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 inp():
    return(int(input()))
def inlt():
    return(list(map(int,input().split())))
def insr():
    s = input()
    return(list(s[:len(s) ]))
def invr():
    return(map(int,input().split()))

entries = inp()

for i in range(entries):
    l = inlt()
    n = l[0]
    k = l[1]
    lp = 2
    rp = 2*k
    normal_sum = []
    l = inlt()
    list_val = [0] * ((2*k) + 2)
    count = [0] * ((2*k) + 2)
    for i in range(n//2):
        val = l[i] + l[-i-1]
        rp = k + max(l[i],l[-i-1])
        lp = 1 + min(l[i],l[-i-1])

        list_val[val] += 1
        count[lp] -= 1
        count[rp + 1] += 1

    #print(count)
    #print(list_val)
    curr = n
    ans = n
    for x in range(2,2*k+2):

        curr += count[x]
        ans = min(ans, curr-list_val[x])
        #print(curr)


    print(ans)