Piggy Zhou loves matrices, especially those that make him get excited, called hot matrix.

A hot matrix of size $n \times n$ can be defined as follows. Let $a_{i, j}$ denote the element in the $i$-th row, $j$-th column ($1 \le i, j \le n$).

1. Each column and row of the matrix is a permutation of all numbers from $0$ to $n-1$.
2. For each pair of indices $i$, $j$, such that $1 \le i, j \le n$, $a_{i, j} + a_{i, n - j + 1} = n - 1$.
3. For each pair of indices $i$, $j$, such that $1 \le i, j \le n$, $a_{i, j} + a_{n - i + 1, j} = n - 1$.
4. All ordered pairs $\left(a_{i, j}, a_{i, j + 1}\right)$, where $1 \le i \le n$, $1 \le j < n$, are distinct.
5. All ordered pairs $\left(a_{i, j}, a_{i + 1, j}\right)$, where $1 \le i < n$, $1 \le j \le n$, are distinct.

Now, Piggy Zhou gives you a number $n$, and you need to provide him with a hot matrix if the hot matrix exists for the given $n$, or inform him that he will never get excited if the hot matrix does not exist for the given $n$.

Each test contains multiple test cases. The first line contains the number of test cases $t$ ($1 \le t \le 1000$). The description of the test cases follows.

The only line of each test case contains one integer $n$ ($1 \le n \le 3000$).

It is guaranteed that the sum of $n$ across all test cases does not exceed $3000$.

For each test case, print "NO" (without quotes) if the hot matrix does not exist for the given $n$.

Otherwise, print "YES" (without quotes) on the first line. Then output $n$ rows, with $n$ numbers in each row, representing the hot matrix of size $n\times n$ that meets the requirements of the problem.

If there are multiple solutions, print any of them.