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 
'''
from itertools import permutations
a = list(permutations([1,2,3,4,5]))
for x in a:
    f = 0
    #x = [2,4,6,8,10,12] + list(x)
    for i in range(1,len(x)):
        if 2<=abs(x[i]-x[i-1]) <=4:
            p = 1
        else:
            f = 1
    if f==0 and x[0]==2 :
        print x
'''
for _ in range(input()):
    n = input()
    l = []
    if n<4:
        print -1
        continue
    for i in range(1,n/2+1):
        print 2*i,
    p = 2*i-3
    while p!=1:
        print p,
        l.append(p)
        p = max(1,p-4)
    i = 0
    while 1:
        if 2*i + 1 > n:
            break
        if 2*i + 1 not in l:
            print 2*i + 1,
        i+=1
    
    print 
        
