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 task(n):
    if n <= 3:
        print(-1)
        return

    if n == 4:
        print('3 1 4 2')
        return

    used = [False] * (n + 1)
    current = 1
    direction = 1
    directionChanged = False
    results = [1]
    used[1] = True

    while True:
        found = False
        if direction == 1:
            for i in [2, 4, 3]:
                if current + i <= n and not used[current + i]:
                    used[current + i] = True
                    current += i
                    results.append(current)
                    found = True
                    directionChanged = False
                    break
        else:
            for i in [-4, -3, -2]:
                if current + i >= 1 and not used[current + i]:
                    used[current + i] = True
                    current += i
                    results.append(current)
                    found = True
                    directionChanged = False
                    break
        if not found:
            if directionChanged:
                break
            else:
                directionChanged = True
                direction *= -1

    print(" ".join(map(str, results)))


t = int(input())
for i in range(0, t):
    n = int(input())
    task(n)
