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:
# -*- coding:utf-8 -*-

"""

created by shuangquan.huang at 2020/6/19

"""

import collections
import time
import os
import sys
import bisect
import heapq
from typing import List


def solve(N, K, A):
    
    M = 2 * K + 1
    x = [0 for _ in range(M)]
    
    add = [0 for _ in range(M)]
    minus = [0 for _ in range(M)]
    wc = collections.defaultdict(int)
    for i in range(N//2):
        a, b = A[i], A[N-i-1]
        wc[a+b] += 1
        s, t = min(a, b) + 1, max(a, b) + K + 1
        if s < M:
            add[s] += 1
        if t < M:
            minus[t] += 1
    
    s = 0
    for i in range(M):
        s += add[i]
        s -= minus[i]
        x[i] = s
        
    ans = N
    for target in range(2, M):
        one = x[target] - wc[target]
        two = N//2-wc[target]-one
        ans = min(ans, one + 2 * two)
        
    return ans
        
        
if __name__ == '__main__':
    T = int(input())
    ans = []
    for ti in range(T):
        N, K = map(int, input().split())
        A = [int(x) for x in input().split()]
        ans.append(solve(N, K, A))
    
    print('\n'.join(map(str, ans)))