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 string
from collections import defaultdict,Counter
from math import sqrt, log10, log2, log, gcd, ceil, floor,factorial
from bisect import bisect_left, bisect_right
from itertools import combinations,combinations_with_replacement
import sys,io,os
input=sys.stdin.readline
# input = io.BytesIO(os.read(0, os.fstat(0).st_size)).readline
# print=sys.stdout.write
sys.setrecursionlimit(10000)
mod=10**9+7
inf = float('inf')
def get_list():
    return [int(i) for i in input().split()]
def yn(a):
    print("YES" if a else "NO",flush=False)
t=1
t=int(input())
for i in range(t):
    n,k=get_list()
    l=get_list()
    pre=[0]*(2*k+2)
    for iter1 in range(n):
        iter2=n-1-iter1
        pre[2]+=2
        pre[2*k+1]-=2
        mina=min(1+l[iter1],1+l[iter2])
        maxa=max(k+l[iter1],k+l[iter2])
        pre[mina]-=1
        pre[maxa+1]+=1
        pre[l[iter1]+l[iter2]]-=1
        pre[l[iter1]+l[iter2]+1]+=1


    for i in range(1,len(pre)):
        pre[i]+=pre[i-1]
    print(min(pre[2:2*k+1])//2)