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 
import sys
# from math import sqrt, floor, factorial, gcd
from collections import Counter, deque
inp = sys.stdin.readline
read = lambda: list(map(int, inp().strip().split()))

def a():
    ans = ""
    for _ in range(int(inp())):
        n = int(inp()); tem = ""; x = 0; c = 0
        while n:
            if n%10:
                c += 1
                tem += str(n%10 * 10**x)+" "
            x +=1; n //= 10
        ans += str(c)+"\n"+tem +"\n"
    print(ans)

def b():
    ans = ""
    for _ in range(int(inp())):
        n, k = read()
        if n == k:
            ans += "YES\n"
            ans += "1 "*k + "\n"
        elif k > n:
            ans += "NO\n"
        elif n%2 == 0:
            if k <= n//2:
                ans += "YES\n"
                # v = 1 if n%2 else 2
                for i in range(k-1):
                    ans += "2 "
                    n -= 2
                ans += str(n)+"\n"
            elif k % 2 == 0:
                ans += "YES\n"
                for i in range(k-1):
                    ans += "1 "
                    n -= 1
                ans += str(n)+"\n"
            else:
                ans += "NO\n"
        else:
            if k%2 == 0:
                ans += "NO\n"
            else:
                ans += "YES\n"
                for i in range(k-1):
                    ans += "1 "
                    n -= 1
                ans += str(n)+"\n"
    print(ans)

def c():
    ans = ""
    for _ in range(int(inp())):
        k, n = read()
        t = n
        while n%k > k:
            n = n + n//k
        ans += str(t+n)+"\n"

    print(ans)

def d():
    ans = ""
    for _ in range(int(inp())):
        n = int(inp()); arr = read()
        tem = 0
        dic = Counter(arr)
        for i in range(n):
            s = arr[i]
            for j in range(i+1, n):
                s += arr[j]
                if s in dic:
                    # print(s)
                    tem += dic[s]
                    del(dic[s])
        ans += str(tem)+"\n"
    print(ans)



def g():
    ans = ""
    for _ in range(int(inp())):
        n = int(inp())
        if n <= 3:
            ans += "-1\n"
        else:
            que = deque(["2", "4", "1", "3"])
            i = 5
            while i <= n:
                if i%2==0:
                    que.appendleft(str(i))
                else:
                    que.append(str(i))
                i += 1
            ans += (" ").join(list(que))+"\n"
    print(ans)




if __name__ == "__main__":
	# a()
    # b()
    # c()
    # d()
    g()
