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 bisect
import collections

t = int(input())
for case_num in range(t):
    n, k = map(int, input().split(' '))
    a = list(map(int, input().split(' ')))
    x = [a[i] + a[n - 1 - i] for i in range(n // 2)]
    x = collections.Counter(x)
    y = [min(a[i], a[n - 1 - i]) + 1 for i in range(n // 2)]
    z = [max(a[i], a[n - 1 - i]) + k for i in range(n // 2)]
    y.sort()
    z.sort()
    ans = n // 2
    for i in range(2, 2 * k + 1):
        zero = x[i]
        two = bisect.bisect_left(z, i) + n // 2 - bisect.bisect_right(y, i)
        one = n // 2 - zero - two
        ans = min(ans, one + two * 2)
    print(ans)