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().split())
    a = [*map(int, input().split())]

    cnt = [0] * (2*k)
    intervals = [0] * (2*k)
    for i in range(n//2):
        v = a[i] + a[n-i-1]

        cnt[v-1] += 1

        ma = max(a[i], a[n-i-1])
        mi = min(a[i], a[n-i-1])

        intervals[mi] += 1
        if ma+k < 2*k:
            intervals[ma+k] -= 1 # -1 at index i+1 to "cancel" the value during prefix sum 

    # prefix sum => thaks to that we are not O(N*K) but O(N + K)
    for i in range(1, 2*k):
        intervals[i] += intervals[i-1]

    ans = 1e9
    for i in range(1, 2*k):
        # min(ans, modif en 1 - modif en 0 + modifs en 2 [=paires - modif en 1 * 2])
        ans = min(ans, intervals[i] - cnt[i] + (n//2 - intervals[i]) * 2)
    
    print(ans)