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
input = sys.stdin.readline
from bisect import bisect_left, bisect_right

Q = int(input())
Query = []
for _ in range(Q):
    N, K = map(int, input().split())
    A = list(map(int, input().split()))
    Query.append((N, K, A))

for N, K, A in Query:
    MIN = []
    MAX = []
    dic = {}
    for n in range(N//2):
        a1 = A[n]; a2 = A[-1-n]
        MIN.append(min(a1+1, a2+1))
        MAX.append(max(a1+K, a2+K))
        p = a1 + a2
        if p in dic:
            dic[p] += 1
        else:
            dic[p] = 1
    
    MIN.sort()
    MAX.sort()
        
    ans = 10**14
    for k in range(2, 2*K+1):
        small_than_k = bisect_left(MAX, k)
        large_than_k = N//2 - bisect_right(MIN, k)
        two = small_than_k + large_than_k
        zero = dic[k] if k in dic else 0
        one = N//2 - two - zero
        ans = min(ans, two*2+one)
    print(ans)