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 os
from collections import defaultdict


def f(nums, k):
    n = len(nums)
    n2 = n // 2
    p = defaultdict(int, {})
    mi = defaultdict(int, {})
    ma = defaultdict(int, {})
    for i in range(n2):
        p[nums[i] + nums[n - i - 1]] += 1
        mi[min(nums[i], nums[n - i - 1])] += 1
        ma[max(nums[i], nums[n - i - 1])] += 1


    mlx = 0
    mgx = 0
    cost = n
    for x in range(2 * k + 1):
        mlx += mi[x - 1]
        mgx += ma[x - k - 1]
        cost = min(n - mlx - p[x] + mgx, cost)

    return cost

#f(list(map(int, "6 1 1 7 6 3 4 6".split())), 7)

def pp(input):
    n_test = int(input())
    for i in range(n_test):
        k = int(input().split()[1])
        print(f(list(map(int, input().split())), k))


if "paalto" in os.getcwd():
    from string_source import string_source

    s = string_source(
        """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"""
    )

    pp(s)
else:
    pp(input)