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 
visited = []

def isValidPair(i, j):
    return not (abs(i - j) > 4 or abs(i - j) < 2)

def isValidPerm(arr):
    if len(arr) != len(visited):
        return False

    for i in range(1, len(arr)):
        if not isValidPair(arr[i - 1], arr[i]):
            return False

    return True

def findPerm(cur, cura):
    # print(cur, cura, visited, isValidPerm(cura + [cur]))
    if visited[cur - 1] != -1:
        return []
    visited[cur - 1] = 1
    cura.append(cur)
    if isValidPerm(cura):
        return cura
    if len(cura) >= len(visited):
        return []

    for i in range(cur - 4, cur + 5):
        if i > 0 and i <= len(visited) and isValidPair(i, cur):
            newa = findPerm(i, cura)
            if len(newa) == len(visited):
                return newa

    return []

t = int(input())

while t > 0:

    n = int(input())
    arr = []
    for i in range(1, n + 1):
        visited = [-1] * n
        arr = findPerm(i, [])
        if len(arr) == n:
            break

    if len(arr) == n:
        print(' '.join([str(x) for x in arr]))
    else:
        print(-1)


    t -= 1
