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 = 'A = [0 for x in range(400005)]\nt = int(input())\ndef mymin(a,b):\n    if(a<b):\n        return a\n    else:\n        return b\n\ndef mymax(a,b):\n    if(a>b):\n        return a\n    else:\n        return b\n\nfor tests in range(t):\n    [n,k] = input().split()\n    n = int(n)\n    k = int(k)\n    B = input().split()\n    for i in range(2,(2*k)+1):\n        A[i] = 0\n    n2 = int(n/2)\n    for i in range(n2):\n        B[i] = int(B[i])\n        B[n-1-i] = int(B[n-1-i])\n        mi = mymin(B[i],B[n-1-i])\n        ma = mymax(B[i],B[n-1-i])\n        A[2] += 2\n        A[mi+1] -= 1\n        A[mi+ma] -= 1\n        if(mi+ma+1 <= 2*k):\n            A[mi+ma+1] +=1\n        if(ma+k+1 <= 2*k):\n            A[ma+k+1] +=1\n    ans = n\n    for i in range(2,(2*k)+1):\n        A[i] += A[i-1]\n        if(A[i]<ans):\n            ans = A[i]\n    print(ans)\n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 3306485