Problem: You are given an array a consisting of n integers (it is guaranteed that n is even, i.e. divisible by 2). All a_i does not exceed some integer k.

Your task is to replace the minimum number of elements (replacement is the following operation: choose some index i from 1 to n and replace a_i with some integer in range [1; k]) to satisfy the following conditions:

  * after all replacements, all a_i are positive integers not greater than k; 
  * for all i from 1 to n/2 the following equation is true: a_i + a_{n - i + 1} = x, where x should be the same for all n/2 pairs of elements. 



You have to answer t independent test cases.

Input

The first line of the input contains one integer t (1 ≤ t ≤ 10^4) — the number of test cases. Then t test cases follow.

The first line of the test case contains two integers n and k (2 ≤ n ≤ 2 ⋅ 10^5, 1 ≤ k ≤ 2 ⋅ 10^5) — the length of a and the maximum possible value of some a_i correspondingly. It is guratanteed that n is even (i.e. divisible by 2). The second line of the test case contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ k), where a_i is the i-th element of a.

It is guaranteed that the sum of n (as well as the sum of k) over all test cases does not exceed 2 ⋅ 10^5 (∑ n ≤ 2 ⋅ 10^5, ∑ k ≤ 2 ⋅ 10^5).

Output

For each test case, print the answer — the minimum number of elements you have to replace in a to satisfy the conditions from the problem statement.

Example

Input


4
4 2
1 2 1 2
4 3
1 2 2 1
8 7
6 1 1 7 6 3 4 6
6 6
5 2 6 1 3 4


Output


0
1
4
2

Solution (in PYTHON3):

Solution:
def swap(i,j):
    arr[i],arr[j]=arr[j],arr[i]
def inversion(li):
    n=len(li)
    inversions=0
    for i in range(n):
        for j in range(i+1,n):
            if(li[j]<li[i]):
                inversions+=1
    return inversions
def right_shift(i):
    arr[i],arr[i+1],arr[i+2]=[arr[i+2],arr[i],arr[i+1]]
t=int(input())
for you in range(t):
    n=int(input())
    l=input().split()
    arr=[int(i) for i in l]
    arr1=list(arr)
    lfi=[]
    lo=[]
    for i in range(n):
        lo.append((arr[i],i))
    lo.sort()
    hashi=dict()
    for i in range(n):
        hashi[lo[i][1]]=i+1
    arr=[]
    for i in range(n):
        arr.append(hashi[i])
    poss=1
    if(inversion(arr)%2):
        for i in range(n):
            for j in range(i+1,n):
                if(arr1[i]==arr1[j]):
                    swap(i,j)
                    poss=0
                    break
            if(poss==0):
                break
    z=list(arr)
    z.sort()
    for j in range(n):
        for i in range(n-2-j):
            maxa=max(arr[i],arr[i+1],arr[i+2])
            if(maxa==arr[i+2]):
                continue
            elif(maxa==arr[i+1]):
                lfi.append(i)
                right_shift(i)
            else:
                lfi.append(i)
                lfi.append(i)
                right_shift(i)
                right_shift(i)
    if(arr==z):
        print(len(lfi))
        for i in lfi:
            print(i+1,end=" ")
        print()
    else:
        print(-1)