#include <bits/stdc++.h>
using namespace std;
const int64_t INF = (int64_t)(2e18);
const int64_t inf = (int64_t)(1e9 + 7);
struct stree {
  vector<int64_t> t;
  int64_t n = 1;
  stree() {}
  stree(int64_t nn) {
    while (n < nn) n *= 2;
    t.assign(2 * n, 0);
  }
  void set(int64_t i, int64_t x) {
    t[i += n] += x;
    for (i /= 2; i; i /= 2) t[i] = t[i + i] + t[i + i + 1];
  }
  int64_t get(int64_t l, int64_t r) {
    int64_t res = 0;
    for (l += n, r += n; l <= r; l /= 2, r /= 2) {
      if (l & 1) res += t[l++];
      if (~r & 1) res += t[r--];
    }
    return res;
  }
};
int32_t main() {
  ios_base::sync_with_stdio(false);
  cout << fixed << setprecision(10);
  cin.tie(nullptr);
  int64_t n;
  cin >> n;
  vector<int64_t> x(n);
  for (auto& it : x) cin >> it;
  vector<int64_t> v(n);
  for (auto& it : v) cin >> it;
  vector<int64_t> vs;
  for (auto& it : v) vs.push_back(it);
  sort((vs).begin(), (vs).end());
  vs.resize(unique((vs).begin(), (vs).end()) - begin(vs));
  for (auto& it : v) it = lower_bound((vs).begin(), (vs).end(), it) - begin(vs);
  vector<pair<int64_t, int64_t>> pts(n);
  for (int64_t i = 0; i < n; ++i) {
    pts[i].first = x[i];
    pts[i].second = v[i];
  }
  sort((pts).begin(), (pts).end());
  stree ls(vs.size());
  stree lc(vs.size());
  stree rs(vs.size());
  stree rc(vs.size());
  for (auto& p : pts) {
    rs.set(p.second, p.first);
    rc.set(p.second, 1);
  }
  int64_t res = 0;
  for (auto& p : pts) {
    rs.set(p.second, -p.first);
    rc.set(p.second, -1);
    res += lc.get(0, p.second) * p.first;
    res -= ls.get(0, p.second);
    res -= rc.get(p.second, vs.size() - 1) * p.first;
    res += rs.get(p.second, vs.size() - 1);
    ls.set(p.second, p.first);
    lc.set(p.second, 1);
  }
  cout << res / 2;
  return 0;
}

### Prompt

Develop a solution in Cpp to the problem described below:

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 int64_t INF = (int64_t)(2e18);
const int64_t inf = (int64_t)(1e9 + 7);
struct stree {
  vector<int64_t> t;
  int64_t n = 1;
  stree() {}
  stree(int64_t nn) {
    while (n < nn) n *= 2;
    t.assign(2 * n, 0);
  }
  void set(int64_t i, int64_t x) {
    t[i += n] += x;
    for (i /= 2; i; i /= 2) t[i] = t[i + i] + t[i + i + 1];
  }
  int64_t get(int64_t l, int64_t r) {
    int64_t res = 0;
    for (l += n, r += n; l <= r; l /= 2, r /= 2) {
      if (l & 1) res += t[l++];
      if (~r & 1) res += t[r--];
    }
    return res;
  }
};
int32_t main() {
  ios_base::sync_with_stdio(false);
  cout << fixed << setprecision(10);
  cin.tie(nullptr);
  int64_t n;
  cin >> n;
  vector<int64_t> x(n);
  for (auto& it : x) cin >> it;
  vector<int64_t> v(n);
  for (auto& it : v) cin >> it;
  vector<int64_t> vs;
  for (auto& it : v) vs.push_back(it);
  sort((vs).begin(), (vs).end());
  vs.resize(unique((vs).begin(), (vs).end()) - begin(vs));
  for (auto& it : v) it = lower_bound((vs).begin(), (vs).end(), it) - begin(vs);
  vector<pair<int64_t, int64_t>> pts(n);
  for (int64_t i = 0; i < n; ++i) {
    pts[i].first = x[i];
    pts[i].second = v[i];
  }
  sort((pts).begin(), (pts).end());
  stree ls(vs.size());
  stree lc(vs.size());
  stree rs(vs.size());
  stree rc(vs.size());
  for (auto& p : pts) {
    rs.set(p.second, p.first);
    rc.set(p.second, 1);
  }
  int64_t res = 0;
  for (auto& p : pts) {
    rs.set(p.second, -p.first);
    rc.set(p.second, -1);
    res += lc.get(0, p.second) * p.first;
    res -= ls.get(0, p.second);
    res -= rc.get(p.second, vs.size() - 1) * p.first;
    res += rs.get(p.second, vs.size() - 1);
    ls.set(p.second, p.first);
    lc.set(p.second, 1);
  }
  cout << res / 2;
  return 0;
}

```