//fully dynamic convex hull trick/ linecontainer practice uwu :3
#include<bits/stdc++.h>
#define ll long long
#define task ""
using namespace std;
const int maxn = 1e5 + 4;
ll n, h[maxn], w[maxn], tw, dp[maxn];
struct Line
{
bool type;
long double i;
ll x, y;
};
bool operator < (const Line& A, const Line& B)
{
if (A.type || B.type) return A.i < B.i; //for binary search
return A.x > B.x; //for the convex hull, change to < if asking for max
}
set<Line> hull;
bool has_prev (set<Line>::iterator it)
{
return it != hull.begin();
}
bool has_next (set<Line>::iterator it)
{
return it != hull.end() && next(it) != hull.end();
}
long double isect (set<Line>::iterator A, set<Line>::iterator B)
{
return (long double)1.0 * (A->y - B->y)/(B->x - A->x);
}
bool check (set<Line>::iterator it)
{
//if (has_next(it) && next(it)->y <= it->y) return false; //it > next(it) for all x
return !(has_prev(it) && has_next(it) && isect(prev(it), next(it)) <= isect(prev(it), it)); //normal convex hull also have this
}
void change_isect (set<Line>::iterator it)
{
if (has_prev(it))
{
Line l = *it;
l.i = isect(prev(it), it);
hull.insert(hull.erase(it), l);
}
}
void add_line (ll x, ll y)
{
set<Line>::iterator it;
//parallel case
it = hull.lower_bound({0, 0, x, y});
if (it != hull.end() && it->x == x)
{
if (it->y <= y) return; //change to >= if asking for max
hull.erase(it);
}
it = hull.insert({0, 0, x, y}).first;
if (check(it))
{
while (has_prev(it) && !check(prev(it))) hull.erase(prev(it));
while (has_next(it) && !check(next(it))) hull.erase(next(it));
if (has_next(it)) change_isect(next(it));
change_isect(it);
}
else hull.erase(it);
}
ll solve (ll q)
{
Line l = *prev(hull.upper_bound({1, (long double)q, 0, 0}));
return l.x*q + l.y;
}
int main ()
{
//freopen(task".INP", "r", stdin);
//freopen(task".OUT", "w", stdout);
ios_base::sync_with_stdio(0);
cin.tie(0);
cin >> n;
for (int i = 1; i <= n; i++) cin >> h[i];
for (int i = 1; i <= n; i++)
{
cin >> w[i];
tw += w[i];
}
dp[1] = -w[1];
for (int i = 2; i <= n; i++)
{
add_line(-2*h[i - 1], dp[i - 1] + h[i - 1]*h[i - 1]);
dp[i] = h[i]*h[i] - w[i] + solve(h[i]);
}
cout << tw + dp[n];
}
