#include <bits/stdc++.h>
#pragma GCC optimize("Ofast")
#pragma GCC target("avx,avx2,fma")
#pragma GCC optimization("unroll-loops")
using namespace std;
using namespace chrono;
template <typename Arg1>
void __f(const char* name, Arg1&& arg1) {
  cout << name << " : " << arg1 << "\n";
}
template <typename Arg1, typename... Args>
void __f(const char* names, Arg1&& arg1, Args&&... args) {
  const char* comma = strchr(names + 1, ',');
  cout.write(names, comma - names) << " : " << arg1 << " | ";
  __f(comma + 1, args...);
}
long long int advceil(long long int num, long long int den) {
  return (num % den == 0 ? num / den : num / den + 1);
}
long long int lstbt(long long int val) {
  long long int msk = val & (val - 1);
  return log2(val ^ msk);
}
long long int modmul(long long int a, long long int b) {
  a %= 1000000007;
  b %= 1000000007;
  long long int res = 0;
  while (b > 0) {
    if (b & 1) res = (res + a) % 1000000007;
    a = (a * 2) % 1000000007;
    b /= 2;
  }
  return res;
}
long long int modexpo(long long int a, long long int b) {
  long long int res = 1;
  while (b > 0) {
    if (b & 1) res = modmul(res, a);
    a = modmul(a, a);
    b /= 2;
  }
  return res;
}
long long int gcd(long long int a, long long int b) {
  return a == 0 ? b : gcd(b % a, a);
}
vector<long long int> CALCfactor(long long int n) {
  vector<long long int> factor(n + 2, 0);
  for (long long int i = 4; i <= n; i += 2) factor[i] = 2;
  for (long long int j = 3; j <= n; j += 2) {
    if (factor[j]) continue;
    for (long long int i = 2 * j; i <= n; i += j) factor[i] = j;
  }
  return factor;
}
vector<long long int> CALCprimeNUM(long long int n) {
  vector<long long int> factor = CALCfactor(n);
  vector<long long int> primeNUM;
  primeNUM.reserve(n + 2);
  for (long long int i = 2; i <= n; i++)
    if (!factor[i]) primeNUM.push_back(i);
  return primeNUM;
}
vector<long long int> CALCprimeFACTOR(long long int n) {
  vector<long long int> factor = CALCfactor(n);
  vector<long long int> ans;
  while (factor[n] != 0) {
    ans.push_back(factor[n]);
    n /= factor[n];
  }
  if (n > 1) ans.push_back(n);
  return ans;
}
vector<long long int> unique(vector<long long int> x) {
  sort(x.begin(), x.end());
  set<long long int> s;
  vector<long long int> ans;
  ans.reserve(x.size());
  for (auto elem : x) s.insert(elem);
  for (auto elem : s) ans.push_back(elem);
  return ans;
}
pair<vector<long long int>, vector<long long int> > getFact(long long int n) {
  vector<long long int> fact(n + 1, 1), invfact(n + 1, 1);
  for (long long int i = 1; i <= n; i++)
    fact[i] = (i * (fact[i - 1])) % 1000000007;
  for (long long int i = 1; i <= n; i++)
    invfact[i] = (modexpo(i, 1000000007 - 2) * invfact[i - 1]) % 1000000007;
  return {fact, invfact};
}
void compress(vector<long long int>& arr, long long int n) {
  map<long long int, vector<long long int> > pos;
  for (long long int i = 1; i <= n; i++) pos[arr[i]].push_back(i);
  long long int cnt = 1;
  for (auto itr : pos) {
    for (auto elem : itr.second) arr[elem] = cnt;
    cnt++;
  }
}
long long int BIT[1000001 + 10] = {};
long long int N;
void update(long long int idx, long long int val) {
  for (long long int i = idx; i <= N; i += (i & (-i))) BIT[i] += val;
}
long long int query(long long int idx) {
  long long int res = 0;
  for (long long int i = idx; i > 0; i -= (i & (-i))) res += BIT[i];
  return res;
}
void solve() {
  long long int n;
  cin >> n;
  vector<long long int> arr(n + 1, 0), pref(n + 1, 0), suff(n + 1, 0);
  for (long long int i = 1; i <= n; i++) cin >> arr[i];
  compress(arr, n);
  N = n + 1;
  for (long long int i = 1; i <= n; i++) {
    update(arr[i], 1);
    pref[i] = (query(N) - query(arr[i]));
  }
  memset(BIT, 0, sizeof(BIT));
  for (long long int i = n + 1 - 1; i >= 1; i--) {
    update(arr[i], 1);
    suff[i] = query(arr[i] - 1);
  }
  long long int ans = 0;
  for (long long int i = 1; i <= n; i++) ans += (pref[i] * suff[i]);
  cout << ans << "\n";
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  auto start1 = high_resolution_clock::now();
  solve();
  auto stop1 = high_resolution_clock::now();
  auto duration = duration_cast<microseconds>(stop1 - start1);
}

