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 sys import stdin,stdout
for _ in range(int(stdin.readline())):
    n=int(input())
    seq=[int(k) for k in range(1,n+1)]
    if n==2 or n==3:
        print(-1)
    else:
        loop=n//5
        rem=n%5
        lis=[]
        for i in range(loop):
            if i%2==0:
                for j in range(5*i,5*(i+1)):
                    if j%2==0:
                        lis.append(seq[j])
                for j in range(5*i,5*(i+1)):
                    if j%2!=0:
                        lis.append(seq[j])
            else:
                for j in range(5*i,5*(i+1)):
                    if j%2!=0:
                        lis.append(seq[j])
                for j in range(5*i,5*(i+1)):
                    if j%2==0:
                        lis.append(seq[j])
        if rem==2:
            el=lis[-1]
            lis.remove(el)
            val1=seq[n-rem]
            val2=seq[(n-rem)+1]
            lis.append(val1)
            lis.append(el)
            lis.append(val2)
        elif rem==3:
            el=lis[-1]
            lis.remove(el)
            val1=seq[n-rem]
            val2=seq[(n-rem)+1]
            val3=seq[(n-rem)+2]
            lis.append(val1)
            lis.append(val3)
            lis.append(el)
            lis.append(val2)
            
        elif rem==4:
            val1=seq[n-rem]
            val2=seq[(n-rem)+1]
            val3=seq[(n-rem)+2]
            val4=seq[(n-rem)+3]
            lis.append(val2)
            lis.append(val4)
            lis.append(val1)
            lis.append(val3)
        else:
            for j in range(n-rem,n):
                if j%2!=0:
                    lis.append(seq[j])
            for j in range(n-rem,n):
                if j%2==0:
                    lis.append(seq[j])
        print(*lis)

            
                
            
                               