#include <bits/stdc++.h>
using namespace std;
bool comp(pair<long long, long long> p1, pair<long long, long long> p2) {
  if (p1.second == p2.second) return p1.first < p2.first;
  return p1.second < p2.second;
}
signed main() {
  long long n;
  cin >> n;
  vector<pair<long long, long long> > v(n);
  for (long long i = 0; i < n; i++) {
    cin >> v[i].first;
  }
  for (long long i = 0; i < n; i++) {
    cin >> v[i].second;
  }
  sort(v.begin(), v.end());
  map<long long, long long> mp;
  long long ans = 0;
  for (long long i = 0; i < n; i++) {
    ans += (2 * i - n + 1) * v[i].first;
    mp[v[i].first] = i;
  }
  sort(v.begin(), v.end(), comp);
  for (long long i = 0; i < n; i++) {
    ans += (i - mp[v[i].first]) * v[i].first;
  }
  cout << ans << endl;
}

### Prompt

Your challenge is to write 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;
bool comp(pair<long long, long long> p1, pair<long long, long long> p2) {
  if (p1.second == p2.second) return p1.first < p2.first;
  return p1.second < p2.second;
}
signed main() {
  long long n;
  cin >> n;
  vector<pair<long long, long long> > v(n);
  for (long long i = 0; i < n; i++) {
    cin >> v[i].first;
  }
  for (long long i = 0; i < n; i++) {
    cin >> v[i].second;
  }
  sort(v.begin(), v.end());
  map<long long, long long> mp;
  long long ans = 0;
  for (long long i = 0; i < n; i++) {
    ans += (2 * i - n + 1) * v[i].first;
    mp[v[i].first] = i;
  }
  sort(v.begin(), v.end(), comp);
  for (long long i = 0; i < n; i++) {
    ans += (i - mp[v[i].first]) * v[i].first;
  }
  cout << ans << endl;
}

```