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 PYTHON):

Solution:
from sys import stdin

rints = lambda: [int(x) for x in stdin.readline().split()]
out = []

for _ in range(int(input())):
    n, k = rints()
    a, mem = rints(), [0] * ((k * 2) + 2)

    for i in range(n // 2):
        s = a[i] + a[-1 - i]
        mi, ma = min(a[i], a[-1 - i]), max(a[i], a[-1 - i])

        mem[s + 1] += 1
        mem[mi + 1] += 1
        mem[s] -= 1
        mem[k + ma + 1] += 1
        if s != 2:
            mem[2] += 2
            mem[mi + 1] -= 2

    # print(mem)
    tem, ans = 0, float('inf')

    for j in mem[2:-1]:
        tem += j
        ans = min(ans, tem)

    out.append(str(ans))
print('\n'.join(out))