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 
t = int(input())

if t<1 or t>100: # t the number of test cases, t =2
    exit()
else:

    dup= []

    for i in range(t):
        n= int(input())
        dup.append(n)  # dup is a list that stores the input e.g [5,10] the 2 values of n



    l = [] # a list for looping





    for i in range(t): # i in range(2)

         if dup[i] < 2 or dup[i]>1000:
             print(-1)
             continue
         elif dup[i]==2 or dup[i]==3:
             print(-1)
             continue
         else:

             for j in range(dup[i]+1): # j =0 and dup[0]=5, dup[1]=10

                 if j==0:
                     continue
                 elif j<dup[i]+1:   # l = [1,2,3,4,5,1,2,3,4,5,6,7,8,9,10]
                     l.append(j)




             k = [] # Another looping variable


             for j in range(int(dup[i])):  # j in range(5) while i =0 and j in range(10) while i =1









                    if dup[i]%2==0 and dup[i]>5:

                            if j==0:
                                continue
                            elif j%2!=0:
                                k.append(l[j])
                                if j%2!=0 and j ==(dup[i]-1):
                                    k.append(l[j-3])
                                    k.append(l[j-1])
                                    k.append(l[j-5])

                                    for a in reversed(range(l[j]-6)):
                                        if a%2==0:
                                            k.append(l[a])
                    elif dup[i] % 2 != 0 and dup[i]>5:


                                if j % 2 == 0:
                                    k.append(l[j])
                                    if j % 2 == 0 and j == (dup[i] - 1):
                                        k.append(l[j - 3])

                                        k.append(l[j - 1])

                                        k.append(l[j - 5])


                                        for a in reversed(range(l[j] - 6)):
                                            if a % 2 != 0:
                                                k.append(l[a])
                    elif dup[i]==4:
                        if j==0:

                            k.append(l[j+1])

                            k.append(l[j +3])
                            k.append(l[j])
                            k.append(l[j + 2])

                    elif dup[i]==5:
                        if j==0:

                            k.append(l[j])
                            k.append(l[j + 2])
                            k.append(l[j + 4])
                            k.append(l[j + 1])
                            k.append(l[j + 3])










                    else:
                            continue



             if k == []:
                 l = []
                 continue

             else:
                 s= ", ".join( repr(e) for e in k)
                 l = []

                 s = s.replace(",", "")
                 print(s)





































































