A. Hossam and Combinatorics
combinatorics; math; sortings
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 \(2\).