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:
t=int(input())
import random
for _ in range(t):
    n,k=map(int,input().split())
    l=list(map(int,input().split()))
    c=[0]*(k+1)
    e=[0]*(k+1)
    d={}
    for i in range(n//2):
        c[min(l[i],l[n-1-i])]+=1
        e[max(l[i],l[n-1-i])]+=1
        try:
            d[l[i]+l[n-1-i]]+=1
        except:
            d[l[i]+l[n-1-i]]=1
    for i in range(1,k+1):
        c[i]+=c[i-1]
        e[i]+=e[i-1]
    ans=n
    for i in range(2,2*k+1):
        if i<=k:
            x=c[i-1]
        else:
            x=e[k]-e[i-k-1]
        try:
            x=x-d[i]
        except:
            pass
        if i>k:
            x = x+(n//2-e[k]+e[i-k-1])*2
        else:
            x = x+(n//2-c[i-1])*2
        #print(i,x)
        ans=min(ans,x)
    print(ans)