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:
import sys
# sys.setrecursionlimit(10**6)
input = sys.stdin.buffer.readline
# arr = [[int(el) for el in input().split()] for i in range(n)]

import collections

def solve(n, k, arr):
    d = collections.defaultdict(int)
    
    for i in range(n // 2):
        t = arr[i] + arr[n - 1 - i]
        d[t] += 1

    count_list = sorted( set(d.values()) )

    # print ('###', count_list, d)

    ans = float('inf')

    for i in count_list:

        upper_near_mid_v = float('inf')
        v1 = 0

        lower_near_mid_v = float('inf')
        v2 = 0

        for j in d:
            if d[j] == i:

                if j > k:
                    if j - k < upper_near_mid_v:
                        upper_near_mid_v = j - k
                        v1 = j

                else:
                    if k - j < lower_near_mid_v:
                        lower_near_mid_v = k - j
                        v2 = j
                # if abs(j - k) < near_mid_v:
                #     near_mid_v = abs(j - k)
                #     v = j

        # print (v)
        def chk(v):
            if not v:
                return float('inf')

            t = 0
            # for j in d:
            #     if j != v:
            #         if abs(j - v) <= k:
            #             t += d[j]
            #         else:
            #             t += 2 * d[j]

            for i in range(n // 2):
                temp = arr[i] + arr[n - 1 - i]
                if temp != v:
                    max_v = max(arr[i], arr[n - 1 - i])
                    min_v = min(arr[i], arr[n - 1 - i])
                    
                    if temp > v:
                        if max_v - 1 >= temp - v:
                            t += 1
                        else:
                            t += 2
                    elif temp < v:
                        if k - min_v >= v - temp:
                            t += 1
                        else:
                            t += 2

            return t

        # print ('#v1', v1, chk(v1), '#v2', v2, chk(v2))
        ans = min(ans, chk(v1), chk(v2))

    return min(ans, n//2)


t = int( input() )

for _ in range(t):

    n, k = map(int, input().split())

    arr = list(map(int, input().split()))

    ans = solve(n, k, arr)

    print (ans)