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 problem1():
    a = int(input())
    k = 4
    while a % (k-1) != 0:
        k *= 2
    print(a//(k-1))

def problem2():
    a = int(input())
    if a % 4 == 2:
        print('NO')
        return
    print('YES')
    x = []
    for i in range(1,a // 2 + 1):
        x.append(2*i)
    for i in range(a // 4):
        x.append(x[i] - 1)
    for i in range(a // 4, a // 2):
        x.append(x[i] + 1)
    print(*x)

def problem3():
    l = int(input())
    a = list(map(int,input().split()))
    k = -1*min(a)
    i = 0
    s = 0
    while i < l:
        mp = 0
        mn = k + 1
        while i < l and a[i] > 0:
            mp = max(a[i],mp)
            i += 1
        while i < l and a[i] < 0:
            mn = min(abs(a[i]),mn)
            i += 1
        s += mp
        if mn != k + 1:
            s -= mn
    print(s)

def problem4():
    l,k = list(map(int,input().split()))
    a = list(map(int,input().split()))
    s = []
    t = []
    u = []
    for i in range(l // 2):
        s.append(a[i] + a[l - i - 1])
        t.append(min(1+a[i],1+a[l-i-1]))
        u.append(max(k+a[i],k+a[l-i-1]))
    v = list(set([(s.count(i),i) for i in s]))
    
cases = int(input())
for _ in range(cases):
    # problem1()
    problem2()
    # problem3()
    # problem4()