#include <bits/stdc++.h>
using namespace std;
long long s[100005], t[100005];
map<long long, long long> mapp1;
map<long long, long long> mapp2;
int main() {
  int n;
  scanf("%d", &n);
  for (int i = 0; i < n; i++) scanf("%lld", &s[i]);
  long long minn = 1000000000;
  for (int i = n - 1, j = 0; i >= 0; i--) {
    if (j < 1) {
      j++;
      minn = min(minn, s[i]);
      mapp1[s[i]]++;
      continue;
    }
    t[i] = s[i] + minn;
    mapp2[i] += mapp1[minn];
    mapp1[s[i]]++;
    minn = min(minn, s[i]);
  }
  minn = 2000000000;
  long long sum = 3000000000, res = 0;
  mapp1.clear();
  for (int i = n - 2, j = 0; i >= 0; i--) {
    if (j < 1) {
      j++;
      minn = min(minn, t[i]);
      mapp1[t[i]] += mapp2[i];
      continue;
    }
    s[i] = s[i] + minn;
    if (s[i] == sum) res += mapp1[minn];
    if (s[i] < sum) {
      sum = s[i];
      res = mapp1[minn];
    }
    mapp1[t[i]] += mapp2[i];
    minn = min(minn, t[i]);
  }
  printf("%lld\n", res);
}

### Prompt

Your task is to create 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>
using namespace std;
long long s[100005], t[100005];
map<long long, long long> mapp1;
map<long long, long long> mapp2;
int main() {
  int n;
  scanf("%d", &n);
  for (int i = 0; i < n; i++) scanf("%lld", &s[i]);
  long long minn = 1000000000;
  for (int i = n - 1, j = 0; i >= 0; i--) {
    if (j < 1) {
      j++;
      minn = min(minn, s[i]);
      mapp1[s[i]]++;
      continue;
    }
    t[i] = s[i] + minn;
    mapp2[i] += mapp1[minn];
    mapp1[s[i]]++;
    minn = min(minn, s[i]);
  }
  minn = 2000000000;
  long long sum = 3000000000, res = 0;
  mapp1.clear();
  for (int i = n - 2, j = 0; i >= 0; i--) {
    if (j < 1) {
      j++;
      minn = min(minn, t[i]);
      mapp1[t[i]] += mapp2[i];
      continue;
    }
    s[i] = s[i] + minn;
    if (s[i] == sum) res += mapp1[minn];
    if (s[i] < sum) {
      sum = s[i];
      res = mapp1[minn];
    }
    mapp1[t[i]] += mapp2[i];
    minn = min(minn, t[i]);
  }
  printf("%lld\n", res);
}

```