A14175 | Not Adjacent Matrix

We will consider the numbers $a$ and $b$ as adjacent if they differ by exactly one, that is, $|a-b|=1$ .

We will consider cells of a square matrix $n \times n$ as adjacent if they have a common side, that is, for cell $(r, c)$ cells $(r, c-1)$ , $(r, c+1)$ , $(r-1, c)$ and $(r+1, c)$ are adjacent to it.

For a given number $n$ , construct a square matrix $n \times n$ such that:

- Each integer from $1$ to $n^2$ occurs in this matrix exactly once;
- If $(r_1, c_1)$ and $(r_2, c_2)$ are adjacent cells, then the numbers written in them must not be adjacent.

The first line contains one integer $t$ ( $1 \le t \le 100$ ). Then $t$ test cases follow.

Each test case is characterized by one integer $n$ ( $1 \le n \le 100$ ).

For each test case, output:

- -1, if the required matrix does not exist;
- the required matrix, otherwise (any such matrix if many of them exist).

The matrix should be outputted as $n$ lines, where each line contains $n$ integers.