#include <bits/stdc++.h>
using namespace std;
long long BIT[200009][4], N = 200009, n, ans, I;
struct st {
  long long x, v;
} a[200009];
bool cmp(st a, st b) {
  if (a.v == b.v) return a.x > b.x;
  return a.v > b.v;
}
bool cmp2(st a, st b) {
  if (a.v == b.v) return a.x > b.x;
  return a.v > b.v;
}
set<long long> s;
map<long long, long long> mp;
void update(long long x, long long val, long long zz) {
  for (; x < N; x += x & -x) BIT[x][zz] += val;
}
long long query(long long x, long long zz) {
  long long sum = 0;
  for (; x > 0; x -= x & -x) sum += BIT[x][zz];
  return sum;
}
long long q(long long l, long long r, long long zz) {
  return query(r, zz) - query(l - 1, zz);
}
int main() {
  cin >> n;
  for (int i = 0; i < n; i++) {
    cin >> a[i].x;
    s.insert(a[i].x);
  }
  for (int i = 0; i < n; i++) {
    cin >> a[i].v;
  }
  for (auto x : s) mp[x] = ++I;
  sort(a, a + n, cmp);
  for (int i = 0; i < n; i++) {
    ans += q(mp[a[i].x] + 1, I, 1) - a[i].x * q(mp[a[i].x] + 1, I, 2);
    update(mp[a[i].x], a[i].x, 1);
    update(mp[a[i].x], 1, 2);
  }
  cout << ans << endl;
}

### Prompt

Your task is to create a cpp solution to the following problem:

There are n points on a coordinate axis OX. The i-th point is located at the integer point x_i and has a speed v_i. It is guaranteed that no two points occupy the same coordinate. All n points move with the constant speed, the coordinate of the i-th point at the moment t (t can be non-integer) is calculated as x_i + t ⋅ v_i.

Consider two points i and j. Let d(i, j) be the minimum possible distance between these two points over any possible moments of time (even non-integer). It means that if two points i and j coincide at some moment, the value d(i, j) will be 0.

Your task is to calculate the value ∑_{1 ≤ i < j ≤ n} d(i, j) (the sum of minimum distances over all pairs of points).

Input

The first line of the input contains one integer n (2 ≤ n ≤ 2 ⋅ 10^5) — the number of points.

The second line of the input contains n integers x_1, x_2, ..., x_n (1 ≤ x_i ≤ 10^8), where x_i is the initial coordinate of the i-th point. It is guaranteed that all x_i are distinct.

The third line of the input contains n integers v_1, v_2, ..., v_n (-10^8 ≤ v_i ≤ 10^8), where v_i is the speed of the i-th point.

Output

Print one integer — the value ∑_{1 ≤ i < j ≤ n} d(i, j) (the sum of minimum distances over all pairs of points).

Examples

Input


3
1 3 2
-100 2 3


Output


3


Input


5
2 1 4 3 5
2 2 2 3 4


Output


19


Input


2
2 1
-3 0


Output


0

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
long long BIT[200009][4], N = 200009, n, ans, I;
struct st {
  long long x, v;
} a[200009];
bool cmp(st a, st b) {
  if (a.v == b.v) return a.x > b.x;
  return a.v > b.v;
}
bool cmp2(st a, st b) {
  if (a.v == b.v) return a.x > b.x;
  return a.v > b.v;
}
set<long long> s;
map<long long, long long> mp;
void update(long long x, long long val, long long zz) {
  for (; x < N; x += x & -x) BIT[x][zz] += val;
}
long long query(long long x, long long zz) {
  long long sum = 0;
  for (; x > 0; x -= x & -x) sum += BIT[x][zz];
  return sum;
}
long long q(long long l, long long r, long long zz) {
  return query(r, zz) - query(l - 1, zz);
}
int main() {
  cin >> n;
  for (int i = 0; i < n; i++) {
    cin >> a[i].x;
    s.insert(a[i].x);
  }
  for (int i = 0; i < n; i++) {
    cin >> a[i].v;
  }
  for (auto x : s) mp[x] = ++I;
  sort(a, a + n, cmp);
  for (int i = 0; i < n; i++) {
    ans += q(mp[a[i].x] + 1, I, 1) - a[i].x * q(mp[a[i].x] + 1, I, 2);
    update(mp[a[i].x], a[i].x, 1);
    update(mp[a[i].x], 1, 2);
  }
  cout << ans << endl;
}

```