B. Imbalanced Arraystime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputNtarsis has come up with an array a of n non-negative integers.Call an array b of n integers imbalanced if it satisfies the following:   -n\le b_i\le n, b_i \ne 0,  there are no two indices (i, j) (1 \le i, j \le n) such that b_i + b_j = 0,  for each 1 \leq i \leq n, there are exactly a_i indices j (1 \le j \le n) such that b_i+b_j>0, where i and j are not necessarily distinct. Given the array a, Ntarsis wants you to construct some imbalanced array. Help him solve this task, or determine it is impossible.InputEach 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.OutputFor 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.ExampleInput
51141 4 3 430 1 044 3 2 131 3 1Output
YES
1 
NO
YES
-3 1 -2 
YES
4 2 -1 -3 
YES
-1 3 -1NoteFor 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].
51141 4 3 430 1 044 3 2 131 3 1
YES 1  NO YES -3 1 -2  YES 4 2 -1 -3  YES -1 3 -1
['constructive algorithms', 'graphs', 'greedy', 'math', 'sortings', 'two pointers', '*1800']