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 = 'def cnt_inv(a):\n    ans = 0\n    for i in range(len(a)):\n        for f in range(i + 1, len(a)):\n            if a[f] < a[i]:\n                ans += 1\n    return ans\n\nfor testcase in range(int(input())):\n    n = int(input())\n    a = list(map(int, input().split()))\n    inv = cnt_inv(a)\n\n    sorted_a = list(sorted(a))\n\n    last_eq = -1\n    for i in range(n - 1):\n        if sorted_a[i] == sorted_a[i + 1]:\n            last_eq = i + 1\n\n    # print("last_eq", last_eq) \n    ans = []\n    def shift(pos):\n        nonlocal inv\n        inv -= int(a[pos] > a[pos + 1]) + int(a[pos] > a[pos + 2]) + int(a[pos + 1] > a[pos + 2])\n        a[pos], a[pos + 1], a[pos + 2] = a[pos + 2], a[pos], a[pos + 1]\n        inv += int(a[pos] > a[pos + 1]) + int(a[pos] > a[pos + 2]) + int(a[pos + 1] > a[pos + 2])\n        ans.append(pos + 1)\n\n    for i in range(n - 3):\n        pos = min(list(range(i, n)), key=lambda x: a[x])\n        # print(a, val, pos) \n        while pos > i + 1:\n            shift(pos - 2)\n            pos -= 2\n        if pos == i + 1:\n            shift(i)\n            shift(i)\n        if i == last_eq and inv % 2 == 1:\n            shift(i)\n            shift(i - 1)\n\n    last_min = min(*a[-3:])\n    while a[-3] != last_min:\n        shift(n - 3)\n    \n    if n - 3 == last_eq and inv % 2 == 1:\n        shift(n - 3)\n        shift(n - 4)\n        \n    cnt = 0\n    while not (a[-3] <= a[-2] <= a[-1]):\n        shift(n - 3) \n        cnt += 1\n        if cnt > 5:\n            break\n    if cnt > 5:\n        print(-1)\n    else:\n        print(len(ans))\n        print(\' \'.join(map(str, ans)))\n\n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: