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 
n=int(input())
for _ in range(n):
    p=int(input())
    if p<4:
        print(-1)
    elif p==4:
        print(3,1,4,2)
    elif p==5:
        print(1,3,5,2,4)
    else:
        # l=[]
        for i in range(1,p+1,2):
            print(i,end=" ")
            # l.append(i)
        if p%2==0:
            print(p-4,end=" ")
            # l.append(p-4)
            print(p,p-2,end=" ")
            # l.append(p)
            # l.append(p-2)
            for i in range(p-6,1,-2):
                print(i,end=" ")
                # l.append(i)
            print("")
        else:
            print(p-3,end=" ")
            # l.append(p-3)
            print(p-1,p-5,end=" ")
            # l.append(p-1)
            # l.append(p-5)
            for i in range(p-7,1,-2):
                print(i,end=" ")
                # l.append(i)
            print("")
        # for i in range(p-1):
        #     if abs(l[i]-l[i+1])<2 or abs(l[i]-l[i+1])>4:
        #         print(p)
        #         break
