1352_G. Special Permutation
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 
```python
"""
Author: guiferviz
Time: 2020-05-09 16:35:02
"""

def solve():
    n = int(input())
    if n < 4:
        print(-1)
    elif n == 4:
        print("3 1 4 2")
    else:
        sol = []
        i = 1
        while i <= n:
            sol.append(i)
            i += 2
        i = sol[-1]
        val = i - 3
        i += -1 if i == n else 1
        sol.append(val)
        while i > 0:
            if i != val: sol.append(i)
            i -= 2
        # Print solution.
        print(" ".join(map(str, sol)))
        # Check solution.
        for i in range(n-1):
            if sol[i] > n:
                raise ValueError("Value out of range")
            diff = abs(sol[i] - sol[i+1])
            if diff > 4 or diff < 2:
                raise ValueError(f"diff={diff}, sol[{i}]={sol[i]} + sol[{i+1}]={sol[i+1]}")


def main():
    t = int(input())
    for _ in range(t):
        solve()


if __name__ == "__main__":
    main()


```