CF1771A 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 $ .