A permutation is a sequenceintegers, where each integer from to appears exactly once. For example, , , are permutations, while , , are not.
Given a permutation, we construct an array , where .
A permutation of numbers super-permutation if is also a permutation of length .is called a
Grisha became interested whether a super-permutation of length exists. Help him solve this non-trivial problem. Output any super-permutation of length , if it exists. Otherwise, output .
The first line contains a single integer( ) — the number of test cases. The description of the test cases follows.
Each test case consists of a single line containing one integer( ) — the length of the desired permutation.
The sum ofover all test cases does not exceed .
For each test case, output in a separate line:
- super-permutation of length , if it exists. integers — a
- , otherwise.
If there are several suitable permutations, output any of them.