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 collections import Counter,defaultdict,deque
#import heapq as hq
#import itertools
from operator import itemgetter
#from itertools import count, islice
#from functools import reduce
#alph = 'abcdefghijklmnopqrstuvwxyz'
#from math import factorial as fact
#a,b = [int(x) for x in input().split()]
#sarr = [x for x in input().strip().split()]
import math
import sys
input=sys.stdin.readline
#sys.setrecursionlimit(2**30)

def solve():
    n = int(input())
    if n<=3:
        print(-1)
        return
    arr = [0]*n
    p1 = 0
    p2 = n-1
    par = 1
    for i in range(1,n+1):
        if par:
            arr[p1]=i
            p1+=1
        else:
            arr[p2]=i
            p2-=1
        par^=1
    if n&1:
        ind = n-(n+1)//2 + 2
        arr[ind],arr[ind-1] = arr[ind-1],arr[ind]
    else:
        ind = (n+1)//2-1
        arr[ind],arr[ind-1] = arr[ind-1],arr[ind]
    print(*arr)

                

tt = int(input())
for test in range(tt):
    solve()















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