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:
t = int(input())
for _t in range(t):
    n, k = map(int, input().strip().split())
    a = [int(x) for x in input().split()]
    ref, intvls = dict(), []
    for i in range(n//2):
        x = a[i]+a[n-i-1]
        ref[x] = ref.get(x, 0) + 1
        intvls += [(min(a[i], a[n-i-1])+1, max(a[i], a[n-i-1])+k)]
    # print(ref)
    # print(intvls)
    ff = [0]*2*(k+1)
    for i, j in intvls:
        ff[i] += 1 
        ff[j+1] += -1
        
    ans = 10**9
    for i in range(2, 2*k+1):
        ff[i] += ff[i-1]
        no_of_0s, no_of_1s = ref.get(i, 0), ff[i]-ref.get(i, 0)
        no_of_2s = n//2 - no_of_1s - no_of_0s
        # print(i, ": ", no_of_2s*2 + no_of_1s*1 + no_of_0s*0)
        ans = min(ans, no_of_2s*2 + no_of_1s*1 + no_of_0s*0)
    print(ans)