#include <bits/stdc++.h>
#define int int64_t
using namespace std;
const int maxn = 1e5 + 10;
int h[maxn], pref[maxn], w[maxn];
int n, dp[maxn];
struct frac {
int a, b;
bool operator<(frac const& c) const {
return a*c.b < c.a*b;
}
};
bool flag = 0;
struct line {
int a, b;
frac x;
bool operator<(line const& l) const {
if(flag == 0) return a > l.a;
else return x < l.x;
}
};
typedef set<line>::iterator sit;
set<line> lines;
bool hasPrev(sit it)
{
return (it != lines.begin());
}
bool hasNext(sit it)
{
return (next(it) != lines.end() && ++it != lines.end());
}
template<typename Arg>
bool bad(Arg&& l1, Arg&& l2, Arg&& l3) {
return (l2.a - l1.a)*(l3.b - l1.b) >= (l3.a - l1.a)*(l2.b - l1.b);
}
frac intersect(line const& l1, line const& l2) {
return {l2.b-l1.b, l1.a-l2.a};
}
void get_x(sit it) {
if (hasPrev(it))
{
line l = *it;
l.x = intersect(*prev(it), *it);
lines.erase(it); lines.insert(l);
}
}
void add(line const& l) {
auto it = lines.lower_bound(l);
if(it != lines.end() && it->a == l.a){
if(it->b <= l.b) return;
lines.erase(it);
}
lines.insert(l);
it = lines.find(l);
if (hasPrev(it) && hasNext(it) && bad(*prev(it), *it, *next(it))) {
lines.erase(it);
return;
}
while(hasNext(it) && hasNext(next(it)) && bad(*it, *next(it), *next(next(it))))
lines.erase(next(it));
while(hasPrev(it) && hasPrev(prev(it)) && bad(*prev(prev(it)), *prev(it), *it))
lines.erase(prev(it));
if (hasNext(it)) get_x(next(it));
get_x(it);
}
inline int f(line const& l, int x) {
return l.a*x + l.b;
}
int query(int x) {
flag = true;
auto it = lines.upper_bound({0, 0, {x, 1}});
flag = false;
it--;
return f(*it, x);
}
int32_t main() {
cin >> n;
for(int i=1;i<=n;i++)
cin >> h[i];
for(int i=1;i<=n;i++)
cin >> w[i], pref[i] = pref[i-1] + w[i];
dp[1] = 0;
add({-2*h[1], h[1]*h[1] + dp[1] - pref[1]});
for(int i=2;i<=n;i++) {
// dp[i] = 0x3f3f3f3f3f3f3f3f;
// for(int j=1;j<i;j++) {
// dp[i] = min(dp[i], dp[j] - pref[j] + h[j]*h[j] - 2*h[j] * h[i]);
// }
dp[i] = query(h[i]);
dp[i] += h[i]*h[i] + pref[i-1];
add({-2*h[i], h[i]*h[i] + dp[i] - pref[i]});
}
cout << dp[n] << "\n";
return 0;
}
