Hossam and Combinatorics
Description
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 $(a_i, a_j)$.
Input
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 $10^5$.
Output
For each test case print an integer — the number of interesting pairs $(a_i, a_j)$.
2
5
6 2 3 8 1
6
7 2 8 3 2 10
2
4
Note
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 $2$.