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:
t = int(input())
from collections import defaultdict
import math
for _ in range(t):
    n, k = list(map(int, input().split()))
    seq = list(map(int, input().split()))

    prefix_arr = [0]*(2*k+10)
    zero_count = defaultdict(int)
    for i in range(n//2):
        zero_count[seq[i] + seq[n-i-1]] += 1

        a, b = sorted((seq[i], seq[n-i-1]))

        L = a + 1
        R = b + k

        prefix_arr[L] += 1
        prefix_arr[R+1] -= 1
        
    prefsum = 0
    for i in range(2*k + 10):
        prefsum +=  prefix_arr[i]
        prefix_arr[i] = prefsum
    
    ans = n
    for i in range(2, 2*k + 1):
        zero = zero_count[i]
        ones = prefix_arr[i] - zero
        twos = n//2 - ones - zero

        total = ones + twos*2
        ans = min(ans, total)
        
    print(ans)