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 math
#from functools import lru_cache
#import heapq
#from collections import defaultdict
#from collections import Counter
#from sys import stdout
#from sys import setrecursionlimit
from sys import stdin
input = stdin.readline
for ti in range(int(input().strip())):
    n, k = [int(x) for x in input().strip().split()]
    a = [int(x) for x in input().strip().split()]
    s, e, h = [0]*(2*k+1), [0]*(2*k+1), [0]*(2*k+1)
    for ai in range(n//2):
        fi, se = a[ai], a[n-ai-1]
        h[fi+se] += 1
        s[min(fi, se)+1] += 1
        e[max(fi, se) + k] += 1
    ans, ss = n//2, 0
    #print(s, e, h)
    for i in range(2, 2*k+1):
        #print(ss, ans)
        ss += s[i]
        ta = 0
        ta += (ss-h[i])
        ta += 2*((n//2) - ss)
        ss -= e[i]
        #print(ta)
        ans = min(ans, ta)
    print(ans)