B. Birthdays!!!
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

Ridham's birthday is coming up and he really loves primes and permutations. Knowing this Aastik decided to gift Ridham a permutation $$$a$$$ of length $$$n$$$ such that $$$a_i + a_{n-i+1}$$$ is prime for all $$$i$$$ such that $$$1 \le i \le n$$$, but just when Aastik sat down to generate this permutation he realised that he did not know how to make such a permutation. Help Aastik to prepare the gift for Ridham.

A permutation of length $$$n$$$ is an array consisting of $$$n$$$ distinct integers from $$$1$$$ to $$$n$$$ in arbitrary order. For example, $$$[2,3,1,5,4]$$$ is a permutation, but $$$[1,2,2]$$$ is not a permutation ($$$2$$$ appears twice in the array), and $$$[1,3,4]$$$ is also not a permutation ($$$n = 3$$$ but there is $$$4$$$ in the array).

Input

The first line contains a single integer $$$t$$$ ($$$1 \le t \le 10^4$$$). The description of the test cases follows.

The first line and only line of each test case contains an integer $$$n$$$ ($$$1 \le n \le 10^6$$$) — the size of the permutation $$$a$$$.

The sum of $$$n$$$ over all testcases does not exceed $$$3 \cdot 10^6$$$.

Output

For each testcase, output $$$n$$$ integers — the elements of the required permutation. If it's not possible, output $$$-1$$$.

Example
Input
2
2
3
Output
1 2 
2 1 3