#include <bits/stdc++.h>
using namespace std;
struct mstree {
  int len;
  vector<vector<int>> t;
  mstree(int l) {
    len = l;
    t.resize(4 * len);
  }
  vector<int> merge(int l, int r) {
    int sz1 = t[l].size(), sz2 = t[r].size();
    vector<int> arr(sz1 + sz2);
    int i = 0, j = 0, idx = 0;
    while (i < sz1 && j < sz2) {
      arr[idx++] = (t[l][i] < t[r][j]) ? t[l][i++] : t[r][j++];
    }
    while (i < sz1) {
      arr[idx++] = t[l][i++];
    }
    while (j < sz2) {
      arr[idx++] = t[r][j++];
    }
    return arr;
  }
  template <typename T>
  void build(const T &arr, const int32_t &v, const int32_t &tl,
             const int32_t &tr) {
    if (tl == tr) {
      t[v].push_back(arr[tl]);
      return;
    }
    int32_t tm = (tl + tr) >> 1;
    build(arr, v << 1, tl, tm);
    build(arr, v << 1 | 1, tm + 1, tr);
    t[v] = merge(v << 1, v << 1 | 1);
  }
  int query(const int32_t &v, const int32_t &tl, const int32_t &tr,
            const int32_t &l, const int32_t &r, int e) {
    if (l > tr || r < tl) return 0;
    if (tl >= l && tr <= r)
      return lower_bound(t[v].begin(), t[v].end(), e) - t[v].begin();
    int32_t tm = (tl + tr) >> 1;
    return query(v << 1, tl, tm, l, r, e) +
           query(v << 1 | 1, tm + 1, tr, l, r, e);
  }

 public:
  template <typename T>
  void build(const T &arr) {
    build(arr, 1, 0, len - 1);
  }
  int query(const int32_t &l, const int32_t &r, int e) {
    return query(1, 0, len - 1, l, r, e);
  }
};
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  int n;
  cin >> n;
  vector<int> arr(n);
  for (int i = 0; i < n; i++) cin >> arr[i];
  mstree ms(n);
  ms.build(arr);
  long long res = 0;
  for (int i = 1; i < n - 1; i++)
    res += (i - ms.query(0, i - 1, arr[i] + 1)) * 1ll *
           ms.query(i + 1, n - 1, arr[i]);
  cout << res << "\n";
  return 0;
}

### Prompt

Construct a Cpp code solution to the problem outlined:

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;
struct mstree {
  int len;
  vector<vector<int>> t;
  mstree(int l) {
    len = l;
    t.resize(4 * len);
  }
  vector<int> merge(int l, int r) {
    int sz1 = t[l].size(), sz2 = t[r].size();
    vector<int> arr(sz1 + sz2);
    int i = 0, j = 0, idx = 0;
    while (i < sz1 && j < sz2) {
      arr[idx++] = (t[l][i] < t[r][j]) ? t[l][i++] : t[r][j++];
    }
    while (i < sz1) {
      arr[idx++] = t[l][i++];
    }
    while (j < sz2) {
      arr[idx++] = t[r][j++];
    }
    return arr;
  }
  template <typename T>
  void build(const T &arr, const int32_t &v, const int32_t &tl,
             const int32_t &tr) {
    if (tl == tr) {
      t[v].push_back(arr[tl]);
      return;
    }
    int32_t tm = (tl + tr) >> 1;
    build(arr, v << 1, tl, tm);
    build(arr, v << 1 | 1, tm + 1, tr);
    t[v] = merge(v << 1, v << 1 | 1);
  }
  int query(const int32_t &v, const int32_t &tl, const int32_t &tr,
            const int32_t &l, const int32_t &r, int e) {
    if (l > tr || r < tl) return 0;
    if (tl >= l && tr <= r)
      return lower_bound(t[v].begin(), t[v].end(), e) - t[v].begin();
    int32_t tm = (tl + tr) >> 1;
    return query(v << 1, tl, tm, l, r, e) +
           query(v << 1 | 1, tm + 1, tr, l, r, e);
  }

 public:
  template <typename T>
  void build(const T &arr) {
    build(arr, 1, 0, len - 1);
  }
  int query(const int32_t &l, const int32_t &r, int e) {
    return query(1, 0, len - 1, l, r, e);
  }
};
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  int n;
  cin >> n;
  vector<int> arr(n);
  for (int i = 0; i < n; i++) cin >> arr[i];
  mstree ms(n);
  ms.build(arr);
  long long res = 0;
  for (int i = 1; i < n - 1; i++)
    res += (i - ms.query(0, i - 1, arr[i] + 1)) * 1ll *
           ms.query(i + 1, n - 1, arr[i]);
  cout << res << "\n";
  return 0;
}

```