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())
for _ in range(t):
    n, k = map(int, input().rstrip().split())
    arr = list(map(int, input().rstrip().split()))
    pairsNeeding0chng = {}
    pairsNeeding01chng = [0]*(2*k+2)
    for pos in range(n//2):
        L = min(arr[pos], arr[n-pos-1])
        R = max(arr[pos], arr[n-pos-1])
        if L+R in pairsNeeding0chng:
            pairsNeeding0chng[L+R] += 1
        else:
            pairsNeeding0chng[L+R] = 1
        pairsNeeding01chng[L+1] += 1
        pairsNeeding01chng[R+k+1] -= 1
    for pos in range(2, len(pairsNeeding01chng)):
        pairsNeeding01chng[pos] += pairsNeeding01chng[pos-1]
    pairsNeeding01chng.pop()

    minChngs = -1
    for x in range(2, 2*k +1):
        noOf0pair = 0
        if x in pairsNeeding0chng:
            noOf0pair += pairsNeeding0chng[x]
        noOf1pair = pairsNeeding01chng[x] - noOf0pair
        noOf2pair = (n//2) - noOf0pair - noOf1pair
        totChngs = noOf1pair + (noOf2pair*2)
        if totChngs < minChngs or minChngs == -1:
            minChngs = totChngs

    print(minChngs)