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 = "for _ in range(int(input())):\n    n,l,out = int(input()),list(map(lambda x: int(x)- 1, input().split())),[];ll = sorted([(l[i], i) for i in range(n)]);swap = (-1,-1);newl = [0]*n    \n    for i in range(n - 1):\n        if ll[i][0] == ll[i + 1][0]:swap = (ll[i][1],ll[i+1][1])  \n    for i in range(n):newl[ll[i][1]] = i\n    l,swapN = newl,0;works,done = True,False\n    for i in range(n):\n        for j in range(i + 1, n):\n            if l[i] > l[j]:swapN += 1\n    if swapN & 1:l[swap[0]],l[swap[1]] = l[swap[1]],l[swap[0]]\n    def shift(i):out.append(i + 1);l[i],l[i+1],l[i+2] = l[i+2],l[i],l[i+1]       \n    while not done:\n        for i in range(n):\n            if l[i] != i:break\n        else:done = True\n        if done:break\n        for find in range(i + 1, n):\n            if l[find] == i:break\n        while find - i >= 2:find -= 2;shift(find)\n        if find - i == 1:\n            if find <= n - 2:shift(find - 1);shift(find - 1)\n            else:works = False;break\n    if works:print(len(out));print(' '.join(map(str,out)))\n    else:print(-1)         "
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 13949