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 bisect
from sys import stdin, stdout
from itertools import repeat
import math
import random

# sys.stdin = open('input')

def inp(force_list=False):
    re = map(int, raw_input().split())
    if len(re) == 1 and not force_list:
        return re[0]
    return re

def inst():
    return raw_input().strip()

def gcd(x, y):
   while(y):
       x, y = y, x % y
   return x


def my_main():
    t = inp()
    for _ in range(t):
        n = inp()
        if n<=3:
            print -1
        else:
            ans = []
            now = 0
            for j in range(n/4-1):
                for k in [2, 4, 1, 3]:
                    ans.append(now+k)
                now += 4
            if n-(n/4-1)*4==4:
                for k in [2, 4, 1, 3]:
                    ans.append(now+k)
            elif n-(n/4-1)*4==5:
                for k in [2, 4, 1, 5, 3]:
                    ans.append(now+k)
            elif n-(n/4-1)*4==6:
                for k in [2, 6, 4, 1, 5, 3]:
                    ans.append(now+k)
            else:
                for k in [2, 6, 4, 1, 5, 7, 3]:
                    ans.append(now+k)
            print ' '.join(map(str, ans))

my_main()
