#include <bits/stdc++.h>
using namespace std;
using LL = long long;
struct Point {
  LL x, v;
  bool operator<(const Point &rhs) const {
    if (v == rhs.v)
      return x < rhs.x;
    else
      return v < rhs.v;
  }
};
Point p[200010];
LL n, x2[200010], idx[200010], c[200010], s[200010];
void update(LL *arr, LL pos, LL val) {
  for (LL i = pos; i <= n; i += i & (-i)) arr[i] += val;
}
LL query(LL *arr, LL pos) {
  LL res = 0;
  for (LL i = pos; i; i -= i & (-i)) res += arr[i];
  return res;
}
int main() {
  scanf("%lld", &n);
  for (LL i = 1; i <= n; i++) scanf("%lld", &p[i].x);
  for (LL i = 1; i <= n; i++) scanf("%lld", &p[i].v);
  for (LL i = 1; i <= n; i++) idx[i] = i;
  sort(p + 1, p + n + 1);
  sort(idx + 1, idx + n + 1, [](LL i, LL j) { return p[i].x < p[j].x; });
  for (LL i = 1; i <= n;) {
    LL j;
    for (j = i; j <= n; j++)
      if (p[idx[j]].x != p[idx[i]].x)
        break;
      else
        x2[idx[j]] = i;
    i = j;
  }
  LL ans = 0;
  for (LL i = 1; i <= n; i++) {
    ans += p[i].x * query(c, x2[i]) - query(s, x2[i]);
    update(c, x2[i], 1);
    update(s, x2[i], p[i].x);
  }
  printf("%lld\n", ans);
  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;
using LL = long long;
struct Point {
  LL x, v;
  bool operator<(const Point &rhs) const {
    if (v == rhs.v)
      return x < rhs.x;
    else
      return v < rhs.v;
  }
};
Point p[200010];
LL n, x2[200010], idx[200010], c[200010], s[200010];
void update(LL *arr, LL pos, LL val) {
  for (LL i = pos; i <= n; i += i & (-i)) arr[i] += val;
}
LL query(LL *arr, LL pos) {
  LL res = 0;
  for (LL i = pos; i; i -= i & (-i)) res += arr[i];
  return res;
}
int main() {
  scanf("%lld", &n);
  for (LL i = 1; i <= n; i++) scanf("%lld", &p[i].x);
  for (LL i = 1; i <= n; i++) scanf("%lld", &p[i].v);
  for (LL i = 1; i <= n; i++) idx[i] = i;
  sort(p + 1, p + n + 1);
  sort(idx + 1, idx + n + 1, [](LL i, LL j) { return p[i].x < p[j].x; });
  for (LL i = 1; i <= n;) {
    LL j;
    for (j = i; j <= n; j++)
      if (p[idx[j]].x != p[idx[i]].x)
        break;
      else
        x2[idx[j]] = i;
    i = j;
  }
  LL ans = 0;
  for (LL i = 1; i <= n; i++) {
    ans += p[i].x * query(c, x2[i]) - query(s, x2[i]);
    update(c, x2[i], 1);
    update(s, x2[i], p[i].x);
  }
  printf("%lld\n", ans);
  return 0;
}

```