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C. Not Adjacent Matrix

time limit per test

4 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputWe 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.

Input

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 $$$n$$$ ($$$1 \le n \le 100$$$).

Output

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.

Example

Input

3 1 2 3

Output

1 -1 2 9 7 4 6 3 1 8 5

Codeforces (c) Copyright 2010-2021 Mike Mirzayanov

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