#include <bits/stdc++.h>
using namespace std;
const int maxn = 1000005;
int a[maxn], sa[maxn];
int n;
long long s[3][maxn];
void add(long long s[], int x, long long y) {
  for (int i = x; i <= n; i += -i & i) s[i] += y;
}
long long get(long long s[], int x) {
  long long res = 0;
  for (int i = n; i > 0; i &= i - 1) res += s[i];
  for (int i = x; i > 0; i &= i - 1) res -= s[i];
  return res;
}
int main() {
  scanf("%d", &n);
  for (int i = 0; i < (n); ++i) scanf("%d", a + i), sa[i] = a[i];
  sort(sa, sa + n);
  for (int i = 0; i < (n); ++i) a[i] = lower_bound(sa, sa + n, a[i]) - sa + 1;
  for (int i = 0; i < (n); ++i) {
    add(s[0], a[i], 1);
    for (int j = 0; j < (2); ++j) {
      long long x = get(s[j], a[i]);
      add(s[j + 1], a[i], x);
    }
  }
  long long res = get(s[2], 0);
  cout << res << endl;
  return 0;
}

### Prompt

Generate a Cpp solution to the following problem:

The Romans have attacked again. This time they are much more than the Persians but Shapur is ready to defeat them. He says: "A lion is never afraid of a hundred sheep". 

Nevertheless Shapur has to find weaknesses in the Roman army to defeat them. So he gives the army a weakness number.

In Shapur's opinion the weakness of an army is equal to the number of triplets i, j, k such that i < j < k and ai > aj > ak where ax is the power of man standing at position x. The Roman army has one special trait — powers of all the people in it are distinct.

Help Shapur find out how weak the Romans are.

Input

The first line of input contains a single number n (3 ≤ n ≤ 106) — the number of men in Roman army. Next line contains n different positive integers ai (1 ≤ i ≤ n, 1 ≤ ai ≤ 109) — powers of men in the Roman army. 

Output

A single integer number, the weakness of the Roman army. 

Please, do not use %lld specificator to read or write 64-bit integers in C++. It is preffered to use cout (also you may use %I64d).

Examples

Input

3
3 2 1


Output

1


Input

3
2 3 1


Output

0


Input

4
10 8 3 1


Output

4


Input

4
1 5 4 3


Output

1

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
const int maxn = 1000005;
int a[maxn], sa[maxn];
int n;
long long s[3][maxn];
void add(long long s[], int x, long long y) {
  for (int i = x; i <= n; i += -i & i) s[i] += y;
}
long long get(long long s[], int x) {
  long long res = 0;
  for (int i = n; i > 0; i &= i - 1) res += s[i];
  for (int i = x; i > 0; i &= i - 1) res -= s[i];
  return res;
}
int main() {
  scanf("%d", &n);
  for (int i = 0; i < (n); ++i) scanf("%d", a + i), sa[i] = a[i];
  sort(sa, sa + n);
  for (int i = 0; i < (n); ++i) a[i] = lower_bound(sa, sa + n, a[i]) - sa + 1;
  for (int i = 0; i < (n); ++i) {
    add(s[0], a[i], 1);
    for (int j = 0; j < (2); ++j) {
      long long x = get(s[j], a[i]);
      add(s[j + 1], a[i], x);
    }
  }
  long long res = get(s[2], 0);
  cout << res << endl;
  return 0;
}

```