#include <bits/stdc++.h>
using namespace std;
long long f(long long sk) { return ((sk * (sk - 1)) / 2) + sk; }
int main() {
  int n;
  cin >> n;
  long long sk[n];
  for (int i = 0; i < n; i++) {
    cin >> sk[i];
  }
  sort(sk, sk + n);
  long long eq = 1;
  for (int i = 1; i < n; i++) {
    if (sk[i] == sk[i - 1]) {
      eq++;
    } else {
      break;
    }
  }
  long long eq2 = 1;
  for (int i = 2; i < n; i++) {
    if (sk[i] == sk[i - 1]) {
      eq2++;
    } else {
      break;
    }
  }
  int eq3 = 1;
  for (int i = 3; i < n; i++) {
    if (sk[i] == sk[i - 1]) {
      eq3++;
    } else {
      break;
    }
  }
  if (eq > 3) {
    long long sum = 0;
    for (int i = 2; i <= eq; i++) {
      sum += f(eq - i);
    }
    cout << sum;
  } else if (eq2 > 2) {
    cout << f(eq2 - 1);
  } else if (eq3 > 1) {
    cout << eq3;
  } else {
    cout << 1;
  }
  return 0;
}

### Prompt

In Cpp, your task is to solve 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;
long long f(long long sk) { return ((sk * (sk - 1)) / 2) + sk; }
int main() {
  int n;
  cin >> n;
  long long sk[n];
  for (int i = 0; i < n; i++) {
    cin >> sk[i];
  }
  sort(sk, sk + n);
  long long eq = 1;
  for (int i = 1; i < n; i++) {
    if (sk[i] == sk[i - 1]) {
      eq++;
    } else {
      break;
    }
  }
  long long eq2 = 1;
  for (int i = 2; i < n; i++) {
    if (sk[i] == sk[i - 1]) {
      eq2++;
    } else {
      break;
    }
  }
  int eq3 = 1;
  for (int i = 3; i < n; i++) {
    if (sk[i] == sk[i - 1]) {
      eq3++;
    } else {
      break;
    }
  }
  if (eq > 3) {
    long long sum = 0;
    for (int i = 2; i <= eq; i++) {
      sum += f(eq - i);
    }
    cout << sum;
  } else if (eq2 > 2) {
    cout << f(eq2 - 1);
  } else if (eq3 > 1) {
    cout << eq3;
  } else {
    cout << 1;
  }
  return 0;
}

```