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())
while t:
    t -= 1
    n, k = map(int, input().split())
    a = list(map(int, input().split()))
    cnt = [0]*(2*k+1)

    #print(cnt)
    for i in range(n//2):
        #print(i)
        #print(n-i-1)
        #print(a[i] + a[n-i-1])
        cnt[a[i] + a[n-i-1]]+=1;
    pref = [0]*(2*k+2)
    for i in range(n//2):
        l1 = 1+a[i]
        l2 = 1+a[n-i-1]
        r1 = k+a[i]
        r2 = k+a[n-i-1]
        pref[min(l1,l2)] +=1
        pref[max(r1,r2) +1] -=1
       # print(pref)

    for i in range(1,2*k+2):
        pref[i] += pref[i-1]
    #print(pref)
    #print(cnt)

    ans = 10**10
    #print(pref)
    for sum in range(2,2*k+1):
        #if sum == 13:
            #print((pref[sum]-cnt[sum]) + (n/2-pref[sum])*2)
        #print(sum)
        #print(pref[sum])
        ta = (pref[sum]-cnt[sum]) + (n/2-pref[sum])*2
        ans= min(ans , ta)

    print(int(ans))