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 = '\n\ndef swap(i):\n\n    tmp = a[i+2]\n    a[i+2] = a[i+1]\n    a[i+1] = a[i]\n    a[i] = tmp\n    ans.append(i+1)\n    #print (*a)\n\ntt = int(input())\n\nfor loop in range(tt):\n\n    n = int(input())\n    a = list(map(int,input().split()))\n    sa = 0.0001\n\n    \n    lis = [sa] * 501\n    \n    b1 = []\n    b2 = []\n    \n    f2 = True\n    for i in range(n):\n        if lis[a[i]] != sa and f2:\n            b1.append(a[i] + lis[a[i]])\n            b2.append(a[i])\n            f2 = False\n        else:\n            b1.append(a[i] + lis[a[i]])\n            b2.append(a[i] + lis[a[i]])\n\n        lis[a[i]] += sa\n\n    #print (b1)\n    #print (b2)   \n\n    ans = []\n    a = b1\n    for last in range(n-3):\n\n        mi = last\n        for i in range(last,n):\n            if a[i] < a[mi]:\n                mi = i\n\n        while mi != last:\n\n            if mi - last >= 2:\n                swap(mi-2)\n                mi -= 2\n            else:\n                swap(mi)\n                mi += 1\n\n    while not ( a[-3] < a[-2] and a[-2] < a[-1] ):\n        swap(n-3)\n\n        if len(ans) > n**2:\n            break\n\n    if len(ans) <= n**2:\n        \n        print(len(ans))\n        print(*ans)\n        continue\n\n    ans = []\n    a = b2\n    for last in range(n-3):\n\n        mi = last\n        for i in range(last,n):\n            if a[i] < a[mi]:\n                mi = i\n\n        while mi != last:\n\n            if mi - last >= 2:\n                swap(mi-2)\n                mi -= 2\n            else:\n                swap(mi)\n                mi += 1\n\n    while not ( a[-3] < a[-2] and a[-2] < a[-1] ):\n        swap(n-3)\n\n        if len(ans) > n**2:\n            break\n\n    if len(ans) <= n**2:\n        \n        print(len(ans))\n        print(*ans)\n        continue\n\n    print(-1)\n\n    \n        \n        \n    \n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 16919