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 
t = int(input())
while t:
    a2 = [2, 5, 1, 4, 6, 3]
    a1 = [2, 4, 1, 3, 5]
    a3 = [3, 7, 5, 1, 4, 6, 2]
    a0 = [2, 4, 1, 3]

    n = int(input())

    if n <= 3:
        print(-1)
        t -= 1
        continue
    diff = [3, 2, -3, 2]
    ans = []
    s = -1
    a = n % 4
    n = n - a - 4
    cur = 0
    while cur < n:
        s += diff[cur % 4]
        ans.append(s)
        cur += 1

    if a == 1:
        a1 = [x + n for x in a1]
        ans.extend(a1)
    elif a == 2:
        a2 = [x + n for x in a2]
        ans.extend(a2)
    elif a == 3:
        a3 = [x + n for x in a3]
        ans.extend(a3)
    else:
        a0 = [x + n for x in a0]
        ans.extend(a0)

    print(" ".join(map(str, ans)))
    t -= 1
