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:
from sys import stdin, stdout

# n k
# 4 2
# 1 2 1 2
#
# 4 3
# 1 2 2 1
# 2 4
#
#  6 6
#  5 2  6 1 3 4
#  9 5  7
# 10 9 12
#  5 3  2
#  8 6
#  6  1   1   7  6 3 4 6
# 12  5   4  13
# 13 11  10  14
#  7  2   2   7
# 7 7 => 8 - 14
# 1 1 => 2 - 8

# sum accumulation
def constant_palindrome_sum(n, k, a):

    sasum = [0 for i in range(2*k+2)]
    acsum = [0 for i in range(2*k+2)]

    for i in range(n//2):
        lv = min(a[i], a[n-i-1]) + 1
        hv = max(a[i], a[n - i - 1]) + k
        acsum[lv] += 1
        acsum[hv+1] -= 1
        sasum[a[i] + a[n - i - 1]] += 1

    res = 2**31 - 1
    cnt = 0
    for i in range(2, 2*k+1):
        cnt += acsum[i]
        res = min(res, (cnt - sasum[i]) + (n//2 - cnt)*2)

    #print(sasum)
    #print(acsum)

    return res


# 2    10
# 2       11
#     7      13
#     7         14
def bs_rb(v, ar):
    l = 0
    h = len(ar)-1

    while l < h:
        m = (l + h)//2
        if v <= ar[m][1]:
            h = m
        else:
            l = m+1

    return h


def bs_lb(v, ar):
    l = 0
    h = len(ar) - 1

    while l < h:
        m = (l + h + 1) // 2
        if v >= ar[m][0]:
            l = m
        else:
            h = m - 1

    return l


if __name__ == '__main__':
    t = int(stdin.readline())

    for i in range(t):
        nk = list(map(int, stdin.readline().split()))
        a = list(map(int, stdin.readline().split()))

        stdout.write(str(constant_palindrome_sum(nk[0], nk[1], a)) + '\n')