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 p in range(0,t):
    n,k = map(int,input().split())
    a = list(map(int,input().split()))

    zerocnt = [0]*((2*k)+1)
    onecnt = [0]*((2*k)+2)
    # twocnt = [0]*((2*k)+2)

    for i in range(0,n//2):
        # print(onecnt)
        # print(a)
        zerocnt[a[i]+a[n-(i+1)]] +=1
        chota = min(a[i],a[n-(i+1)])
        bada = max(a[i],a[n-(i+1)])
        onecnt[chota+1] +=1
        onecnt[bada+k+1] -=1
        # for i in range(chota+1,bada+k+1):
        #     onecnt[i]+=1
        # twocnt[a[i]+a[n-(i+1)]] =
    # print(onecnt)
    for i in range(1,2*k+1):
        onecnt[i] += onecnt[i-1]
    # print(onecnt)
    # print(zerocnt)
    m = 10**9
    for i in range(2,(2*k)+1):
        if((onecnt[i] - zerocnt[i])+((n//2) - onecnt[i])*2 < m):
            m = (onecnt[i] - zerocnt[i])+((n//2) - onecnt[i])*2
        # print(m)
    print(m)

    # if(len(set(summ)) == len(summ)):
    #     temp = sum(summ)/len(summ)
    #     mini = abs(summ[0] - temp)
    #     m = summ[0]
    #     for i in range(1,len(summ)):
    #         if(abs(summ[i] - temp) < mini):
    #             m= summ[i]
    #             mini = abs(summ[i] - temp)
        # print(mini)
        # print(m)
    # ans = 10**9
    # for j in range(2,(2*k)+1):
    #     m = j
    #     cnt = 0
    #     for i in range(0,n//2):
    #
    #         x = a[i]
    #         y = a[n-(i+1)]
    #         chota = min(x,y)
    #         bada = max(x,y)
    #         if(chota+bada == m):
    #             cnt+=0
    #         elif(chota >= m):
    #             cnt +=2
    #         else:
    #             if(bada<=m):
    #                 if(bada+k >=m):
    #                     cnt +=1
    #                 else:
    #                     cnt +=2
    #             else:
    #                 if(chota+1<=m):
    #                     cnt +=1
    #                 else:
    #                     cnt +=2
    #     #     print(cnt,end='   enjoy   ')
    #     # print()
    #     # print(m,end='=====')
    #     # print(cnt,end='+++++++')
    #     # print()
    #     ans = min(ans,cnt)
    #
    # print(ans)
    #
    # else:
    #     countt = 0
    #     new = sorted(summ)
    #     chck = new[0]
    #     i = 0
    #     c = 0
    #     while(i<n):
    #         if(new[i] == chck):
    #             c =+1
    #         else:
    #             if(c>countt):
    #                 countt = c
    #             chck = new[i]
    #             c = 1
    #         i+=1
    #     m = chck
    #     cnt = 0
    #     for i in range(0,len(summ)):
    #         if(summ[i] == m):
    #             continue
    #         else:
    #             x = a[i]
    #             y = a[n-(i+1)]
    #             chota = min(x,y)
    #             bada = max(x,y)
    #
    #             if(chota > m):
    #                 cnt +=2
    #             else:
    #                 if(bada<m):
    #                     if(chota+k >=m):
    #                         cnt +=1
    #                     else:
    #                         cnt +=2
    #                 else:
    #                     if(chota+1<=m):
    #                         cnt +=1
    #                     else:
    #                         cnt +=2
    #
    #
    #     print(cnt)
    #
    #
    #