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:
#!/usr/bin/env python3
# -*- coding: utf-8 -*-
##################################
# University of Wisconsin-Madison
# Author: Yaqi Zhang
##################################

# standard library
import sys


def main():
    T = int(input())
    for _ in range(T):
        n, k = map(int, input().split())
        nums = list(map(int, input().split()))
        # x <= 2k
        # a <= k
        # make them same
        dp = [0] * (2 * k + 2)
        for i in range(n // 2):
            a, b = nums[i], nums[n - 1 - i]
            if a > b:
                a, b = b, a
            s = a + b
            lo = s - (b - 1)
            hi = s + (k - a)
            # print(lo, s, hi)
            dp[lo] -= 1
            dp[s] -= 1
            dp[s + 1] += 1
            dp[hi + 1] += 1
        mn = n
        cur = n
        for i in range(2, 2 * k + 1):
            cur += dp[i]
            mn = min(cur, mn)
        print(mn)


if __name__ == "__main__":
    main()