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:
t=1
t=int(input())
for _ in range(t):
    n=int(input())
    a=list(map(int,input().split()))
    a=[(a[i],i) for i in range(n)]
    a.sort()
    rev=0
    for i in range(n):
        val,id=a[i]
        for j in range(i):
            sval,sid=a[j]
            if sid>id:
                rev+=1
    if rev%2==1:
        for i in range(1,n):
            if a[i][0]==a[i-1][0]:
                a[i-1],a[i]=a[i],a[i-1]
                break
        else:
            print(-1)
            continue

    A=[-1]*n
    for i in range(n):
        val,id=a[i]
        A[id]=i+1

    a=[0]+A
    ID=[-1]*(n+1)
    for i in range(1,n+1):
        ID[a[i]]=i

    goal=1
    res=[]

    def swap(i):
        res.append(i)
        ID[a[i]],ID[a[i+1]],ID[a[i+2]]=i+1,i+2,i
        a[i],a[i+1],a[i+2]=a[i+2],a[i],a[i+1]

    while n>=goal:
        start=ID[goal]
        if (start-goal)%2==1:
            if start==n:
                swap(start-2)
                swap(start-2)
                start=ID[goal]
            else:
                swap(start-1)
                start=ID[goal]
        while start!=goal:
            swap(start-2)
            start=ID[goal]
        goal+=1

    print(len(res))
    print(*res)