Read problems statements in Mandarin and Russian. Translations in Vietnamese to be uploaded soon.
You are given an integer N. Consider a vector a of length N^{2} accessible via 0-based indexing.
Let's call the following transformation a TVT-transformation (Terrible Vector transformation).

We will call a vector g a good vector if

For some reason, you want to find a vector a of length N^{2} such that it's elements are either 1 or -1 and after applying TVT-transformation (i.e. b), it results in a good vector.

------ Input ------

The first line of input contains an integer T denoting the number of test cases. Each test case is described by one line containing one integer N.

------ Output ------

For each test case output one line with the word NO if it's not possible to find such vector. Otherwise output YES on the first line and N^{2} space-separated integers (each either -1 or 1) on the second - the answer for this test case.
If there are multiple possible answers, output any one of them.

------ Constraints ------

$1 ≤ T ≤ 100$
$1 ≤ N ≤ 100$

----- Sample Input 1 ------
2
1
2
----- Sample Output 1 ------
YES
1
YES
1 1 1 -1
----- explanation 1 ------
Sample example 2: After TVT-transformation, the vector will transform to (4, 0, 0, 4) which is a good vector for N = 2

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