You are given an array $a$ consisting of $n$ integers (it is guaranteed that $n$ is even, i.e. divisible by $2$). All $a_i$ does not exceed some integer $k$.

Your task is to replace the minimum number of elements (replacement is the following operation: choose some index $i$ from $1$ to $n$ and replace $a_i$ with some integer in range $[1; k]$) to satisfy the following conditions:  after all replacements, all $a_i$ are positive integers not greater than $k$;  for all $i$ from $1$ to $\frac{n}{2}$ the following equation is true: $a_i + a_{n - i + 1} = x$, where $x$ should be the same for all $\frac{n}{2}$ pairs of elements. 

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 first line of the test case contains two integers $n$ and $k$ ($2 \le n \le 2 \cdot 10^5, 1 \le k \le 2 \cdot 10^5$) — the length of $a$ and the maximum possible value of some $a_i$ correspondingly. It is guratanteed that $n$ is even (i.e. divisible by $2$). The second line of the test case contains $n$ integers $a_1, a_2, \dots, a_n$ ($1 \le a_i \le k$), where $a_i$ is the $i$-th element of $a$.

It is guaranteed that the sum of $n$ (as well as the sum of $k$) over all test cases does not exceed $2 \cdot 10^5$ ($\sum n \le 2 \cdot 10^5$, $\sum k \le 2 \cdot 10^5$).


-----Output-----

For each test case, print the answer — the minimum number of elements you have to replace in $a$ to satisfy the conditions from the problem statement.


-----Example-----
Input
4
4 2
1 2 1 2
4 3
1 2 2 1
8 7
6 1 1 7 6 3 4 6
6 6
5 2 6 1 3 4

Output
0
1
4
2

```python

USER_FILENAME = "<user_code>"
import sys, json, builtins
import math, heapq, bisect, itertools, functools, collections, statistics, fractions, decimal, operator, array, random, re, string, os, pathlib
try:
    import resource as _res
except Exception:
    _res = None
from collections import Counter, defaultdict, deque, OrderedDict
from functools import lru_cache, reduce
from itertools import accumulate, permutations, combinations, product
from math import gcd, ceil, floor, sqrt
from decimal import Decimal
try:
    from typing import *
except Exception:
    pass
try:
    sys.setrecursionlimit(1_000_000)
except Exception:
    pass
try:
    import site as _site
    try:
        _sys_sites = _site.getsitepackages() if hasattr(_site, "getsitepackages") else []
        for _p in _sys_sites:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
    try:
        _usp = _site.getusersitepackages()
        if isinstance(_usp, str):
            _usp = [_usp]
        for _p in _usp:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
except Exception:
    pass

ns = {"__name__": "__main__"}
for _k, _v in list(globals().items()):
    if not _k.startswith("_"):
        ns[_k] = _v
_CODE = "from bisect import bisect_left as bl\nfrom bisect import bisect_right as br\nfrom heapq import heappush,heappop\nimport math\nfrom collections import *\nfrom functools import reduce,cmp_to_key\n# import io, os\n# input = io.BytesIO(os.read(0,os.fstat(0).st_size)).readline\nimport sys\ninput = sys.stdin.readline\n\nM = mod = 998244353\ndef factors(n):return sorted(set(reduce(list.__add__, ([i, n//i] for i in range(1, int(n**0.5) + 1) if n % i == 0))))\ndef inv_mod(n):return pow(n, mod - 2, mod)\n\ndef li():return [int(i) for i in input().split()]\ndef st():return input()\ndef val():return int(input().rstrip('\\n'))\ndef li2():return [i for i in input()]\ndef li3():return [int(i) for i in input()]\n\n\nfor _ in range(val()):\n    n,k = li()\n    l = li()\n    cnt = Counter()\n    mins = []\n    maxs = []\n    sums = []\n    arr = [0]*(2*k + 5)\n    for i in range(n//2):\n        cnt[l[i] + l[n-i-1]] += 1\n        a,b = max(l[i],l[n-i-1]),min(l[i],l[n-i-1])\n\n\n        arr[b] += 1\n        arr[a + k] -= 1\n\n\n        maxs.append(a + k - b)\n        mins.append(b + 1)\n\n    mins.sort()\n    maxs.sort()\n\n    ans = n\n    curr = arr[1]\n    for i in range(2,2*k + 1,1):\n        onecost = curr - cnt[i]\n        twocost =  n//2 - curr\n        ans = min(ans,onecost + twocost*2)\n        curr += arr[i]\n    print(ans)\n"
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 16555