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 
import sys
range = xrange
input = raw_input

rint = lambda: int(input())
rints = lambda: [int(x) for x in input().split()]

def ablock(i):
    if i == 4:
        return [2,0,3,1]
    elif i == 5:
        return [2,0,3,1,4]
    elif i == 6:
        return [2,0,4,1,3,5]
    else:
        return [2,0,4,1,5,3,6]

def bblock(i):
    if i == 4:
        return [1,3,0,2]
    elif i == 5:
        return [1,3,0,2,4]
    elif i == 6:
        return [1,4,0,3,5,2]
    else:
        return [1,4,0,3,5,2,6]

t = int(input())
for _ in range(t):
    n = rint()
    if n == 1:
        print 1
        continue
    if 1 < n < 4:
        print -1
        continue
    
    par = 1
    ans = []
    while n > 7:
        tmp = (ablock if par else bblock)(4)
        tmp = [len(ans) + 1 + x for x in tmp]
        ans += tmp
        par ^= 1
        n -= 4

    tmp = (ablock if par else bblock)(n)
    tmp = [len(ans) + 1 + x for x in tmp]
    ans += tmp
    par ^= 1
    
    print ' '.join(str(x) for x in ans)
