#include <bits/stdc++.h>
const long long N = 100100;
const long long MAX = 1000000100;
using namespace std;
long long a[N] = {0};
int main() {
  long long n;
  while (scanf("%lld", &n) != EOF) {
    map<long long, long long> num;
    for (long long i = 0; i < n; i++) {
      scanf("%lld", &a[i]);
      num[a[i]]++;
    }
    sort(a, a + n);
    long long min1 = MAX + 1, min2 = MAX + 2, min3 = MAX + 3;
    for (long long i = 0; i < n; i++) {
      if (a[i] < min1) {
        min1 = a[i];
      } else if (a[i] > min1 && a[i] < min2) {
        min2 = a[i];
      } else if (a[i] > min2 && a[i] < min3) {
        min3 = a[i];
        break;
      }
    }
    if (num[min1] >= 3) {
      long long sum = 1;
      for (long long i = 3; i >= 1; i--) sum *= num[min1]--;
      cout << sum / 6 << endl;
    } else if (num[min1] == 2) {
      cout << num[min2] << endl;
    } else {
      if (num[min2] >= 2) {
        long long sum = 1;
        for (long long i = 2; i >= 1; i--) sum *= num[min2]--;
        cout << sum / 2 << endl;
      } else {
        cout << num[min3] << endl;
      }
    }
  }
  return 0;
}

### Prompt

Please formulate a Cpp solution to 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>
const long long N = 100100;
const long long MAX = 1000000100;
using namespace std;
long long a[N] = {0};
int main() {
  long long n;
  while (scanf("%lld", &n) != EOF) {
    map<long long, long long> num;
    for (long long i = 0; i < n; i++) {
      scanf("%lld", &a[i]);
      num[a[i]]++;
    }
    sort(a, a + n);
    long long min1 = MAX + 1, min2 = MAX + 2, min3 = MAX + 3;
    for (long long i = 0; i < n; i++) {
      if (a[i] < min1) {
        min1 = a[i];
      } else if (a[i] > min1 && a[i] < min2) {
        min2 = a[i];
      } else if (a[i] > min2 && a[i] < min3) {
        min3 = a[i];
        break;
      }
    }
    if (num[min1] >= 3) {
      long long sum = 1;
      for (long long i = 3; i >= 1; i--) sum *= num[min1]--;
      cout << sum / 6 << endl;
    } else if (num[min1] == 2) {
      cout << num[min2] << endl;
    } else {
      if (num[min2] >= 2) {
        long long sum = 1;
        for (long long i = 2; i >= 1; i--) sum *= num[min2]--;
        cout << sum / 2 << endl;
      } else {
        cout << num[min3] << endl;
      }
    }
  }
  return 0;
}

```