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
import sys
input = sys.stdin.readline

pat4 = [2, 4, 1, 3]
pat5 = [2, 4, 1, 3, 5]
pat6 = [2, 4, 1, 5, 3, 6]
pat7 = [2, 4, 1, 5, 7, 3, 6]
t = int(input())
for _ in range(t):
    n = int(input())
    if n < 4:
        print("-1")
        continue
    loop = n // 4 - 1
    rest = n % 4 + 4
    ans = []
    for i in range(loop):
        base = i * 4
        ans += [base + 2, base + 4, base + 1, base + 3]
    if rest == 4:
        for item in pat4:
            ans.append(loop * 4 + item)
    elif rest == 5:
        for item in pat5:
            ans.append(loop * 4 + item)
    elif rest == 6:
        for item in pat6:
            ans.append(loop * 4 + item)
    elif rest == 7:
        for item in pat7:
            ans.append(loop * 4 + item)
    print(*ans)