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
"""T=int(input())
for _ in range(0,T):
    n=int(input())
    a,b=map(int,input().split())
    s=input()
    s=[int(x) for x in input().split()]
    for i in range(0,len(s)):
        a,b=map(int,input().split())"""



T=int(input())
for _ in range(0,T):
    n,k=map(int,input().split())
    s=[int(x) for x in input().split()]
    dp=[0]*((2*k)+5)
    tt=[0]*((2*k)+5)
    for i in range(n//2):
        a=min(s[i],s[n-i-1])
        b=max(s[i],s[n-i-1])
        low=a+1
        high=min(b+k,2*k)
        dp[low]+=1
        dp[high+1]-=1

        dp[2]+=2
        dp[low]-=2
        dp[high+1]+=2
        dp[(2*k)+1]-=2

        tt[a+b]-=1

    ans=(2*n)
    for i in range(3,len(dp)):
        dp[i]+=dp[i-1]

    for i in range(2,(2*k)+1):
        ans=min(ans,dp[i]+tt[i])

    print(ans)

    



        
    """low=2
    high=(2*k)
    ans=n//2
    while(low<=high):
        mid=(low+high)>>1
        r=0
        for i in range(0,n//2):
            if(s[i]>=mid and s[n-i-1]>=mid):
                r+=2
            else:
                r+=1
        ans=min(ans,r)
    print(ans)"""
    
    
