#include <bits/stdc++.h>
using namespace std;
const long long maxn = 200000 + 50;
const long long LIM = 17;
const long long INF = (long long)1e9 + 7;
long long N;
long long h[maxn];
long long sum[maxn << 1], cnt[maxn << 1];
struct node {
  long long x, v;
} a[maxn];
bool cmp(const node& a, const node& b) { return a.x < b.x; }
inline long long lowerbit(long long x) { return x & -x; }
void updata(long long x, long long val, long long tree[]) {
  while (x <= N) {
    tree[x] += val;
    x += lowerbit(x);
  }
}
long long query(long long x, long long tree[]) {
  long long sum = 0;
  while (x > 0) {
    sum += tree[x];
    x -= lowerbit(x);
  }
  return sum;
}
int main() {
  scanf("%lld", &N);
  for (long long i = 1; i <= N; i++) {
    scanf("%lld", &a[i].x);
  }
  for (long long i = 1; i <= N; i++) {
    scanf("%lld", &a[i].v);
  }
  sort(a + 1, a + 1 + N, cmp);
  long long l = -1e8;
  for (long long i = 1; i <= N; i++) {
    h[i] = a[i].v;
  }
  sort(h + 1, h + 1 + N);
  long long d = unique(h + 1, h + 1 + N) - h - 1;
  long long ans = 0;
  for (long long i = 1; i <= N; i++) {
    long long x = lower_bound(h + 1, h + 1 + d, a[i].v) - h;
    ans += (query(x, cnt) * (a[i].x - l) - query(x, sum));
    updata(x, 1, cnt);
    updata(x, a[i].x - l, sum);
  }
  cout << ans << endl;
}

### Prompt

Your challenge is to write 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 long long maxn = 200000 + 50;
const long long LIM = 17;
const long long INF = (long long)1e9 + 7;
long long N;
long long h[maxn];
long long sum[maxn << 1], cnt[maxn << 1];
struct node {
  long long x, v;
} a[maxn];
bool cmp(const node& a, const node& b) { return a.x < b.x; }
inline long long lowerbit(long long x) { return x & -x; }
void updata(long long x, long long val, long long tree[]) {
  while (x <= N) {
    tree[x] += val;
    x += lowerbit(x);
  }
}
long long query(long long x, long long tree[]) {
  long long sum = 0;
  while (x > 0) {
    sum += tree[x];
    x -= lowerbit(x);
  }
  return sum;
}
int main() {
  scanf("%lld", &N);
  for (long long i = 1; i <= N; i++) {
    scanf("%lld", &a[i].x);
  }
  for (long long i = 1; i <= N; i++) {
    scanf("%lld", &a[i].v);
  }
  sort(a + 1, a + 1 + N, cmp);
  long long l = -1e8;
  for (long long i = 1; i <= N; i++) {
    h[i] = a[i].v;
  }
  sort(h + 1, h + 1 + N);
  long long d = unique(h + 1, h + 1 + N) - h - 1;
  long long ans = 0;
  for (long long i = 1; i <= N; i++) {
    long long x = lower_bound(h + 1, h + 1 + d, a[i].v) - h;
    ans += (query(x, cnt) * (a[i].x - l) - query(x, sum));
    updata(x, 1, cnt);
    updata(x, a[i].x - l, sum);
  }
  cout << ans << endl;
}

```