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:
q = int(input())

for _ in range(q):
    n, k = list(map(int, input().split(" ")))
    arr = list(map(int, input().split(" ")))
    ans = [0 for i in range(2*k + 1)]
#    count = 0
    if n == 2:
        print(0)
        continue
    
    for j in range(n//2):
        x, y = arr[j], arr[n-1-j]
        
        mid = x + y
            
        
        endr = max(x, y) + k
        endl = min(x, y) + 1
        
        if mid < endr:
            ans[mid+1] += 1
            
            if endr < 2*k:
                ans[endr+1] += 1
        
        
        
        

        if endl < mid:
            ans[endl] += 1
            ans[mid] -= 1
            
            if 2 < endl:
                ans[2] += 2
                ans[endl] -= 2
        
#        if endl != 2:
#            ans[2] += 2
#            ans[endl] -= 2
    
    for i in range(1, 2*k + 1):
        ans[i] += ans[i-1]
    
    ans[0], ans[1] =float("inf"), float("inf")  
#    print(ans)
    print(min(ans))