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 bs(a):
    low = 0
    high = len(li) - 1
    while low <= high:
        if high - low < 5:
            for i in range(low, high+1):
                if li[i] >= a:
                    return i
            return 0
        mid = (low + high) // 2
        if li[mid] >= a:
            high = mid
        else:
            low = mid + 1


def bs2(a):
    low = 0
    high = len(l) - 1
    while low <= high:
        if high - low < 5:
            for i in range(low, high+1):
                if l[i] > a:
                    return len(l) - i
            return 0
        mid = (low + high) // 2
        if l[mid] > a:
            high = mid
        else:
            low = mid+1


t = int(input())
for _ in range(t):
    n, k = [int(x) for x in input().split()]
    s = list(map(int, input().split()))
    l = []
    li = []
    sum = []
    dict = {}
    for i in range(n // 2):
        l.append(min(s[i], s[n - 1 - i]))
        li.append(max(s[i], s[n - 1 - i]))
        if dict.get(s[i] + s[n - 1 - i]) is None:
            dict[s[i] + s[n - 1 - i]] = 0
        dict[s[i] + s[n - 1 - i]] += 1
    for x in dict.keys():
        sum.append((x, dict[x]))
    l.sort()
    li.sort()
    ans = n // 2
    for p in sum:
        x = 0
        y = 0
        if p[0] > k:
            x = p[0] - k
            y = k
            z = bs(x)
            ans = min(ans, (2 * z) + (n // 2) - z - p[1])
        else:
            x = 1
            y = p[0] - 1
            z = bs2(y)
            ans = min(ans, 2 * z + (n // 2) - z - p[1])
    print(ans)