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 queue

def permutation():
    t = int(input())

    for i in range(0, t):
        num = int(input())
        if (num < 4):
            print("-1")
        else:
            plist = list()
            odds = list()
            evens = queue.Queue()

            for j in range(1, num+1):
                if(j % 2 == 0):
                    if(j == 2):
                        evens.put(4)
                    elif (j == 4):
                        evens.put(2)
                    else:
                        evens.put(j)
                else:
                    odds.append(j)

            while (len(odds) > 0):
                plist.append(odds.pop())
            while(not evens.empty()):
                plist.append(evens.get())
            
            for e in plist:
                print(e, end = " ")


                
                 
        





if __name__ == "__main__":
    permutation()