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 = 'class BIT():\n    def __init__(self, n):\n        self.n = n\n        self.bit = [0] * (n + 1)\n\n    def _add(self, i, val):\n        while i > 0:\n            self.bit[i] += val\n            i -= i & -i\n\n    def get_val(self, i):\n        i = i + 1\n        s = 0\n        while i <= self.n:\n            s += self.bit[i]\n            i += i & -i\n        return s\n\n    def add(self, l, r, val):\n        self._add(r, val)\n        self._add(l, -val)\n\nimport sys\ninput = sys.stdin.readline\n\n\nt = int(input())\nfor _ in range(t):\n    n, k = list(map(int, input().split()))\n    a = list(map(int, input().split()))\n    b = a[n // 2:n][::-1]\n    a = a[0:n // 2]\n    \n    bit = BIT(2 * k + 1)\n    bit.add(0, 2 * k + 1, (2 * n // 2))\n    for i in range(n // 2):\n        ran = [min(a[i] + 1, b[i] + 1), max(a[i] + k + 1, b[i] + k + 1)]\n        bit.add(ran[0], ran[1], -1)\n        bit.add(a[i] + b[i], a[i] + b[i] + 1, -1)\n    print(min([bit.get_val(i) for i in range(2 * k + 1)]))\n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 16955