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):

    tmp = a[i+2]
    a[i+2] = a[i+1]
    a[i+1] = a[i]
    a[i] = tmp
    ans.append(i+1)
    #print (*a)

tt = int(input())

for loop in range(tt):

    n = int(input())
    a = list(map(int,input().split()))
    sa = 0.0001

    
    lis = [sa] * 501
    
    b1 = []
    b2 = []
    
    f2 = True
    for i in range(n):
        if lis[a[i]] != sa and f2:
            b1.append(a[i] + lis[a[i]])
            b2.append(a[i])
            f2 = False
        else:
            b1.append(a[i] + lis[a[i]])
            b2.append(a[i] + lis[a[i]])

        lis[a[i]] += sa

    #print (b1)
    #print (b2)   

    ans = []
    a = b1
    for last in range(n-3):

        mi = last
        for i in range(last,n):
            if a[i] < a[mi]:
                mi = i

        while mi != last:

            if mi - last >= 2:
                swap(mi-2)
                mi -= 2
            else:
                swap(mi)
                mi += 1

    while not ( a[-3] < a[-2] and a[-2] < a[-1] ):
        swap(n-3)

        if len(ans) > n**2:
            break

    if len(ans) <= n**2:
        
        print (len(ans))
        print (*ans)
        continue

    ans = []
    a = b2
    for last in range(n-3):

        mi = last
        for i in range(last,n):
            if a[i] < a[mi]:
                mi = i

        while mi != last:

            if mi - last >= 2:
                swap(mi-2)
                mi -= 2
            else:
                swap(mi)
                mi += 1

    while not ( a[-3] < a[-2] and a[-2] < a[-1] ):
        swap(n-3)

        if len(ans) > n**2:
            break

    if len(ans) <= n**2:
        
        print (len(ans))
        print (*ans)
        continue

    print (-1)