C. Ammar-utiful Permutations
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

Turns out Ammar is not that bad at setting problems, as he came up with this problem himself. He wasn't as good as the other judges at coming up with new and fun problem ideas. So instead, he came up with the answer to the problem first, and that's how he proposed this problem.

We define a permutation $$$P$$$ of length $$$N$$$ to be called an Ammar-utiful permutation if it satisfies the following condition:

  • There's exactly one index $$$i$$$, $$$(1 \le i \lt N)$$$ where $$$P_i + P_{i + 1}$$$ is odd.

Given an integer $$$N$$$, you must find an Ammar-utiful permutation $$$P$$$ of length $$$N$$$.

A permutation of length $$$N$$$ is an array of size $$$N$$$ consisting of $$$N$$$ distinct integers in the range $$$[1, N]$$$. For example, $$$\{3, 2, 4, 1\}$$$ is a permutation of length $$$4$$$, but $$$\{3, 3, 1, 4\}$$$ and $$$\{2, 3, 4, 5\}$$$ are not.

Note that if there are multiple valid permutations, print any.

Input

The first line of input contains a single integer $$$T$$$ $$$(1 \le T \le 1000)$$$ — the number of testcases.

The only line of each testcase contains a single integer $$$N$$$ $$$(2 \le N \le 10^5)$$$ – the size of the permutation $$$P$$$.

It's guaranteed that the sum of $$$N$$$ over all testcases does not exceed $$$10^5$$$

Output

For each testcase, print in a separate line any permutation of length $$$N$$$ that is an Ammar-utiful permutation.

Example
Input
1
7
Output
6 2 4 3 1 7 5