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 sys
input = sys.stdin.buffer.readline

def getInts():
    return [int(s) for s in input().split()]

def getInt():
    return int(input())

def getStrs():
    return [s for s in input().split()]

def getStr():
    return input()

def listStr():
    return list(input())

def solve():
    N = getInt()
    if N < 4:
        print(-1)
        return
    lookup = dict()
    lookup[4] = [2, 4, 1, 3]
    lookup[5] = [2, 5, 3, 1, 4]
    lookup[6] = [2, 4, 6, 3, 5, 1]
    lookup[7] = [2, 5, 1, 4, 6, 3, 7]
    start = 0
    ans = []
    while N > 7:
        for j in range(4):
            ans.append(start+lookup[4][j])
        N -= 4
        start += 4
    for element in lookup[N]:
        ans.append(start+element)
    print(*ans)
    #blocks of 4, when we hit 4, 5, 6 or 7 left, we use this
    
    
T = getInt()
for t in range(T):
    solve()
