问题 J: Permutation and Primes

链接：https://ac.nowcoder.com/acm/contest/57362/J
来源：牛客网
Given $n$, you should construct a permutation $P$ of $\{1,2,\dots ,n\}$ satisfying that for all $1\le i<n$, either Pi+Pi+1P_i + P_{i+1}Pi+Pi+1 is an odd prime or ∣Pi−Pi+1∣|P_i - P_{i+1}|∣Pi−Pi+1∣ is an odd prime.

If multiple solutions exist, print any of them. If no solution, print "-1" in one line.

The first line contains one integer $T$ (1≤T≤1051\le T \le 10^51≤T≤105), denoting the number of test cases.
For each test case, input only one line containing one integer $n$ (2≤n≤1052\le n \le 10^52≤n≤105).
It is guaranteed that the sum of $n$ among all test cases in one test file does not exceed 10610^6106.

For each test case:

If solution exists, print one line containing $n$ integers P1,P2,…,PnP_1, P_2, \ldots, P_nP1,P2,…,Pn (1≤Pi≤n1 \le P_i \le n1≤Pi≤n, ∀1≤i<j≤n,Pi≠Pj\forall \, 1 \le i < j \le n, P_i \neq P_j∀1≤i<j≤n,Pi=Pj), denoting the permutation you construct.
If no solution, print "-1" in one line.

2
3
5

1 2 3
5 2 1 4 3

In the first test case, $1+2=3,2+3=5$ are odd primes.
In the second test case, $|5-2|=3,2+1=3,|1-4|=3,4+3=7$ are odd primes.