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:
from collections import defaultdict
for _ in range(int(input())):
    n,k=map(int,input().split())
    l=list(map(int,input().split()))
    hashtable=defaultdict(int)
    prefix=[0]*(2*k+2)
    for i in range(n//2):
        hashtable[l[i]+l[n-i-1]]+=1
        prefix[min(l[i],l[n-i-1])+1]+=1
        prefix[max(l[i],l[n-i-1])+k+1]-=1
    presum=0
    for i in range(2*k+1):
        presum+=prefix[i]
        prefix[i]=presum
    minreplace=10**6
    #print(prefix,hashtable)
    for i in range(2,2*k+1):
        ch0=hashtable[i]
        ch1=prefix[i]-ch0
        ch2=(n//2-ch1-ch0)*2
        minreplace=min(minreplace,ch1+ch2)
    print(minreplace)