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 PYTHON):

Solution:
# coding=utf-8
# Author: lee215
# Date: 2020-04-23 00:00

get = lambda: int(raw_input().strip())
getl = lambda: raw_input().strip()
gets = lambda: map(int, raw_input().strip().split())
getss = lambda n: [gets() for _ in xrange(n)]

import collections

def solve(n, k, A):
    AI = sorted([A[i], i] for i in xrange(n))
    window = set()
    count = collections.Counter()
    left = right = 0
    max_save = save = 0
    # print 'AI', AI
    for S in xrange(2, k * 2 + 1):
        while right < n and AI[right][0] < S:
            a, i = AI[right]
            if n - 1 - i not in window:
                save += 1
            else:
                count[A[i] + A[n - 1 - i]] += 1
            window.add(i)
            right += 1

        while left < n and AI[left][0] < S - k:
            a, i = AI[left]
            if n - 1 - i not in window:
                save -= 1
            else:
                count[A[i] + A[n - 1 - i]] += 1
            window.remove(i)
            left += 1
        max_save = max(max_save, save + count[S])
        # print window, save, count
    return n - max_save

T = get()
for _ in xrange(T):
    n, k = gets()
    A = gets()
    res = solve(n, k, A)
    print res