#include <bits/stdc++.h>
using namespace std;
pair<long long int, long long int> final[200001];
void up(long long int i, long long int x, long long int j) {
  while (i < 200001) {
    j == 0 ? final[i].first += x : final[i].second += x;
    i += (i & (-i));
  }
}
long long int q(long long int i, long long int j) {
  long long int ans = 0;
  while (i) {
    ans += (j == 0 ? final[i].first : final[i].second);
    i -= (i & (-i));
  }
  return ans;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  long long int n;
  cin >> n;
  long long int a[n];
  pair<long long int, long long int> b[n];
  for (long long int i = 0; i < n; i++) {
    cin >> a[i];
  }
  for (long long int i = 0; i < n; i++) {
    cin >> b[i].first;
    b[i].second = a[i];
  }
  sort(b, b + n);
  map<long long int, long long int> mapper;
  sort(a, a + n);
  for (long long int i = 0; i < n; i++) {
    mapper[a[i]] = i + 1;
  }
  long long int ans = 0;
  for (auto e : b) {
    long long int sp = e.first, pos = e.second;
    long long int ind = mapper[pos];
    long long int sum = q(ind - 1, 1);
    long long int points = q(ind - 1, 0);
    ans += pos * points - sum;
    up(ind, 1, 0);
    up(ind, pos, 1);
  }
  cout << ans;
}

### 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;
pair<long long int, long long int> final[200001];
void up(long long int i, long long int x, long long int j) {
  while (i < 200001) {
    j == 0 ? final[i].first += x : final[i].second += x;
    i += (i & (-i));
  }
}
long long int q(long long int i, long long int j) {
  long long int ans = 0;
  while (i) {
    ans += (j == 0 ? final[i].first : final[i].second);
    i -= (i & (-i));
  }
  return ans;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  long long int n;
  cin >> n;
  long long int a[n];
  pair<long long int, long long int> b[n];
  for (long long int i = 0; i < n; i++) {
    cin >> a[i];
  }
  for (long long int i = 0; i < n; i++) {
    cin >> b[i].first;
    b[i].second = a[i];
  }
  sort(b, b + n);
  map<long long int, long long int> mapper;
  sort(a, a + n);
  for (long long int i = 0; i < n; i++) {
    mapper[a[i]] = i + 1;
  }
  long long int ans = 0;
  for (auto e : b) {
    long long int sp = e.first, pos = e.second;
    long long int ind = mapper[pos];
    long long int sum = q(ind - 1, 1);
    long long int points = q(ind - 1, 0);
    ans += pos * points - sum;
    up(ind, 1, 0);
    up(ind, pos, 1);
  }
  cout << ans;
}

```