Description

Input

Each test contains multiple test cases. The first line contains the number of test cases $t$ ($1 \leq t \leq 100$). The description of the test cases follows.

The only line of each test case contains a single integer $n$ ($2 \leq n \leq 1000$) — the length of the array.

Output

For each test case, print "YES" if an array of length $n$ satisfying the conditions exists. Otherwise, print "NO". If the answer is "YES", on the next line print a sequence $s_1,s_2, \ldots, s_n$ satisfying the conditions. Each element should be a non-zero integer in the range $[-5000,5000]$, i. e. $-5000 \leq s_i \leq 5000$ and $s_i \neq 0$ should hold for each $1 \leq i \leq n$.

It can be proved that if a solution exists then there also exists one which satisfies the additional constraints on the range.

If there are several correct answers, print any of them.

2
2
3

YES
9 5
NO

Note

In the first test case, $[9,5]$ is a valid answer since $9+5$ (the sum of the two adjacent elements $s_1+s_2$) is equal to $9+5$ (the sum of all elements). Other solutions include $[6,-9], [-1,-2], [-5000,5000], \ldots$

For the second test case, let us show why some arrays do not satisfy the constraints:

• $[1,1,1]$  — $s_1+s_2 = 1+1 = 2$ and $s_1+s_2+s_3=1+1+1 = 3$ differ;
• $[1,-1,1]$  — $s_1+s_2=1+(-1)=0$ and $s_1+s_2+s_3=1+(-1)+1 = 1$ differ;
• $[0,0,0]$  — The array $s$ cannot contain a $0$.

This is not a proof, but it can be shown that the answer is "NO".