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 ($$$1 \le i, j \le n$$$).

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

Input

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 $$$3000$$$.

Output

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.

Note

In the first, second and fourth test case, it can be verified that the matrix provided in the example meets all the conditions stated in the problem.

In the third test case, by enumerating all possible matrices, it can be proven that there is no hot matrix that satisfies the conditions of the problem.

Hot Matrix

Examples