Construct the Lexicographically Largest Valid Sequence

You are provided with a positive integer N. The goal is to generate the lexicographically largest sequence of length 2*N - 1, containing integers ranging from 1 to N, such that:

1. The integer 1 appears exactly once in the sequence.
2. Every integer from 2 to N (inclusive) appears exactly twice in the sequence.
3. For each integer i from 2 to N, the distance between its two occurrences is exactly i.

Input:

The first line contains an integer, 'T', indicating the number of test cases. For each test case, there is one line containing a single integer N.

Output:

For each test case, output a single line with 2*N - 1 space-separated integers representing the lexicographically largest sequence.

Example:

Input:

2
3
4

Output:

3 1 2 3 2
4 2 3 4 3 2 1 4

Constraints:

• 1 <= T <= 100
• 1 <= N <= 20

Note: You are not required to print the output. Implement the function to generate the sequence.