A15752 | Matrix of Differences

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.