#include <bits/stdc++.h>
using namespace std;
const int maxn = 2e5 + 5;
long long positions[maxn], speeds[maxn];
pair<long long, long long> pairs[maxn];
map<long long, long long> m;
bool comp(pair<long long, long long>& a, pair<long long, long long>& b) {
  if (a.second == b.second) return a.first < b.first;
  return a.second < b.second;
}
int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  int n;
  cin >> n;
  for (int i = 0; i < n; ++i) cin >> positions[i];
  for (int i = 0; i < n; ++i) cin >> speeds[i];
  for (long long i = 0; i < n; ++i) pairs[i] = {positions[i], speeds[i]};
  sort(positions, positions + n);
  sort(pairs, pairs + n, comp);
  long long ans = 0;
  for (long long i = 0; i < n; ++i) {
    ans += ((2 * i) - n + 1) * positions[i];
    m[positions[i]] = i;
  }
  for (int i = 0; i < n; ++i) ans -= pairs[i].first * (m[pairs[i].first] - i);
  cout << ans;
}

### Prompt

Generate 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;
const int maxn = 2e5 + 5;
long long positions[maxn], speeds[maxn];
pair<long long, long long> pairs[maxn];
map<long long, long long> m;
bool comp(pair<long long, long long>& a, pair<long long, long long>& b) {
  if (a.second == b.second) return a.first < b.first;
  return a.second < b.second;
}
int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  int n;
  cin >> n;
  for (int i = 0; i < n; ++i) cin >> positions[i];
  for (int i = 0; i < n; ++i) cin >> speeds[i];
  for (long long i = 0; i < n; ++i) pairs[i] = {positions[i], speeds[i]};
  sort(positions, positions + n);
  sort(pairs, pairs + n, comp);
  long long ans = 0;
  for (long long i = 0; i < n; ++i) {
    ans += ((2 * i) - n + 1) * positions[i];
    m[positions[i]] = i;
  }
  for (int i = 0; i < n; ++i) ans -= pairs[i].first * (m[pairs[i].first] - i);
  cout << ans;
}

```