You are given an array $a$ consisting of $n$ integers.

In one move, you can choose some index $i$ ($1 \le i \le n - 2$) and shift the segment $[a_i, a_{i + 1}, a_{i + 2}]$ cyclically to the right (i.e. replace the segment $[a_i, a_{i + 1}, a_{i + 2}]$ with $[a_{i + 2}, a_i, a_{i + 1}]$). 

Your task is to sort the initial array by no more than $n^2$ such operations or say that it is impossible to do that.

You have to answer $t$ independent test cases.


-----Input-----

The first line of the input contains one integer $t$ ($1 \le t \le 100$) — the number of test cases. Then $t$ test cases follow.

The first line of the test case contains one integer $n$ ($3 \le n \le 500$) — the length of $a$. The second line of the test case contains $n$ integers $a_1, a_2, \dots, a_n$ ($1 \le a_i \le 500$), where $a_i$ is the $i$-th element $a$.

It is guaranteed that the sum of $n$ does not exceed $500$.


-----Output-----

For each test case, print the answer: -1 on the only line if it is impossible to sort the given array using operations described in the problem statement, or the number of operations $ans$ on the first line and $ans$ integers $idx_1, idx_2, \dots, idx_{ans}$ ($1 \le idx_i \le n - 2$), where $idx_i$ is the index of left border of the segment for the $i$-th operation. You should print indices in order of performing operations.


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

Output
0

6
3 1 3 2 2 3 
13
2 1 1 6 4 2 4 3 3 4 4 6 6 
-1
4
3 3 4 4

```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 = "import collections\n\nline = input()\nt = int(line)\nfor _i in range(t):\n    \n    line = input()\n    n = int(line)\n    line = input()\n    nums = [int(i) for i in line.split(' ')]\n    \n    res = collections.deque()\n    for i in range(n - 2):\n        for j in range(n - 3, i-1, -1):\n            if nums[j + 2] < nums[j + 1] and nums[j + 2] < nums[j]:\n                a, b, c = nums[j + 2], nums[j + 1], nums[j]\n                nums[j], nums[j + 1], nums[j + 2] = a, c, b\n                res.append(j + 1)\n        if nums[i] > nums[i + 1]:\n            a, b, c = nums[i], nums[i + 1], nums[i + 2]\n            nums[i], nums[i + 1], nums[i + 2] = b, c, a\n            res.append(i + 1)\n            res.append(i + 1)\n        \n        # print(nums)\n    if nums[n - 3] == nums[n - 1] and nums[n - 2] > nums[n - 1]:\n        res.append(n - 2)\n        nums[n - 1], nums[n - 2] = nums[n - 2], nums[n - 1]\n    if nums[-1] < nums[-2]:\n        i = n - 2\n        while i >= 0 and nums[i] != nums[i + 1]:\n            i -= 1\n        if i < 0:\n            print(-1)\n        else:\n            while i < n - 2:\n                res.append(i + 1)\n                res.append(i + 1)\n                i += 1\n            print(len(res))\n            for i in res:\n                print(i, end= ' ')\n            print()\n    else:\n        print(len(res))\n        for i in res:\n            print(i, end= ' ')\n        print()\n\n"
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 14299