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constructive algorithms

math

*1100

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B. Matrix of Differences

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputFor 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.

Input

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 $$$n$$$ ($$$2 \le n \le 50$$$).

Output

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.

Example

Input

223

Output

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

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