#include <bits/stdc++.h>
using namespace std;
int a[1000000], tl[4000000 + 10], tr[4000000 + 10], lmore[1000000],
    rless[1000000];
void updatemore(int l, int r, int index, int i) {
  int mid = (l + r) / 2;
  if (l == r) {
    if (l == index) tl[i]++;
    return;
  }
  if (index < l || r < index)
    return;
  else {
    updatemore(l, mid, index, 2 * i + 1);
    updatemore(mid + 1, r, index, 2 * i + 2);
    tl[i] = tl[2 * i + 1] + tl[2 * i + 2];
  }
}
int querymore(int l, int r, int ql, int qr, int i) {
  int mid = (l + r) / 2;
  if (qr < l || r < ql) return 0;
  if (ql <= l && r <= qr)
    return tl[i];
  else {
    return querymore(l, mid, ql, qr, 2 * i + 1) +
           querymore(mid + 1, r, ql, qr, 2 * i + 2);
  }
}
void updateless(int l, int r, int index, int i) {
  int mid = (l + r) / 2;
  if (l == r) {
    if (l == index) tr[i]++;
    return;
  }
  if (index < l || r < index)
    return;
  else {
    updateless(l, mid, index, 2 * i + 1);
    updateless(mid + 1, r, index, 2 * i + 2);
    tr[i] = tr[2 * i + 1] + tr[2 * i + 2];
  }
}
int queryless(int l, int r, int ql, int qr, int i) {
  int mid = (l + r) / 2;
  if (qr < l || r < ql) return 0;
  if (ql <= l && r <= qr)
    return tr[i];
  else {
    return queryless(l, mid, ql, qr, 2 * i + 1) +
           queryless(mid + 1, r, ql, qr, 2 * i + 2);
  }
}
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  int n;
  cin >> n;
  set<int> s;
  for (int i = 0; i < n; i++) {
    cin >> a[i];
    s.insert(a[i]);
  }
  int cnt = 0;
  map<int, int> mp;
  for (auto &x : s) {
    cnt++;
    mp[x] = cnt;
  }
  for (int i = 0; i < n; i++) {
    a[i] = mp[a[i]];
  }
  updatemore(0, cnt, a[0], 0);
  for (int i = 1; i < n; i++) {
    lmore[i] = querymore(0, cnt, a[i], cnt, 0);
    updatemore(0, cnt, a[i], 0);
  }
  updateless(0, cnt, a[n - 1], 0);
  for (int i = n - 2; i >= 0; i--) {
    rless[i] = queryless(0, cnt, 0, a[i], 0);
    updateless(0, cnt, a[i], 0);
  }
  long long ans = 0;
  for (int i = 1; i < n - 1; i++) {
    ans += (long long)lmore[i] * (long long)rless[i];
  }
  cout << ans;
  return 0;
}

### Prompt

Create a solution in cpp for 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;
int a[1000000], tl[4000000 + 10], tr[4000000 + 10], lmore[1000000],
    rless[1000000];
void updatemore(int l, int r, int index, int i) {
  int mid = (l + r) / 2;
  if (l == r) {
    if (l == index) tl[i]++;
    return;
  }
  if (index < l || r < index)
    return;
  else {
    updatemore(l, mid, index, 2 * i + 1);
    updatemore(mid + 1, r, index, 2 * i + 2);
    tl[i] = tl[2 * i + 1] + tl[2 * i + 2];
  }
}
int querymore(int l, int r, int ql, int qr, int i) {
  int mid = (l + r) / 2;
  if (qr < l || r < ql) return 0;
  if (ql <= l && r <= qr)
    return tl[i];
  else {
    return querymore(l, mid, ql, qr, 2 * i + 1) +
           querymore(mid + 1, r, ql, qr, 2 * i + 2);
  }
}
void updateless(int l, int r, int index, int i) {
  int mid = (l + r) / 2;
  if (l == r) {
    if (l == index) tr[i]++;
    return;
  }
  if (index < l || r < index)
    return;
  else {
    updateless(l, mid, index, 2 * i + 1);
    updateless(mid + 1, r, index, 2 * i + 2);
    tr[i] = tr[2 * i + 1] + tr[2 * i + 2];
  }
}
int queryless(int l, int r, int ql, int qr, int i) {
  int mid = (l + r) / 2;
  if (qr < l || r < ql) return 0;
  if (ql <= l && r <= qr)
    return tr[i];
  else {
    return queryless(l, mid, ql, qr, 2 * i + 1) +
           queryless(mid + 1, r, ql, qr, 2 * i + 2);
  }
}
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  int n;
  cin >> n;
  set<int> s;
  for (int i = 0; i < n; i++) {
    cin >> a[i];
    s.insert(a[i]);
  }
  int cnt = 0;
  map<int, int> mp;
  for (auto &x : s) {
    cnt++;
    mp[x] = cnt;
  }
  for (int i = 0; i < n; i++) {
    a[i] = mp[a[i]];
  }
  updatemore(0, cnt, a[0], 0);
  for (int i = 1; i < n; i++) {
    lmore[i] = querymore(0, cnt, a[i], cnt, 0);
    updatemore(0, cnt, a[i], 0);
  }
  updateless(0, cnt, a[n - 1], 0);
  for (int i = n - 2; i >= 0; i--) {
    rless[i] = queryless(0, cnt, 0, a[i], 0);
    updateless(0, cnt, a[i], 0);
  }
  long long ans = 0;
  for (int i = 1; i < n - 1; i++) {
    ans += (long long)lmore[i] * (long long)rless[i];
  }
  cout << ans;
  return 0;
}

```