Time Limit: 1.5 s

Memory Limit: 256.0 MB

Description

You are given a permutation of integers from \(1\) to \(N\). Your task is to rearrange the permutation in such a way that for every consecutive pair of elements \(A_i\) and \(A_{i+1}\) in the array \(A[]\)( \(1 \leq i < N\)) the following two conditions are satisfied:

1. \(\gcd(A_i, A_{i+1}) = 1\)
2. \(|A_i - A_{i+1}| > 1\)

You must print any such valid rearrangement of the numbers from 1 to N if it exists.
If no such rearrangement exists, print -1.

Note : gcd means greatest common divisor, for example gcd(2,4)=2, gcd(15,10)=5 etc.
'| |' means absolute value, for example |2-4| = |-2|= 2.

Input

• The first line contains an integer \(T\)(\(1 \leq T \leq 100\) ) — the number of test cases.
• Each of the next \(T\) lines contains a single integer \(N\)(\(2 \leq N \leq 2000\)) — the length of the permutation.
• Sum of \(N\) overall test cases doesn't exceed 2000.

Output

• For each test case, print:
• A line containing \(N\) space-separated integers — a valid rearrangement of permutation \(N\). If multiple valid rearrangements exist, you are allowed to print any of them.
• if no such arrangement exists print -1.

Sample

3
4
5
8

-1
2 5 3 1 4 
2 5 8 3 7 4 1 6