B. Matrix of Differences
constructive algorithms; math
For a square matrix of integers of size \(n \times n\), let's define its beauty as follows: for each pair of side-adjacent elements \(x\) and \(y\), write out the number \(|x-y|\), and then find the number of different numbers among them.For example, for the matrix \(\begin{pmatrix} 1 & 3\\ 4 & 2 \end{pmatrix}\) the numbers we consider are \(|1-3|=2\), \(|1-4|=3\), \(|3-2|=1\) and \(|4-2|=2\); there are \(3\) different numbers among them (\(2\), \(3\) and \(1\)), which means that its beauty is equal to \(3\).You are given an integer \(n\). You have to find a matrix of size \(n \times n\), where each integer from \(1\) to \(n^2\) occurs exactly once, such that its beauty is the maximum possible among all such matrices.
The first line contains a single integer \(t\) (\(1 \le t \le 49\)) – the number of test cases.The first (and only) line of each test case contains a single integer \(n\) (\(2 \le n \le 50\)).
For each test case, print \(n\) rows of \(n\) integers — a matrix of integers of size \(n \times n\), where each number from \(1\) to \(n^2\) occurs exactly once, such that its beauty is the maximum possible among all such matrices. If there are multiple answers, print any of them.