C. Elemental Decompresstime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputYou are given an array a of n integers.Find two permutations^\dagger p and q of length n such that \max(p_i,q_i)=a_i for all 1 \leq i \leq n or report that such p and q do not exist.^\dagger A permutation of length n is an array consisting of n distinct integers from 1 to n in arbitrary order. For example, [2,3,1,5,4] is a permutation, but [1,2,2] is not a permutation (2 appears twice in the array), and [1,3,4] is also not a permutation (n=3 but there is 4 in the array).InputThe first line contains a single integer t (1 \le t \le 10^4) — the number of test cases. The description of test cases follows.The first line of each test case contains a single integer n (1 \le n \le 2 \cdot 10^5).The second line of each test case contains n integers a_1,a_2,\ldots,a_n (1 \leq a_i \leq n) — the array a.It is guaranteed that the total sum of n over all test cases does not exceed 2 \cdot 10^5. OutputFor each test case, if there do not exist p and q that satisfy the conditions, output "NO" (without quotes).Otherwise, output "YES" (without quotes) and then output 2 lines. The first line should contain n integers p_1,p_2,\ldots,p_n and the second line should contain n integers q_1,q_2,\ldots,q_n.If there are multiple solutions, you may output any of them.You can output "YES" and "NO" in any case (for example, strings "yEs", "yes" and "Yes" will be recognized as a positive response).ExampleInput
31155 3 4 2 521 1Output
YES
1 
1 
YES
1 3 4 2 5 
5 2 3 1 4 
NO
NoteIn the first test case, p=q=[1]. It is correct since a_1 = max(p_1,q_1) = 1.In the second test case, p=[1,3,4,2,5] and q=[5,2,3,1,4]. It is correct since:  a_1 = \max(p_1, q_1) = \max(1, 5) = 5,  a_2 = \max(p_2, q_2) = \max(3, 2) = 3,  a_3 = \max(p_3, q_3) = \max(4, 3) = 4,  a_4 = \max(p_4, q_4) = \max(2, 1) = 2,  a_5 = \max(p_5, q_5) = \max(5, 4) = 5. In the third test case, one can show that no such p and q exist.
31155 3 4 2 521 1
YES 1  1  YES 1 3 4 2 5  5 2 3 1 4  NO 
['constructive algorithms', 'greedy', 'implementation', 'sortings', '*1300']