human
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 
The above is tricky. Write me a correct solution in PYTHON3.
 ... Can you provide a Python code to 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?
assistant
#Here is Python code to 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.

from functools import cmp_to_key
class Solution:

    def __init__(self):
        test = int(input())
        for t in range(0, test):
            n = int(input())
            self.solve(n)
    
    def solve(self, n):
        def cmp(a, b):
            x = len(f[a])
            y = len(f[b])
            return (x > y) - (x < y)

        f = [[] for i in range(0, n)]
        for i in range(0, n):
            for j in range(2, 5):
                if i + j >= 0 and i + j < n:
                    f[i].append(i + j)
                    f[i + j].append(i)
        res = []
        can = [i for i in range(0, n)]
        while len(res) < n:
            if not can:
                print("-1")
                return
            smallest = min(can, key=cmp_to_key(cmp))
            res.append(smallest)
            can = f[smallest]
            for i in can:
                f[i].remove(smallest)

        print(" ".join(list(map(str, [i + 1 for i in res]))))
            

Solution()