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 update(bit, l, r, n, val):
    updatebit(bit, n, l, val)
    updatebit(bit, n, r+1, -val)

def updatebit(bit, n, i, val):
    i += 1
    while i <= n:
        bit[i] += val
        i += i & (-i)

def get(bit, i):
    res = 0
    i += 1
    while i > 0:
        res += bit[i]
        i -= i & (-i)
    return res


t = int(input())
for tt in range(t):
    N, K = (int(i) for i in input().split())
    A = [int(i) for i in input().split()]
    pos = [0]*(2*K+2)
    n = len(pos) - 1
    for i in range(N//2):
        cur, mir = A[i], A[N-i-1]
        L = R = cur + mir
        update(pos, L, R, n, -1)
        
        L, R = 2, min(cur, mir)
        if L <= R:
            update(pos, L, R, n, 1)
            
        L, R = max(cur, mir) + K + 1, n - 1
        if L <= R:
            update(pos, L, R, n, 1)
            
    ans = N//2 + min(get(pos, i) for i in range(2, n))
    print(ans)