human
Write me a Python program to 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 given the following:
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
assistant
#Here is Python program to 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.

import sys
sys.setrecursionlimit(1500)

def check(perm):
    for i in range(len(perm) - 1):
        if not (
            2 <= abs(perm[i] - perm[i - 1]) <= 4
        ):
            return False
    return True

import itertools
def brute(n):
    nums = list(range(1, n + 1))
    perms = list(itertools.permutations(nums))
    # print(f'{len(perms) = }')
    for perm in perms:
        if check(perm):
            return perm
    return []

def soln(n):
    def neighbors(i):
        result = []
        for cands in [range(i - 4, i - 1), range(i + 2, i + 5)]:
            for cand in cands:
                if 1 <= cand <= n:
                    result.append(cand)
        return result

    adj = {
        i : neighbors(i) for i in range(1, n + 1)
    }

    def dfs(i, currPath, seen):
        if len(currPath) == n:
            return currPath
        for j in adj[i]:
            if j not in seen:
                path = dfs(j, currPath + [j], seen | set([j]))
                if len(path) > 0:
                    return path
        return []
    
    return dfs(1, [], set([]))

def main():
    t = int(input())
    for _ in range(t):
        n = int(input())
        # result = brute(n)
        result = soln(n)

        # check(result)

        if len(result) == 0:
            resultStr = '-1'
        else:
            resultStr = ' '.join(str(x) for x in result)
        print(resultStr)

if __name__ == '__main__':
    main()