HZNUOJ

Card Trick

Tags:
Time Limit:  1 s      Memory Limit:   64 MB
Submission:53     AC:31     Score:98.06

Description

The magician shuffles a small pack of cards, holds it face down and performs the following procedure:

This impressive trick works if the magician knows how to arrange the cards beforehand (and knows how to give a false shuffle). Your program has to determine the initial order of the cards for a given number of cards, 1 ≤ n ≤ 13.

Input

On the first line of the input is a single positive integer, telling the number of test cases to follow. Each case consists of one line containing the integer n.

Output

For each test case, output a line with the correct permutation of the values 1 to n, space separated. The first number showing the top card of the pack, etc…

Samples

input
2 4 5
output
2 1 4 3 3 1 4 5 2