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:
import collections

line = input()
t = int(line)
for _i in range(t):
    
    line = input()
    n = int(line)
    line = input()
    nums = [int(i) for i in line.split(' ')]
    
    res = collections.deque()
    for i in range(n - 2):
        for j in range(n - 3, i-1, -1):
            if nums[j + 2] < nums[j + 1] and nums[j + 2] < nums[j]:
                a, b, c = nums[j + 2], nums[j + 1], nums[j]
                nums[j], nums[j + 1], nums[j + 2] = a, c, b
                res.append(j + 1)
        if nums[i] > nums[i + 1]:
            a, b, c = nums[i], nums[i + 1], nums[i + 2]
            nums[i], nums[i + 1], nums[i + 2] = b, c, a
            res.append(i + 1)
            res.append(i + 1)
        
        # print(nums)
    if nums[n - 3] == nums[n - 1] and nums[n - 2] > nums[n - 1]:
        res.append(n - 2)
        nums[n - 1], nums[n - 2] = nums[n - 2], nums[n - 1]
    if nums[-1] < nums[-2]:
        i = n - 2
        while i >= 0 and nums[i] != nums[i + 1]:
            i -= 1
        if i < 0:
            print(-1)
        else:
            while i < n - 2:
                res.append(i + 1)
                res.append(i + 1)
                i += 1
            print(len(res))
            for i in res:
                print(i, end= ' ')
            print()
    else:
        print(len(res))
        for i in res:
            print(i, end= ' ')
        print()