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:
from collections import defaultdict

n = int(input())

for i in range(n):
    m, k = map(int, input().split())
    nums = list(map(int, input().split()))

    #All of the sums: 0 changes
    h = defaultdict(int)
    pair = []
    s, e = 0, len(nums) - 1

    #Two-pointer Algorithm to store all pairs and store all sums in hashmap
    while s < e:
        h[nums[s] + nums[e]] += 1
        pair.append((min(nums[s], nums[e]), max(nums[s], nums[e])))
        s += 1
        e -= 1

    #Prefix Sum ALgorithm
    p = [0] * ((2 * k) + 1)
    for s, e in pair:
        new_range = (s + 1, e + k)
        p[new_range[0]] += 1
        if new_range[1] + 1 < len(p):
            p[new_range[1] + 1] -= 1

    #Prefix sum of all ranges: 1 change
    for i in range(1, len(p)):
        p[i] += p[i - 1]

    final = []

    
    for i in range(2, (2*k) + 1):
        changes = len(pair)
        
        zero, one, two = 0, 0, 0
        if i in h:
            zero += h[i]
            changes -= zero

        if changes:
            one = p[i] - zero
            changes -= one

        if changes:
            two = changes
        final.append(2 * two + one)
        

    print(min(final))