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:
''' Constant Palindrome Sum
'''

def search(cumurange, target, lwr=0, upr=False):
    if not upr:
        upr = len(cumurange) - 1
    if upr - lwr == 1:
        if cumurange[upr][0] < target:
            return cumurange[upr]
        else:
            return cumurange[lwr] 

    avg = (upr + lwr) // 2
    test = cumurange[avg]
    if test[0] > target:
        return search(cumurange, target, lwr, avg)
    else:
        return search(cumurange, target, avg, upr)

''' routine '''

T = int(input())

for test in range(T):
    N , K = list(map(int, input().split()))
    array = list(map(int, input().split()))

    totalpairs = N // 2
    pairsum = {}
    exceed2 = 0
    exceed1 = 0
    bounds = {}

    for n in range(totalpairs):
        a1 = array[n]
        a2 = array[N - 1 - n]
        sm = a1 + a2
        if a1 > K and a2 > K:
            exceed2 += 1
            continue
        elif a1 > K or a2 > K:
            a = min(a1, a2)
            minsum = a + 1
            maxsum = a + K + 1
        else:
            minsum = min(a1, a2) + 1
            maxsum = max(a1, a2) + K + 1
            asum = a1 + a2
            if asum in pairsum.keys():
                pairsum[asum] += 1
            else:
                pairsum[asum] = 1

        if minsum in bounds.keys():
                bounds[minsum] += 1
        else:
            bounds[minsum] = 1
        if maxsum in bounds.keys():
            bounds[maxsum] -= 1
        else:
            bounds[maxsum] = -1

    boundorder = sorted(bounds.items(), key=lambda x:x[0])
    # print(boundorder)
    cumulativerange = [boundorder[0]]
    for n in range(1, len(boundorder)):
        pos, qty = boundorder[n]
        prevqty = cumulativerange[n - 1][1]
        cumulativerange.append((pos, qty + prevqty))

    pairsum = list(pairsum.items())

    changes = []
    for cumu in cumulativerange:
        changes.append(N - cumu[1])
    for pair in pairsum:
        pos, val = pair
        cumu = search(cumulativerange, pos)
        # print(cumu, pair)
        changes.append((N - cumu[1] - val))

    minchanges = min(changes)
    # print(cumulativerange)
    # print(pairsum)
    # print(changes)
    print(minchanges)