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())
for tests in range(t):
    n = int(input())
    if n < 4:
        print(-1)
    else:
        answers = []
        evens = True
        minus_3 = False
        plus_2 = False
        minus_4 = False
        special_minus_2 = False
        for num in range(n):
            if special_minus_2:
                answers.append(answers[num-1] - 2)
                special_minus_2 = False
            elif evens:
                answers.append(2 * (num+1))
                if n - 2*(num+1) <= 1:
                    evens = False
            else:
                if not minus_3:
                    answers.append(answers[num-1] - 3)
                    minus_3 = True
                elif not plus_2:
                    if n % 2 == 1:
                        answers.append(answers[num-1] + 4)
                        special_minus_2 = True
                    else:
                        answers.append(answers[num-1] + 2)
                    plus_2 = True
                elif not minus_4:
                    answers.append(answers[num-1] - 4)
                    minus_4 = True
                else:
                    answers.append(answers[num-1] - 2)
        print(*answers)