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 PYTHON):

Solution:
import sys

__author__ = 'ratmir'

from bisect import bisect_right

[t] = [int(x) for x in sys.stdin.readline().split()]


def solve(n, k, a):
    cnt = dict()
    cnmn = dict()
    cnmx = dict()
    for i in range(0, n / 2):
        v = a[i] + a[n - i - 1]
        if not v in cnt:
            cnt[v] = 0
        cnt[v] += 1
        cmn = min(a[i], a[n - i - 1]) + 1
        if not cmn in cnmn:
            cnmn[cmn] = 0
        cnmn[cmn] += 1
        cmx = max(a[i], a[n - i - 1]) + k
        if not cmx in cnmx:
            cnmx[cmx] = 0
        cnmx[cmx] += 1

    maximums = sorted(cnmx.keys())
    v = 0
    cm2 = dict()
    for m in maximums:
        v += cnmx[m]
        cm2[m] = v
    maximums = [0] + maximums
    cm2[0] = 0

    minimums = sorted(cnmn.keys())
    v = 0
    cmi2 = dict()
    for i in range(0, len(minimums)):
        m = minimums[len(minimums)-i-1]
        v += cnmn[m]
        cmi2[m] = v
    minimums = minimums + [1000000000000]
    cmi2[1000000000000] = 0

    #print cnmn
    #print minimums, cmi2
    cr = n
    for i in range(2, 2 * k + 1):
        x = i
        start = bisect_right(minimums, x)
        q = cmi2[minimums[start]]

        start = 0
        end = len(maximums)
        while end - start > 1:
            test = (start + end) / 2
            if maximums[test] < x:
                start = test
            if maximums[test] == x:
                start = test-1
                end = test-1
            if maximums[test] > x:
                end = test

        q += cm2[maximums[start]]
        if x in cnt:
            cntx = cnt[x]
        else:
            cntx = 0
        single = n / 2 - q - cntx
        total = single + 2 * q
        if total < cr:
            cr = total
            #print x, total
    return cr


for ti in range(0, t):
    [n, k] = [int(x1) for x1 in sys.stdin.readline().split()]
    a = [int(x1) for x1 in sys.stdin.readline().split()]

    sm = solve(n, k, a)
    print sm