#include <bits/stdc++.h>
using namespace std;
typedef long long LL;
const int MAXN = 100000;
LL h[MAXN + 10], prew[MAXN + 10];
LL dp[MAXN + 10];
void mineq(LL &dst, LL val)
{
dst = min(dst, val);
}
struct Point
{
LL x, y;
int ndx;
Point(LL x1 = 0, LL y1 = 0, int n1 = 0)
: x(x1)
, y(y1)
, ndx(n1)
{
}
bool operator<(const Point &p) const
{
if(x == p.x) return y < p.y;
return x < p.x;
}
} point[MAXN + 10], tmp[MAXN + 10];
class Deque
{
Point q[MAXN + 10];
int front, rear;
public:
void clear()
{
front = rear = 0;
}
int size()
{
return rear - front;
}
Point& back()
{
return q[rear - 1];
}
void popfront()
{
front++;
}
void popback()
{
rear--;
}
void pushback(Point p)
{
q[rear++] = p;
}
void pushback(LL x = 0, LL y = 0, int ndx = 0)
{
q[rear++] = Point(x, y, ndx);
}
Point& operator[](int ndx)
{
return q[ndx + front];
}
Point& bsslope(int k)
{
int l = front, r = rear - 1, m;
while(l < r)
{
m = (l + r) / 2;
if(q[m + 1].y - q[m].y <= k * (q[m + 1].x - q[m].x)) l = m + 1;
else r = m;
}
return q[l];
}
} dq;
void cdq(int l, int r)
{
if(l == r)
{
int ni = point[l].ndx;
point[l].y = dp[l] - prew[ni] + h[ni] * h[ni];
return;
}
int m = (l + r) / 2;
int lb = l, rb = m + 1;
int i;
for(i = l; i <= r; i++)
{
if(point[i].ndx <= m) tmp[lb++] = point[i];
else tmp[rb++] = point[i];
}
memcpy(point + l, tmp + l, sizeof(Point) * (r - l + 1));
cdq(l, m);
dq.clear();
//dq.pushback();
for(i = l; i <= m; i++)
{
if(i > l && dq.back().x == point[i].x) continue;
while(dq.size() > 1 && (dq.back().y - dq[dq.size() - 2].y) * (point[i].x - dq.back().x) >= (point[i].y - dq.back().y) * (dq.back().x - dq[dq.size() - 2].x)) dq.popback();
dq.pushback(point[i]);
}
for(i = m + 1; i <= r; i++)
{
LL k = h[point[i].ndx] * 2;
while(dq.size() > 1 && dq[1].y - dq[0].y <= k * (dq[1].x - dq[0].x)) dq.popfront();
int ni = point[i].ndx, nj = dq[0].ndx;
mineq(dp[ni], dp[nj] + prew[ni - 1] - prew[nj] + (h[ni] - h[nj]) * (h[ni] - h[nj]));
}
cdq(m + 1, r);
sort(point + l, point + r + 1);
}
int main()
{
int n;
int i, w;
scanf("%d", &n);
for(i = 1; i <= n; i++)
{
scanf("%lld", h + i);
point[i].x = h[i];
point[i].ndx = i;
dp[i] = 1e18;
}
for(i = 1; i <= n; i++)
{
scanf("%d", &w);
prew[i] = prew[i - 1] + w;
}
dp[1] = 0;
sort(point + 1, point + n + 1);
cdq(1, n);
printf("%lld\n", dp[n]);
return 0;
}
