A15629. Hossam and Combinatorics

Hossam woke up bored, so he decided to create an interesting array with his friend Hazem.

Now, they have an array $a$ of $n$ positive integers, Hossam will choose a number $a_i$ and Hazem will choose a number $a_j$ .

Count the number of interesting pairs $(a_i, a_j)$ that meet all the following conditions:

- $1 \le i, j \le n$ ;
- $i \neq j$ ;
- The absolute difference $|a_i - a_j|$ must be equal to the maximum absolute difference over all the pairs in the array. More formally, $|a_i - a_j| = \max_{1 \le p, q \le n} |a_p - a_q|$ .

The input consists of multiple test cases. The first line contains a single integer $t$ ( $1 \le t \le 100$ ), which denotes the number of test cases. Description of the test cases follows.

The first line of each test case contains an integer $n$ ( $2 \le n \le 10^5$ ).

The second line of each test case contains $n$ integers $a_1, a_2, \dots, a_n$ ( $1 \le a_i \le 10^5$ ).

It is guaranteed that the sum of $n$ over all test cases does not exceed $10^5$ .

For each test case print an integer — the number of interesting pairs $(a_i, a_j)$ .

In the first example, the two ways are:

- Hossam chooses the fourth number $8$ and Hazem chooses the fifth number $1$ .
- Hossam chooses the fifth number $1$ and Hazem chooses the fourth number $8$ .

In the second example, the four ways are:

- Hossam chooses the second number $2$ and Hazem chooses the sixth number $10$ .
- Hossam chooses the sixth number $10$ and Hazem chooses the second number $2$ .
- Hossam chooses the fifth number $2$ and Hazem chooses the sixth number $10$ .
- Hossam chooses the sixth number $10$ and Hazem chooses the fifth number $2$ .