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:
def solve(n, k, arr):
    temp = [0 for i in range(0, 2*k + 10)]
    for i in range(0, n//2):
        v1 = arr[i]
        v2 = arr[n - 1 - i]
        # p1 = 2
        p1 = min(v1, v2) + 1
        p2 = v1 + v2
        p3 = max(v1, v2) + k
        # p5 = k + k
        temp[2] += 2
        temp[p1] -= 1
        temp[p2] -= 1
        temp[p2 + 1] += 1
        temp[p3 + 1] += 1
    res = n
    cur = 0
    for i in range(2, 2*k + 1):
        cur += temp[i]
        res = min(cur, res)
    return res



t = int(input())
for i in range(0, t):
    n, k = map(int, input().split())
    arr = list(map(int, input().split()))
    res = solve(n, k, arr)
    print(res)