]);
for(int i = m + 1; i <= r; ++i)
rt[i] = i;
sort(rt + m + 1, rt + r + 1, [&](int i, int j) {
return h[i] < h[j];
});
for(int j = m + 1; j <= r; ++j) {
int i = rt[j];
f[i] = min(f[i], c.query(h[i]) + (ll)h[i] * h[i] + s[i - 1]);
}
dq(m + 1, r);
}
int main() {
ios::sync_with_stdio(false);
cin.tie(NULL);
int n;
cin >> n;
for(int i = 1; i <= n; ++i)
cin >> h[i];
for(int i = 1; i <= n; ++i) {
cin >> s[i];
s[i] += s[i - 1];
}
memset(f, 0x3f, sizeof(f));
f[1] = 0;
dq(1, n);
cout << f[n];
return 0;
}
