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
import math
from collections import defaultdict
def lower(arr,num):
    if num>arr[-1]:
        return len(arr)
    l,r=0,len(arr)-1
    ans=-1
    while l<=r:
        mid=(l+r)//2
        if arr[mid]<num:
            l=mid+1
            ans=mid
        else:
            r=mid-1
    return ans
def lowera(arr,num):
    if num>arr[-1]:
        return len(arr)-1
    l,r=0,len(arr)-1
    ans=-1
    while l<=r:
        mid=(l+r)//2
        if arr[mid]<=num:
            l=mid+1
            ans=mid
        else:
            r=mid-1
    return ans
t=int(sys.stdin.readline())
for _ in range(t):
    dic=defaultdict(int)
    n,k=map(int,sys.stdin.readline().split())
    arr=list(map(int,sys.stdin.readline().split()))
    small=[]
    large=[]
    l,r=0,n-1
    while l<=r:
        dic[arr[l]+arr[r]]+=1
        small.append(min(arr[l],arr[r]))
        large.append(max(arr[l],arr[r]))
        l+=1
        r-=1
    small.sort()
    large.sort()
    for i in range(len(small)):
        small[i]+=1
    for i in range(len(large)):
        large[i]+=k
    small=[small[0]-1]+small
    large=[large[0]-1]+large
    #print(small,'small')
    #print(large,'large')
    #print(dic,'dic')
    ans=1e10
    for i in range(2,2*k+1):
        #print(i,'i')
        a=lowera(small,i)
        b=lower(large,i)
        #print(a,'a',b,'b')
        #a-=1
        x=n//2-a
        if b<1:
            y=0
            b=0
        #print(x,'x',y,'y')
        s=x*2+a+y*2+b-dic[i]
        #print(s,'s')
        ans=min(ans,s)
    print(ans)