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 bisect import bisect_left
from collections import Counter


def solve(n, k, a):
    s = [a[i] + a[n-i-1] for i in range(n//2)]
    amin    = sorted([min(a[i], a[n-i-1]) for i in range(n//2)])
    amax    = sorted([max(a[i], a[n-i-1]) for i in range(n//2)])
    ans     = float('inf')
    counter = Counter(s)
    for v in range(2*k+1):
        count  = n//2 - bisect_left(amin, v)
        count1 = bisect_left(amax, v-k)
        count2 = n//2 - count - count1
        count3 = counter[v]
        ans    = min(ans, (count+count1)*2 + count2 - count3)
    return ans



def main():
    tc = int(input())
    inp = lambda: [int(x) for x in input().split()]
    for _ in range(tc):
        n, k = inp()
        a = inp()
        print(solve(n, k, a))


if __name__ == '__main__':
    main()