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 itertools

perms = {}
for t in range(1, 10):
    l = list(itertools.permutations([i for i in range(1, t + 1)]))
    perms[t] = l

def is_good_perm(perm):
    n = len(perm)
    for i in range(n-1):
        a = abs(perm[i] - perm[i+1])
        if a >= 2 and a <= 4:
            continue
        else:
            return False
    return True

T = int(input())
for t in range(T):
    # print("-"*40)
    n = int(input())
    if n < 4:
        print(-1)
    else:
        # print("n", n)
        nb_multiple_5 = n // 5
        # print("nb_multiple_5", nb_multiple_5)
        if nb_multiple_5 > 1:
            # First we construct the
            remaining_numbers = n - (nb_multiple_5 - 1) * 5

            # We have (nb_multiple_5 - 1) * 5 numbers
            # to fill like [1, 4, 2, 5, 3] and so on with increment of 5
            res = []
            # print("remaining_numbers :", remaining_numbers)
            for i in range(nb_multiple_5 - 1):
                s = [1, 4, 2, 5, 3]
                s = list(map(lambda x: x + (5*i), s))
                res += s
            # print("res:", res)

            # Next we need to find a perm with remaining_numbers:
            assert remaining_numbers < 10
            for perm in perms[remaining_numbers]:
                if is_good_perm(perm):
                    # print("is_good_perm")
                    # print(perm)
                    perm = list(perm)
                    perm = list(map(lambda x: x + (5*(nb_multiple_5-1)), perm))
                    # print("perm", perm)
                    res += list(perm)
                    # print(res)
                    break
        else:
            for perm in perms[n]:
                if is_good_perm(perm):
                    # print("is_good_perm")
                    res = perm
                    break

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