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 
for i1 in range(int(input())):
    n=int(input())
    if n==2 or n==3:
        print(-1)
        continue
    elif n==4:
        print(3,1,4,2)
        continue
    c=3
    d=2
    t=0
    l1=[1]*n
    # for i in range(1,n):
    i=1
    while i<n:
        if t==0 and c<=n and c+2<=n:
            l1[i]=c
            i=i+1
            c+=2
            l1[i]=c
            i=i+1
            c+=2
            t=1

        elif t==1 and (d<=n and d+2<=n):
            l1[i]=d
            i=i+1
            d+=2
            l1[i]=d
            i=i+1
            d+=2
            t=0
        elif t==1 or (d<=n and d+2<=n):
            l1[i]=d
            i=i+1
            d+=2
            l1[i]=d
            i=i+1
            d+=2
            t=0
        
        else:
            break
    if l1[-1]==1:        
        l1[-1]=n
        if n%2!=0:
            l1[-2]=l1[-3]
            l1[-3]=n-1
    if n%4==0:
        l1[-2]=n-1
        l1[-2],l1[-5]=l1[-5],l1[-2]
        l1[-2],l1[-3]=l1[-3],l1[-2]

    



    for i in l1:
        print(i,end=" ")
    print()
