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 $\frac{n}{2}$ elements of $a$ are even (divisible by $2$);  the second $\frac{n}{2}$ 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 ($\sum\limits_{i=1}^{\frac{n}{2}} a_i = \sum\limits_{i=\frac{n}{2} + 1}^{n} a_i$). 

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 $t$ ($1 \le t \le 10^4$) — the number of test cases. Then $t$ test cases follow.

The only line of the test case contains one integer $n$ ($2 \le n \le 2 \cdot 10^5$) — 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 $2 \cdot 10^5$ ($\sum n \le 2 \cdot 10^5$).


-----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 $a_1, a_2, \dots, a_n$ ($1 \le a_i \le 10^9$) 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
[{"code": "for _ in range(int(input())):\n    n=int(input())\n    if(n%4!=0):\n        print('NO')\n    elif(n%4==0):\n        print('YES')\n        a=[]\n        for i in range(1,n//2+1):\n            a.append(i*2)\n        s=sum(a)\n        s1=0\n        for i in range(1,n//2):\n            x=i*2-1\n            a.append(x)\n            s1+=x\n        a.append(s-s1)\n        print(*a)", "passed": true, "time": 0.14, "memory": 14196.0, "status": "done"}, {"code": "t = int(input())\nfor rew in range(t):\n\tn = int(input())\n\tif n%4 == 2:\n\t\tprint(\"NO\")\n\telse:\n\t\tprint(\"YES\")\n\t\tn//=2\n\t\tpocz = [2*(i+1) for i in range(n)]\n\t\tkon = [2*i+1 for i in range(n-1)]\n\t\tdod = sum(pocz)-sum(kon)\n\t\todp = pocz + kon + [dod]\n\t\tprint(*odp)", "passed": true, "time": 0.14, "memory": 14076.0, "status": "done"}, {"code": "for i in range(int(input())):\n\tn=int(input())\n\tk=int(n/2)\n\tif(k%2==1):\n\t\tprint(\"NO\")\n\telse:\n\t\tprint(\"YES\")\n\t\ts1=0\n\t\tfor i in range(k):\n\t\t\tprint(2*(i+1), end=\" \")\n\t\t\ts1+=2*(i+1)\n\t\ts2=0\n\t\tfor i in range(k-1):\n\t\t\tprint(2*i+1, end=\" \")\n\t\t\ts2+=2*i+1\n\t\tprint(s1-s2)", "passed": true, "time": 0.14, "memory": 14180.0, "status": "done"}, {"code": "t = int(input())\nfor _ in range(t):\n    n = int(input())\n    if (n // 2) % 2:\n        print(\"NO\")\n        continue\n    a = []\n    s = 0\n    for i in range(n // 2):\n        s += 2*(i + 1)\n        a.append(2*(i + 1))\n    for j in range(n // 2 - 1):\n        s -= 2*j + 1\n        a.append(2*j + 1)\n    a.append(s)\n    print(\"YES\")\n    print(*a)\n\n\n# a = list(map(int,input().split()))\n# n,m = map(int,input().split())\n\n", "passed": true, "time": 0.14, "memory": 14248.0, "status": "done"}, {"code": "import sys\nlines = sys.stdin.readlines()\nT = int(lines[0].strip())\nfor t in range(1, T+1):\n    n = int(lines[t].strip())\n    if n % 4 == 2: print(\"NO\"); continue\n    print(\"YES\")\n    res = []\n    tmp = 0\n    for i in range(1, n//2+1):\n        res.append(2*i)\n        tmp += 2*i\n    for i in range(1, n//2):\n        res.append(2*i-1)\n        tmp -= 2*i-1\n    res.append(tmp)\n    print(\" \".join(map(str, res)))\n", "passed": true, "time": 0.42, "memory": 14200.0, "status": "done"}, {"code": "t = int(input())\nfor tt in range(t):\n\tn = int(input())\n\tif n % 4 == 0:\n\t\tprint('YES')\n\t\ta = list(range(2, n + 1, 2)) + list(range(1, n - 1, 2)) + [sum(range(2, n + 1, 2)) - sum(range(1, n - 1, 2))]\n\t\tprint(' '.join(map(str, a)))\n\telse:\n\t\tprint('NO')\n", "passed": true, "time": 0.14, "memory": 14288.0, "status": "done"}, {"code": "t = int(input())\nfor _ in range(t):\n    n = int(input())\n    if (n//2)%2 == 1:\n        print(\"NO\")\n    else:\n        print(\"YES\")\n        even = [i*2 for i in range(1, n//2 + 1)]\n        odd = [(i*2 - 1) for i in range(1, n//2)]\n        odd.append((sum(even) - sum(odd)))\n        print(*even, *odd)\n", "passed": true, "time": 0.14, "memory": 14316.0, "status": "done"}]