G. Unequal Adjacent Elementstime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputYou are given an array a consisting of n positive integers. Find any permutation p of [1,2,\dots,n] such that:  p_{i-2} < p_i for all i, where 3 \leq i \leq n, and  a_{p_{i-1}} \neq a_{p_i} for all i, where 2 \leq i \leq n. Or report that no such permutation exists.InputEach test contains multiple test cases. The first line contains a single integer t (1 \leq t \leq 10^5) — the number of test cases. The description of the test cases follows.The first line of each test case contains a single integer n (3 \leq n \leq 3 \cdot 10^5) — the length of the array a.The second line of each test case contains n space-separated integers a_1,a_2,\ldots,a_n (1 \leq a_i \leq n) — representing the array a.It is guaranteed that the sum of n over all test cases does not exceed 3 \cdot 10^5.OutputFor each test case, output "NO" if no such permutation exists, otherwise output "YES" in the first line and print the permutation p in the next line.In case there are multiple permutations, print any one of them.You can output "YES" and "NO" in any case (for example, the strings "yEs", "yes", "Yes" and "YES" will be recognized as a positive response).ExampleInput
431 2 141 2 3 431 1 171 2 1 1 3 1 4Output
YES
1 2 3
YES
3 1 4 2
NO
YES
1 2 3 5 4 7 6
NoteIn the first test case, p=[1,2,3] is the only permutation of [1,2,3] that satisfy the given constraints.In the second test case, [1,3,2,4], [2,1,4,3] and some other permutations are also acceptable.In the third test case, it can be proved that there does not exist any permutation of [1,2,3] satisfying the given constraints.
431 2 141 2 3 431 1 171 2 1 1 3 1 4
YES 1 2 3 YES 3 1 4 2 NO YES 1 2 3 5 4 7 6 
['constructive algorithms', 'sortings', '*3100']