Problem: You are given a positive integer n, it is guaranteed that n is even (i.e. divisible by 2).

You want to construct the array a of length n such that: 

  * The first n/2 elements of a are even (divisible by 2); 
  * the second n/2 elements of a are odd (not divisible by 2); 
  * all elements of a are distinct and positive; 
  * the sum of the first half equals to the sum of the second half (∑_{i=1}^{n/2} a_i = ∑_{i=n/2 + 1}^{n} a_i). 



If there are multiple answers, you can print any. It is not guaranteed that the answer exists.

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 only line of the test case contains one integer n (2 ≤ n ≤ 2 ⋅ 10^5) — the length of the array. It is guaranteed that that n is even (i.e. divisible by 2).

It is guaranteed that the sum of n over all test cases does not exceed 2 ⋅ 10^5 (∑ n ≤ 2 ⋅ 10^5).

Output

For each test case, print the answer — "NO" (without quotes), if there is no suitable answer for the given test case or "YES" in the first line and any suitable array a_1, a_2, ..., a_n (1 ≤ a_i ≤ 10^9) satisfying conditions from the problem statement on the second line.

Example

Input


5
2
4
6
8
10


Output


NO
YES
2 4 1 5
NO
YES
2 4 6 8 1 3 5 11
NO

Solution (in PYTHON3):

Solution:
def solve():
    T = int(input())
    while (T > 0):
        nk = input().split()
        a = list(map(int, input().split()))
        n = int(nk[0])
        k = int(nk[1])
        result = 10**9

        mn = [0 for _ in range(2*k+1)]
        mx = [0 for _ in range(2*k+1)]
        cnt = [0 for _ in range(2*k+1)]
        x = [0 for _ in range(2*k+1)]
        x[0] = 0
        x[1] = 0

        for i in range(n//2):
            sum = a[i] + a[n-i-1]
            cnt[sum] += 1
            cur_mn = min(a[i] + 1, a[n-i-1] + 1)
            cur_mx = max(a[i] + k, a[n-i-1] + k)
            mn[cur_mn] += 1
            mx[cur_mx] += 1

        for i in range(2, 2*k+1):
            x[i] = x[i-1] + (mn[i] - mx[i-1])
            y = n/2 - x[i]
            total = x[i] + 2*y - cnt[i]
            result = min(result, total)

        print(int(result))
        T -= 1


solve()