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())
for g in range(0,t):
    n=int(input())
    if(n==2):
        print(-1)
    elif(n==3):
        print(-1)
    elif(n%2==0):
        even=[]
        odd=[]
        for i in range(1,n+1):
            if(i%2==0):
                even.append(i)
            else:
                odd.append(i)
        even.append(odd[int(n/2)-2])
        even.append(odd[int(n/2)-1])
        for i in range(int(n/2)-3,-1,-1):
            even.append(odd[i])
        for i in range(0,n):
            print(even[i],end=" ")
        print("")
    elif(n%2!=0):
        even=[]
        odd=[]
        for i in range(1,n+1):
            if(i%2==0):
                even.append(i)
            else:
                odd.append(i)
        odd.append(even[int(n/2)-2])
        odd.append(even[int(n/2)-1])
        for i in range(int(n/2)-3,-1,-1):
            odd.append(even[i])
        for i in range(0,n):
            print(odd[i],end=" ")
        print("")