#include <bits/stdc++.h>
using namespace std;
const int kMaxN = 200001;
struct E {
  int x, v, w;
  bool operator<(const E &e) const { return x < e.x; }
} e[kMaxN];
struct T {
  long long c, v;
} t[kMaxN];
int a[kMaxN];
int n;
long long ans;
int LowBit(int x) { return x & (-x); }
void Calc(int x) {
  t[0] = {0, 0};
  while (x) {
    t[0].c += t[x].c;
    t[0].v += t[x].v;
    x -= LowBit(x);
  }
}
void Add(int x, int v) {
  while (x <= n) {
    t[x].c++;
    t[x].v += v;
    x += LowBit(x);
  }
}
void Dis() {
  sort(a + 1, a + 1 + n, [](int i, int j) { return e[i].v < e[j].v; });
  e[0].v = 1 << 31;
  for (int i = 1, j = 0; i <= n; i++) {
    j += e[a[i]].v != e[a[i - 1]].v;
    e[a[i]].w = j;
  }
}
int main() {
  cin >> n;
  for (int i = 1; i <= n; i++) {
    cin >> e[i].x;
  }
  for (int i = 1; i <= n; i++) {
    cin >> e[i].v;
    a[i] = i;
  }
  Dis();
  sort(e + 1, e + 1 + n);
  for (int i = 1; i <= n; i++) {
    Calc(e[i].w);
    ans += e[i].x * t[0].c - t[0].v;
    Add(e[i].w, e[i].x);
  }
  cout << ans << endl;
  return 0;
}

### Prompt

Please create a solution in cpp 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 kMaxN = 200001;
struct E {
  int x, v, w;
  bool operator<(const E &e) const { return x < e.x; }
} e[kMaxN];
struct T {
  long long c, v;
} t[kMaxN];
int a[kMaxN];
int n;
long long ans;
int LowBit(int x) { return x & (-x); }
void Calc(int x) {
  t[0] = {0, 0};
  while (x) {
    t[0].c += t[x].c;
    t[0].v += t[x].v;
    x -= LowBit(x);
  }
}
void Add(int x, int v) {
  while (x <= n) {
    t[x].c++;
    t[x].v += v;
    x += LowBit(x);
  }
}
void Dis() {
  sort(a + 1, a + 1 + n, [](int i, int j) { return e[i].v < e[j].v; });
  e[0].v = 1 << 31;
  for (int i = 1, j = 0; i <= n; i++) {
    j += e[a[i]].v != e[a[i - 1]].v;
    e[a[i]].w = j;
  }
}
int main() {
  cin >> n;
  for (int i = 1; i <= n; i++) {
    cin >> e[i].x;
  }
  for (int i = 1; i <= n; i++) {
    cin >> e[i].v;
    a[i] = i;
  }
  Dis();
  sort(e + 1, e + 1 + n);
  for (int i = 1; i <= n; i++) {
    Calc(e[i].w);
    ans += e[i].x * t[0].c - t[0].v;
    Add(e[i].w, e[i].x);
  }
  cout << ans << endl;
  return 0;
}

```