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 sys import stdin,stdout

for case in range(int(stdin.readline())):
    n,k = [int(x) for x in stdin.readline().split()]

    a = [int(x) for x in stdin.readline().split()]

    a1 = a[:n//2]
    a2 = a[n//2:][::-1]

    for x in range(n//2):
        if a1[x] > a2[x]:
            a1[x], a2[x] = a2[x], a1[x]

    lows = {}
    lowCount = [0 for x in range(max(a1)+1)]
    highCount = [0 for x in range(max(a2)+1)]

    for x in a1:
        lowCount[x] += 1
    for x in a2:
        highCount[x] += 1

    lowSums = [highCount[0]]
    highSums = [lowCount[-1]]

    for x in highCount[1:]:
        lowSums.append(lowSums[-1]+x)

    for x in lowCount[:-1][::-1]:
        highSums.append(highSums[-1]+x)
    highSums = highSums[::-1]
        
    sums = {}

    for x in range(n//2):
        if a1[x]+a2[x] in sums:
            sums[a1[x]+a2[x]] += 1
        else:
            sums[a1[x]+a2[x]] = 1

    best = n//2

    for x in sums:
        total = n//2-sums[x]
        if x > k:
            total += lowSums[x-k-1]
        if x < len(highSums):
            total += highSums[x]
        best = min(best, total)
        
    print(best)