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 
def arrange(N):
    l=[]
    f=[]
    if (N == 1) : 
        return [-1]
        return
    if (N == 2 or N == 3) : 
        return [-1]
    even = -1
    odd = -1
    if (N % 2 == 0): 
        even = N 
        odd = N - 1
    else : 
        odd = N 
        even = N - 1
    while (odd >= 1): 
        l.append(odd)
        odd = odd - 2
    while (even >= 2): 
        f.append(even)
        even = even - 2
    ans= l+sorted(f)
    return ans
for u in range(int(input())):
    n=int(input())
    x=arrange(n)
    if x==[-1]:
        print(-1)
    else:
        i=x.index(2)
        j=x.index(4)
        x[i],x[j]=x[j],x[i]
        print(*x)