### 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>
#pragma GCC optimize("Ofast")
#pragma GCC target("avx,avx2,fma")
#pragma GCC optimization("unroll-loops")
using namespace std;
using namespace chrono;
template <typename Arg1>
void __f(const char* name, Arg1&& arg1) {
  cout << name << " : " << arg1 << "\n";
}
template <typename Arg1, typename... Args>
void __f(const char* names, Arg1&& arg1, Args&&... args) {
  const char* comma = strchr(names + 1, ',');
  cout.write(names, comma - names) << " : " << arg1 << " | ";
  __f(comma + 1, args...);
}
long long int advceil(long long int num, long long int den) {
  return (num % den == 0 ? num / den : num / den + 1);
}
long long int lstbt(long long int val) {
  long long int msk = val & (val - 1);
  return log2(val ^ msk);
}
long long int modmul(long long int a, long long int b) {
  a %= 1000000007;
  b %= 1000000007;
  long long int res = 0;
  while (b > 0) {
    if (b & 1) res = (res + a) % 1000000007;
    a = (a * 2) % 1000000007;
    b /= 2;
  }
  return res;
}
long long int modexpo(long long int a, long long int b) {
  long long int res = 1;
  while (b > 0) {
    if (b & 1) res = modmul(res, a);
    a = modmul(a, a);
    b /= 2;
  }
  return res;
}
long long int gcd(long long int a, long long int b) {
  return a == 0 ? b : gcd(b % a, a);
}
vector<long long int> CALCfactor(long long int n) {
  vector<long long int> factor(n + 2, 0);
  for (long long int i = 4; i <= n; i += 2) factor[i] = 2;
  for (long long int j = 3; j <= n; j += 2) {
    if (factor[j]) continue;
    for (long long int i = 2 * j; i <= n; i += j) factor[i] = j;
  }
  return factor;
}
vector<long long int> CALCprimeNUM(long long int n) {
  vector<long long int> factor = CALCfactor(n);
  vector<long long int> primeNUM;
  primeNUM.reserve(n + 2);
  for (long long int i = 2; i <= n; i++)
    if (!factor[i]) primeNUM.push_back(i);
  return primeNUM;
}
vector<long long int> CALCprimeFACTOR(long long int n) {
  vector<long long int> factor = CALCfactor(n);
  vector<long long int> ans;
  while (factor[n] != 0) {
    ans.push_back(factor[n]);
    n /= factor[n];
  }
  if (n > 1) ans.push_back(n);
  return ans;
}
vector<long long int> unique(vector<long long int> x) {
  sort(x.begin(), x.end());
  set<long long int> s;
  vector<long long int> ans;
  ans.reserve(x.size());
  for (auto elem : x) s.insert(elem);
  for (auto elem : s) ans.push_back(elem);
  return ans;
}
pair<vector<long long int>, vector<long long int> > getFact(long long int n) {
  vector<long long int> fact(n + 1, 1), invfact(n + 1, 1);
  for (long long int i = 1; i <= n; i++)
    fact[i] = (i * (fact[i - 1])) % 1000000007;
  for (long long int i = 1; i <= n; i++)
    invfact[i] = (modexpo(i, 1000000007 - 2) * invfact[i - 1]) % 1000000007;
  return {fact, invfact};
}
void compress(vector<long long int>& arr, long long int n) {
  map<long long int, vector<long long int> > pos;
  for (long long int i = 1; i <= n; i++) pos[arr[i]].push_back(i);
  long long int cnt = 1;
  for (auto itr : pos) {
    for (auto elem : itr.second) arr[elem] = cnt;
    cnt++;
  }
}
long long int BIT[1000001 + 10] = {};
long long int N;
void update(long long int idx, long long int val) {
  for (long long int i = idx; i <= N; i += (i & (-i))) BIT[i] += val;
}
long long int query(long long int idx) {
  long long int res = 0;
  for (long long int i = idx; i > 0; i -= (i & (-i))) res += BIT[i];
  return res;
}
void solve() {
  long long int n;
  cin >> n;
  vector<long long int> arr(n + 1, 0), pref(n + 1, 0), suff(n + 1, 0);
  for (long long int i = 1; i <= n; i++) cin >> arr[i];
  compress(arr, n);
  N = n + 1;
  for (long long int i = 1; i <= n; i++) {
    update(arr[i], 1);
    pref[i] = (query(N) - query(arr[i]));
  }
  memset(BIT, 0, sizeof(BIT));
  for (long long int i = n + 1 - 1; i >= 1; i--) {
    update(arr[i], 1);
    suff[i] = query(arr[i] - 1);
  }
  long long int ans = 0;
  for (long long int i = 1; i <= n; i++) ans += (pref[i] * suff[i]);
  cout << ans << "\n";
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  auto start1 = high_resolution_clock::now();
  solve();
  auto stop1 = high_resolution_clock::now();
  auto duration = duration_cast<microseconds>(stop1 - start1);
}

```