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
from collections import defaultdict as dd,deque as dq
t=int(input())
import bisect
while t:
    d=dd(int)
    n,k=map(int,input().split())
    l=list(map(int,input().split()))
    ll=[]
    mx=1000000000000000
    mi=-1
    ll=[]
    l2=[]
    ri=-1
    le=mx
    for i in range(n//2):
        d[l[i]+l[n-i-1]]+=1
        
        mx=min(mx,max(l[i],l[n-i-1]))
        mi=max(mi,min(l[i],l[n-i-1]))
        ll.append(max(l[i],l[n-i-1])+k)
        l2.append(min(l[i],l[n-i-1])+1)
        le=min(le,l[i]+l[n-i-1])
        ri=max(ri,l[i]+l[n-i-1])
    res=n//2
    ll.sort()
    l2.sort()
    ri=ll[-1]
    if(le>ri):
        le,ri=ri,le
    #print(mi,mx,le,ri)
    mx=0
    ind=100000000000
    #print(ll,le,ri)
    #print(mx)
    #print(l2)
    for i in range(le,ri+1):
        cou=bisect.bisect_left(ll,i)
        cou2=n//2-bisect.bisect_right(l2,i)
        #print(cou,cou2,i)
        if(mx<d[i]-cou-cou2):
            #print("lol",d[i],cou,i)
            mx=d[i]-cou-cou2
            #ind=min(ind,i)
    cou=0
    print(res-mx)
    t-=1