Imbalanced Arrays

Description:

Input:

Each test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1 \le t \le 10^5$$$). The description of the test cases follows.

The first line of each test case has a single integer $$$n$$$ ($$$1 \leq n \leq 10^5$$$).

The next line contains $$$n$$$ integers $$$a_1, a_2, \ldots, a_n$$$ ($$$0 \leq a_i \leq n$$$).

It is guaranteed that the sum of $$$n$$$ across all test cases does not exceed $$$10^5$$$.

Output:

For each test case, output "NO" if there exists no imbalanced array.

Otherwise, output "YES". Then, on the next line, output $$$n$$$ integers $$$b_1, b_2, \ldots, b_n$$$ where $$$b_i \neq 0$$$ for all $$$1 \leq i \leq n$$$ — an imbalanced array.

Sample Input:

5
1
1
4
1 4 3 4
3
0 1 0
4
4 3 2 1
3
1 3 1

Sample Output:

YES
1 
NO
YES
-3 1 -2 
YES
4 2 -1 -3 
YES
-1 3 -1

Note:

For the first test case, $$$b = [1]$$$ is an imbalanced array. This is because for $$$i = 1$$$, there is exactly one $$$j$$$ ($$$j = 1$$$) where $$$b_1 + b_j > 0$$$.

For the second test case, it can be shown that there exists no imbalanced array.

For the third test case, $$$a = [0, 1, 0]$$$. The array $$$b = [-3, 1, -2]$$$ is an imbalanced array.

• For $$$i = 1$$$ and $$$i = 3$$$, there exists no index $$$j$$$ such that $$$b_i + b_j > 0$$$.
• For $$$i = 2$$$, there is only one index $$$j = 2$$$ such that $$$b_i + b_j > 0$$$ ($$$b_2 + b_2 = 1 + 1 = 2$$$).

Another possible output for the third test case could be $$$b = [-2, 1, -3]$$$.