AT_arc223_c [ARC223C] Whole Product of Pairwise Distances

You are given a sequence $ A $ of $ N $ positive integers. Find the remainder when $ \prod_{1 \leq i < j \leq N}|A_i-A_j| $ is divided by $ N $ . Solve $ T $ test cases per input.

The input is given from Standard Input in the following format: > $ T $ $ \mathrm{case}_1 $ $ \mathrm{case}_2 $ $ \vdots $ $ \mathrm{case}_T $ Each test case $ \mathrm{case}_t $ is given in the following format: > $ N $ $ A_1 $ $ A_2 $ $ \ldots $ $ A_N $

Output the answers over a total of $ T $ lines. The $ t $ -th line should contain the answer for the $ t $ -th test case.

### Sample Explanation 1 For the first test case, $ |A_1-A_2| \times |A_1-A_3| \times |A_2-A_3|=8 \times 4 \times 4=128 $ , and the remainder when this is divided by $ 3 $ is $ 2 $ . ### Constraints - $ 1 \leq T \leq 10^5 $ - $ 2 \leq N \leq 2 \times 10^5 $ - $ 1 \leq A_i \leq 10^9 $ - The sum of $ N $ over all test cases is at most $ 2 \times 10^5 $ . - All input values are integers.