B. Matrix of Differences
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

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.

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