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:
t = int(input())

z = []


def oddIntegers(n , k ):

    if (n % 2 != k % 2):
        z.append("NO")

        return

    else:


        z.append("YES")

        sum = 0
        i = 1
        j = 1

        # Loop to find first K-1
        # distinct odd integers
        while (j < k):
            sum += i
            a.append(i)
            i += 2
            j += 1

            # Final Kth odd number
        finalOdd = n - sum

        a.append(finalOdd)


zz = []
for ii in range(t):
    c = 0
    n = int(input())
    if n==2:
        z.append('NO')
    else:
        a = []
        s = 0
        ss = n//2
        for i in range(2, n+1, +2):
            s = s+i
            a.append(i)
        oddIntegers(s, ss)
        if z[ii]=='YES':
            zz.append(a)



b = 0
for i in z:
    if i=="NO":
        print('NO')
    elif i=="YES":
        print('YES')
        for ii in zz[b]:
            print(ii, end=" ")
        print()
        b+=1