Woburn Challenge 1999 - Suicidal

The Impossible Mission Force had some cutbacks and Ethan Hunt was disavowed. His story is now told in the sequel to the popular Good Will Hunting, tentatively titled Good Ethan Hunt. Ethan needs to pay the bills in his currently unemployed state and has taken a job as a janitor at a local college. Here, his tasks include resetting the key combinations to several doors periodically. However, the man's a genius and choosing a random code would be beneath him and so he will reset the code in the following way: The code will involve all the numbers from ~0~ to ~n~, where ~n \le 15\,000~. The code will be a permutation of the numbers ~0~ to ~n~ such that no ~k~-term subsequence (~k \ge 3~) of these numbers forms an arithmetic sequence. Note that "subsequence" implies that the elements are in the same relative order as in the original code.

For example, if ~n = 4~, you must use all the numbers from ~0~ to ~4~ and a valid code would be ~\{3, 4, 1, 0, 2\}~. Your task is to generate ONE such code given a value for ~n~.

Input Specification

~1~st line: ~\text{# of inputs} = m~, the number of test cases.
Next ~m~ lines: Different values for ~n~.

Output Specification

For each value of ~n~, output ONE valid code (each code on a separate line).

Sample Input

1
4

Sample Output

3 4 1 0 2