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 
T = int(input())
r = 1
while r<=T:
    n = int(input())
    if n<4: 
        print(-1)
        r += 1
        continue
    if n==4:
        print(3,1,4,2)
        r += 1
        continue
    block = [3,1,5,2,4]
    rest = n%5
    
    ans = []
    for i in range(n//5-1):
        ans += [3+5*i,1+5*i,5+5*i,2+5*i,4+5*i]

    rest = n%5+5

    base = [5*(n//5-1)]*rest

    if n%5==0:
        arr = [3,1,5,2,4]
    if n%5==1:
        arr = [3,1,5,2,4,6]
    if n%5==2:
        arr = [3,1,4,6,2,5,7]
    if n%5==3:
        arr = [3,1,4,2,6,8,5,7]
    if n%5==4:
        arr = [3,1,5,2,4,8,6,9,7]




    for i in range(rest):
        base[i] += arr[i]
    ans += base
  
    print(" ".join(map(str,ans)))
    r += 1

