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 
FAST_IO = 0
if FAST_IO:
    import io, sys, atexit
    rr = iter(sys.stdin.read().splitlines()).next
    sys.stdout = _OUTPUT_BUFFER = io.BytesIO()
    @atexit.register
    def write():
        sys.__stdout__.write(_OUTPUT_BUFFER.getvalue())
else:
    rr = raw_input
rri = lambda: int(rr())
rrm = lambda: map(int, rr().split())

####

from collections import deque
####

def solve(N):
    if N == 1:
        return [1]
    if N == 2 or N == 3:
        return [-1]
    if N == 4:
        return [2,4,1,3]
    if N == 5:
        return [2,4,1,3,5]
    if N == 6:
        return [1,3,6,4,2,5]
    if N == 7:
        return [1,5,2,6,3,7,4]
    if N == 8:
        return [1,3,5,7,4,8,6,2]
    if N == 9:
        return [1,3,5,7,9,6,8,4,2]
    if N == 10:
        return [1,3,5,7,9,6,10,8,4,2]
    if N == 11:
        return [1,3,5,7,9,11,8,10,6,4,2]
    if N == 12:
        return [1,3,5,7,9,11,8,12,10,6,4,2]
    if N == 13:
        return [1,3,5,7,9,11,13,10,12,8,6,4,2]
        
    ans = []
    floor = 0
    while N >= 14:
        ans.append(floor + 1)
        ans.append(floor + 5)
        ans.append(floor + 2)
        ans.append(floor + 6)
        ans.append(floor + 3)
        ans.append(floor + 7)
        ans.append(floor + 4)
        floor += 7
        N -= 7
    if N == 0: return ans
    residue = solve(N)
    ans.extend(floor+x for x in residue)
    return ans

if 0:
    def check(a):
        if not all(2<=abs(a[i] - a[i+1])<=4 for i in xrange(len(a) - 1)):
            return False
        if len(set(a))!=len(a):
            return False
        return True
        
    for n in xrange(1, 200):
        #print solve(n)
        ans = solve(n)
        if n > 3: assert check(ans), n
    print('good')

T = rri()
for _ in xrange(T):
    print " ".join(map(str, solve(rri())))
