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 
#!/usr/bin/env python3

T = int(input())

def ans(n):
    if n <= 3:
        return "-1"
    if n % 3 == 2:
        left_peak = n
    else:
        left_peak = n - 1

    if left_peak % 3 == 0:
        left = list(range(2, left_peak+1, 3))
        left[-1] += 1
        mid = list(range(3, left_peak, 3))[::-1]
        right = list(range(1, n+1, 3))

        ans = left + mid + right + [n-2]
        return ' '.join(str(x) for x in ans)
    else:
        left = list(range(2, left_peak+1, 3))
        mid = list(range(3, left_peak, 3))[::-1]
        right = list(range(1, n, 3))

        adj = []
        if n % 3 == 0:
            adj = [n]

        ans = left + mid + right + adj
        return ' '.join(str(x) for x in ans)
    
for t in range(T):
    n = int(input())
    print(ans(n))