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:
x=int(input())
for b in range(x):
    y=list(map(int,input().split()))
    z=list(map(int,input().split()))
    d={}
    s1=[]
    s=sum(z)/(y[0]/2)
    arr=[0 for i in range(int(y[1]*2)+2)]
    for a in range(y[0]//2):
        s2=z[a]+z[y[0]-a-1]
        d[s2]=d.get(s2,0)+1
        arr[max(z[a],z[y[0]-a-1])+y[1]+1]-=1
        arr[min(z[a],z[y[0]-a-1])+1]+=1
    for a in range(1,len(arr)):
        arr[a]+=arr[a-1]
    #print(arr)
    #print(d)
    ans=100000000000
    for each in d:
        ans=min(ans,arr[each]+(y[0]//2-arr[each])*2-d[each])
    print(min(ans,max(arr)+(y[0]//2-max(arr))*2))
    '''
    for a in range(y[0]//2):
        s2=z[a]+z[y[0]-a-1]
        if abs(s-s2)<d:
            d=abs(s-s2)
            s1=[s2]
        elif abs(s-s2)==d:
            s1.append(s2)
    s1.append(s)
    r=100000000000
    for each in s1:
        r1=0
        #print(each)
        for a in range(y[0]//2):
            s2=z[a]+z[y[0]-a-1]
            if s2<each:
                if max(z[a],z[y[0]-a-1])+y[1]>=each:
                    r1+=1
                else:
                    r1+=2
            elif s2>each:
                if min(z[a],z[y[0]-a-1])+1<=each:
                    r1+=1
                else:
                    r1+=2
            print(s2)
            print(r1)
            print('-')
        r=min(r,r1)
        print('======')
    print(r)'''