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 
# -*- coding: utf-8 -*-
"""
Created on Sat May  9 10:00:54 2020

@author: xdcao@zju.edu.cn
"""
def solve(n):
    if n == 2 or n == 3:
        print(-1)
        return
    if n == 4:
        print(' '.join(list(map(str, [2, 4, 1, 3]))))
        return
    if n == 5:
        print(' '.join(list(map(str, [1,3,5,2,4]))))
        return
    if n == 6:
        print(' '.join(list(map(str, [1,4,6,3,5,2]))))
        print()
    else:
        arr1 = []
        arr2 = []
        for i in range(1, n+1):
            if i % 2 == 1:
                arr1.append(i)
            else:
                arr2.append(i)        
        if n % 2 == 1:
            t1 = arr2.pop()
            t2 = arr2.pop()
            arr2.append(t1)
            arr2.append(t2)
            arr2 = arr2[::-1]
            print(' '.join(list(map(str, arr1+arr2))))
        else:
            t1 = arr1.pop()
            t2 = arr1.pop()
            t3 = arr2.pop()
            t4 = arr2.pop()
            arr1.append(t4)
            arr1.append(t3)
            arr2.append(t1)
            arr2.append(t2)
            arr2 = arr2[::-1]
            print(' '.join(list(map(str, arr1+arr2))))
        
T = int(input())

for ti in range(1, T+1):
    n = int(input())
    solve(n)