Codeforces Round 640 (Div. 4) |
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Finished |

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constructive algorithms

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G. Special Permutation

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputA permutation of length $$$n$$$ is an array $$$p=[p_1,p_2,\dots,p_n]$$$, which contains every integer from $$$1$$$ to $$$n$$$ (inclusive) and, moreover, each number appears exactly once. For example, $$$p=[3,1,4,2,5]$$$ is a permutation of length $$$5$$$.

For a given number $$$n$$$ ($$$n \ge 2$$$), find a permutation $$$p$$$ in which absolute difference (that is, the absolute value of difference) of any two neighboring (adjacent) elements is between $$$2$$$ and $$$4$$$, inclusive. Formally, find such permutation $$$p$$$ that $$$2 \le |p_i - p_{i+1}| \le 4$$$ for each $$$i$$$ ($$$1 \le i < n$$$).

Print any such permutation for the given integer $$$n$$$ or determine that it does not exist.

Input

The first line contains an integer $$$t$$$ ($$$1 \le t \le 100$$$) — the number of test cases in the input. Then $$$t$$$ test cases follow.

Each test case is described by a single line containing an integer $$$n$$$ ($$$2 \le n \le 1000$$$).

Output

Print $$$t$$$ lines. Print a permutation that meets the given requirements. If there are several such permutations, then print any of them. If no such permutation exists, print -1.

Example

Input

6 10 2 4 6 7 13

Output

9 6 10 8 4 7 3 1 5 2 -1 3 1 4 2 5 3 6 2 4 1 5 1 3 6 2 4 7 13 9 7 11 8 4 1 3 5 2 6 10 12

Codeforces (c) Copyright 2010-2024 Mike Mirzayanov

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