Special Permutation

A permutation of length n is an array p=[p_1,p_2,...,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 ≥ 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 ≤ |p_i - p_{i+1}| ≤ 4 for each i (1 ≤ 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 ≤ t ≤ 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 ≤ n ≤ 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

inputFormat

Input

The first line contains an integer t (1 ≤ t ≤ 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 ≤ n ≤ 1000).

outputFormat

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

样例

6
10
2
4
6
7
13

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

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