#include <bits/stdc++.h>
using namespace std;
const int maxn = 2e5 + 10;
long long c1[maxn], c2[maxn];
void add(long long *c, int x, int y) {
  for (; x < maxn; x += x & -x) c[x] += y;
}
long long ask(long long *c, int x) {
  long long ret = 0;
  for (; x > 0; x -= x & -x) ret += c[x];
  return ret;
}
struct node {
  int x, v;
} p[maxn];
int b[maxn];
bool cmp(node a, node b) {
  if (a.x == b.x) return a.v < b.v;
  return a.x < b.x;
}
int main() {
  int n;
  cin >> n;
  int m = 0;
  for (int i = 0; i < n; i++) scanf("%d", &p[i].x);
  for (int i = 0; i < n; i++) {
    scanf("%d", &p[i].v);
    b[m++] = p[i].v;
  }
  sort(b, b + m);
  m = unique(b, b + m) - b;
  for (int i = 0; i < n; i++) {
    p[i].v = lower_bound(b, b + m, p[i].v) - b + 1;
  }
  sort(p, p + n, cmp);
  long long Ans = 0;
  for (int i = 0; i < n; i++) {
    long long cnt = ask(c1, p[i].v), sum = ask(c2, p[i].v);
    Ans += cnt * p[i].x - sum;
    add(c1, p[i].v, 1);
    add(c2, p[i].v, p[i].x);
  }
  cout << Ans << endl;
}

### Prompt

Please provide a CPP coded solution 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 int maxn = 2e5 + 10;
long long c1[maxn], c2[maxn];
void add(long long *c, int x, int y) {
  for (; x < maxn; x += x & -x) c[x] += y;
}
long long ask(long long *c, int x) {
  long long ret = 0;
  for (; x > 0; x -= x & -x) ret += c[x];
  return ret;
}
struct node {
  int x, v;
} p[maxn];
int b[maxn];
bool cmp(node a, node b) {
  if (a.x == b.x) return a.v < b.v;
  return a.x < b.x;
}
int main() {
  int n;
  cin >> n;
  int m = 0;
  for (int i = 0; i < n; i++) scanf("%d", &p[i].x);
  for (int i = 0; i < n; i++) {
    scanf("%d", &p[i].v);
    b[m++] = p[i].v;
  }
  sort(b, b + m);
  m = unique(b, b + m) - b;
  for (int i = 0; i < n; i++) {
    p[i].v = lower_bound(b, b + m, p[i].v) - b + 1;
  }
  sort(p, p + n, cmp);
  long long Ans = 0;
  for (int i = 0; i < n; i++) {
    long long cnt = ask(c1, p[i].v), sum = ask(c2, p[i].v);
    Ans += cnt * p[i].x - sum;
    add(c1, p[i].v, 1);
    add(c2, p[i].v, p[i].x);
  }
  cout << Ans << endl;
}

```