#include <bits/stdc++.h>
using namespace std;
const int N = 100010;
map<int, long long> mp;
int a[N];
int main() {
  ios::sync_with_stdio(0), cin.tie(0), cout.tie(0);
  int n;
  cin >> n;
  for (int i = 0; i < n; i++) cin >> a[i];
  sort(a, a + n);
  set<int> st;
  int i = 0;
  while (i < 3) {
    st.insert(a[i]);
    i++;
  }
  int all = 0;
  for (int i = 0; i < n; i++) {
    if (st.count(a[i])) mp[a[i]]++, all++;
  }
  long long ans = 1;
  if (st.size() == 2) {
    long long mn = *st.begin();
    if (mp[mn] > 1) {
      mn = mp[mn];
      ans *= mn * (mn - 1) / 2;
      ans *= mp[*++st.begin()];
    } else {
      mn = *++st.begin();
      ans *= mp[mn] * (mp[mn] - 1) / 2;
    }
  } else if (st.size() == 1) {
    int i = *st.begin();
    ans = (mp[i] * (mp[i] - 1) * (mp[i] - 2)) / 6LL;
  } else {
    for (auto i : st) ans *= (long long)mp[i];
  }
  cout << ans;
  return 0;
}

### Prompt

Create a solution in Cpp for the following problem:

After returning from the army Makes received a gift — an array a consisting of n positive integer numbers. He hadn't been solving problems for a long time, so he became interested to answer a particular question: how many triples of indices (i, j, k) (i < j < k), such that ai·aj·ak is minimum possible, are there in the array? Help him with it!

Input

The first line of input contains a positive integer number n (3 ≤ n ≤ 105) — the number of elements in array a. The second line contains n positive integer numbers ai (1 ≤ ai ≤ 109) — the elements of a given array.

Output

Print one number — the quantity of triples (i, j, k) such that i, j and k are pairwise distinct and ai·aj·ak is minimum possible.

Examples

Input

4
1 1 1 1


Output

4


Input

5
1 3 2 3 4


Output

2


Input

6
1 3 3 1 3 2


Output

1

Note

In the first example Makes always chooses three ones out of four, and the number of ways to choose them is 4.

In the second example a triple of numbers (1, 2, 3) is chosen (numbers, not indices). Since there are two ways to choose an element 3, then the answer is 2.

In the third example a triple of numbers (1, 1, 2) is chosen, and there's only one way to choose indices.

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
const int N = 100010;
map<int, long long> mp;
int a[N];
int main() {
  ios::sync_with_stdio(0), cin.tie(0), cout.tie(0);
  int n;
  cin >> n;
  for (int i = 0; i < n; i++) cin >> a[i];
  sort(a, a + n);
  set<int> st;
  int i = 0;
  while (i < 3) {
    st.insert(a[i]);
    i++;
  }
  int all = 0;
  for (int i = 0; i < n; i++) {
    if (st.count(a[i])) mp[a[i]]++, all++;
  }
  long long ans = 1;
  if (st.size() == 2) {
    long long mn = *st.begin();
    if (mp[mn] > 1) {
      mn = mp[mn];
      ans *= mn * (mn - 1) / 2;
      ans *= mp[*++st.begin()];
    } else {
      mn = *++st.begin();
      ans *= mp[mn] * (mp[mn] - 1) / 2;
    }
  } else if (st.size() == 1) {
    int i = *st.begin();
    ans = (mp[i] * (mp[i] - 1) * (mp[i] - 2)) / 6LL;
  } else {
    for (auto i : st) ans *= (long long)mp[i];
  }
  cout << ans;
  return 0;
}

```