#include <bits/stdc++.h>
using namespace std;
vector<long long> V;
int f(long long a, long long left, long long right, long long N) {
  int L, R, mid;
  while (right - left > 1) {
    mid = (left + right) / 2;
    if (V[mid] >= a)
      right = mid;
    else
      left = mid;
  }
  L = right;
  left = -1;
  right = N;
  while (right - left > 1) {
    mid = (left + right) / 2;
    if (V[mid] > a)
      right = mid;
    else
      left = mid;
  }
  R = left;
  return R - L + 1;
}
int main() {
  long long N, a, i, mas[3];
  cin >> N;
  for (i = 0; i < N; i++) {
    cin >> a;
    V.push_back(a);
  }
  sort(V.begin(), V.end());
  for (i = 0; i < 3; i++) mas[i] = f(V[i], -1, N, N);
  if (V[0] == V[1] && V[0] == V[2])
    cout << mas[0] * (mas[0] - 1) * (mas[0] - 2) / 6;
  else if (V[0] != V[1] && V[0] != V[2] && V[1] != V[2])
    cout << mas[0] * mas[1] * mas[2];
  else if (V[0] == V[1])
    cout << mas[0] * (mas[0] - 1) * mas[2] / 2;
  else if (V[0] == V[2])
    cout << mas[0] * (mas[0] - 1) * mas[1] / 2;
  else
    cout << mas[1] * (mas[1] - 1) * mas[0] / 2;
  return 0;
}

### Prompt

Develop a solution in cpp to the problem described below:

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;
vector<long long> V;
int f(long long a, long long left, long long right, long long N) {
  int L, R, mid;
  while (right - left > 1) {
    mid = (left + right) / 2;
    if (V[mid] >= a)
      right = mid;
    else
      left = mid;
  }
  L = right;
  left = -1;
  right = N;
  while (right - left > 1) {
    mid = (left + right) / 2;
    if (V[mid] > a)
      right = mid;
    else
      left = mid;
  }
  R = left;
  return R - L + 1;
}
int main() {
  long long N, a, i, mas[3];
  cin >> N;
  for (i = 0; i < N; i++) {
    cin >> a;
    V.push_back(a);
  }
  sort(V.begin(), V.end());
  for (i = 0; i < 3; i++) mas[i] = f(V[i], -1, N, N);
  if (V[0] == V[1] && V[0] == V[2])
    cout << mas[0] * (mas[0] - 1) * (mas[0] - 2) / 6;
  else if (V[0] != V[1] && V[0] != V[2] && V[1] != V[2])
    cout << mas[0] * mas[1] * mas[2];
  else if (V[0] == V[1])
    cout << mas[0] * (mas[0] - 1) * mas[2] / 2;
  else if (V[0] == V[2])
    cout << mas[0] * (mas[0] - 1) * mas[1] / 2;
  else
    cout << mas[1] * (mas[1] - 1) * mas[0] / 2;
  return 0;
}

```