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 sys
input=sys.stdin.readline
def bs(l,target,n):
    low=0
    high=n
    ans=-1
    while low<=high:
        mid=low+(high-low)//2
        if l[mid]<=target:
            ans=max(ans,mid)
            low=mid+1
        else:
            high=mid-1
    return ans
t=int(input())
for r in range(t):
    n,k=map(int,input().split())
    l=list(map(int,input().split()))
    d={}
    start=[]
    end=[]
    i=0
    j=n-1
    while i<j:
        start.append(min(l[i],l[j])+1)
        end.append(max(l[i],l[j])+k)
        try:
            d[l[i]+l[j]]+=1
        except:
            d[l[i]+l[j]]=1
        i+=1
        j-=1


    start.sort()
    end.sort()
    mini=999999999999999
    for i in range(1,(2*k)+1):
        a=bs(start,i,len(start)-1)+1
        b=bs(end,i-1,len(end)-1)+1
        # print(a,b)
        one=a-b
        zero=0
        try:
            zero=d[i]
        except:
            pass
        twos=(n//2)-(one)
        ans=(twos*2)+(one-zero)
        # print("x: "+str(i)+" ans: "+str(ans))
        # print("0: "+str(zero)+" 1: "+str(one-zero)+" 2: "+str(twos))
        mini=min(mini,ans)
    print(mini)