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())
    l = list(map(int, input().split()))
    a = []
    b = []
    d = []
    for i in range(0,n//2):
        b.append(l[i]+l[n-i-1])
        d.append(max(l[i],l[n-i-1])+k)
        a.append(min(l[i],l[n-i-1]))
    b.sort()
    d.sort()
    a.sort()
    c = []
    last = -1
    cnt = 0
    for i in b:
        if last == -1:
            last = i
            cnt = 1
        elif last == i:
            cnt += 1
        else:
            c.append([last,cnt])
            cnt = 1
            last = i
    c.append([last,cnt])
    ans = n-2
    curr = n
    i = 0
    j = 0
    k = 0
    sa = len(a)
    sc = len(c)
    sd = len(d)
    #print(a,b,c,d)
    while i<sa and j<sc and k<sd:
        if curr < ans:
            ans = curr
        if c[j][0] <= a[i] and c[j][0] <= d[k]:
            if curr-c[j][1] < ans:
                ans = curr-c[j][1]
            j += 1
        elif a[i] <= d[k]:
            curr -= 1
            i += 1
        else:
            curr += 1
            k += 1
        #print(i,j,k,curr,ans)
    while j<sc and k<sd:
        if curr < ans:
            ans = curr
        if c[j][0] <= d[k]:
            if curr-c[j][1] < ans:
                ans = curr-c[j][1]
            j += 1
        else:
            curr += 1
            k += 1
        #print(i,j,k,curr,ans)
    if curr < ans:
        ans = curr
    print(ans)