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 
def adv4(num):
    return [num + 2, num, num + 3, num + 1, num + 4]

def adv5(num):
    return [num + 3, num + 1, num + 4, num + 2, num + 5]

def adv6(num):
    return [num + 4, num + 2, num + 5, num + 1, num + 3, num + 6]

def adv7(num):
    return [num + 4, num + 2, num + 6, num + 3, num + 1, num + 5, num + 7]

def adv8(num):
    return [num + 3, num + 7, num + 4, num + 1, num + 5, num + 2, num + 6, num + 8]
    
def solve():
    n = int(input())
    sequence = []
    
    if n < 4:
        return [-1]
    elif n == 4:
        return [2, 4, 1, 3]
    
    curr = 1
    if n % 5 == 1:
        sequence.append(1)
        sequence.extend(adv5(curr))
        curr += 5
    elif n % 5 == 2:
        sequence.append(1)
        sequence.extend(adv6(curr))
        curr += 6
    elif n % 5 == 3:
        sequence.append(1)
        sequence.extend(adv7(curr))
        curr += 7
    elif n % 5 == 4:
        sequence.append(1)
        sequence.extend(adv8(curr))
        curr += 8
    else:
        sequence.extend(adv4(curr))
        curr += 4
    
    while curr < n:
        sequence.extend(adv5(curr))
        curr += 5
    return sequence


T = int(input())
for i in range(T):
    print(*solve())