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 
import sys
reader = (s.rstrip() for s in sys.stdin)
input = reader.__next__

def gift():
    for _ in range(t):
        num=int(input())
        if num<=3:
            yield -1
        else:
            ans=list(map(lambda x:x*2,range(1,num//2+1)))
            ans.append(num//2*2-3)
            for i in range(num//2+num%2,0,-1):
                if i*2-1!=num//2*2-3:
                    ans.append(i*2-1)
            yield " ".join(str(x) for x in ans)
        
                
            
if __name__ == '__main__':
    t= int(input())
    ans = gift()
    print(*ans,sep='\n')



##2 4 6 8 10 12 9 11 7 5 3 1
##2 4 1 3
