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 inp():
    return(int(input()))
def inlt():
    return(list(map(int,input().split())))
def insr():
    s = input()
    return(list(s[:len(s) ]))
def invr():
    return(map(int,input().split()))

entries = inp()

for i in range(entries):
    l = inlt()
    n = l[0]
    k = l[1]
    lp = 2
    rp = 2*k
    normal_sum = []
    l = inlt()
    list_val = [0] * ((2*k) + 2)
    count = [0] * ((2*k) + 2)
    for i in range(n//2):
        val = l[i] + l[-i-1]
        rp = k + max(l[i],l[-i-1])
        lp = 1 + min(l[i],l[-i-1])

        list_val[val] += 1
        count[lp] -= 1
        count[rp + 1] += 1

    #print(count)
    #print(list_val)
    curr = n
    ans = n
    for x in range(2,2*k+2):

        curr += count[x]
        ans = min(ans, curr-list_val[x])
        #print(curr)


    print(ans)