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:
#!/usr/bin/env python
import sys
sys.setrecursionlimit(10**9)
input=sys.stdin.readline
from collections import deque

t=int(input())
for ii in range(t):
    n,k=map(int,input().split())
    l=list(map(int,input().split()))
    d=[0]*(2*k+2)
    for i in range(n//2):
        a=l[i]
        b=l[n-1-i]
        p=min(a,b)
        q=max(a,b)
        mi=p+1
        ma=q+k
        d[0]+=2
        d[mi-1]-=2
        d[mi-1]+=1
        d[p+q-1]-=1
        d[p+q]+=1
        d[ma]-=1
        d[ma]+=2
        d[-1]-=2
    for i in range(2*k+1):
        d[i+1]+=d[i]
    print(min(d[:-1]))
sys.exit()

N = 5
es = [[1,2,3],[0,2],[0,1],[0,4],[3]] # False
#es = [[1,3],[0,2],[1,3],[0,2,4],[3]] # True
colors = [0 for i in range(N)]
def dfs(v,color):
    print(v,color)
    colors[v] = color
    for to in es[v]:
        if colors[to] == color:
            return False
        if colors[to] == 0 and not dfs(to, -color):
            return False
    return True

def is_bipartite():
    return dfs(0,1)
print(is_bipartite())