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 heapq\nimport sys\ninput=sys.stdin.readline\n\nt=int(input())\nfor _ in range(t):\n    n=int(input())\n    arr=list(map(int,input().split()))\n    turned=0\n    q=[]\n    for i in range(n):\n        heapq.heappush(q,arr[i])\n        for j in range(i+1,n):\n            if arr[i]>arr[j]:\n                turned+=1\n    if turned==0:\n        print(0)\n        print('')\n    else:\n        if n==3:\n            if n==len(set(arr)):\n                if turned%2==1:\n                    print(-1)\n                else:\n                    cnt=1\n                    ans=[1]\n                    arr[0],arr[1],arr[2]=arr[2],arr[0],arr[1]\n                    if arr[0]<=arr[1]<=arr[2]:\n                        print(cnt)\n                        print(*ans)\n                    else:\n                        cnt+=1\n                        ans.append(1)\n                        print(cnt)\n                        print(*ans)\n            else:\n                cnt=1\n                ans=[1]\n                arr[0],arr[1],arr[2]=arr[2],arr[0],arr[1]\n                if arr[0]<=arr[1]<=arr[2]:\n                    print(cnt)\n                    print(*ans)\n                else:\n                    cnt+=1\n                    ans.append(1)\n                    print(cnt)\n                    print(*ans)\n            continue\n        if n==len(set(arr)):\n            if turned%2==1:\n                print(-1)\n            else:\n                cnt=0\n                pos=0\n                ans=[]\n                while pos<n:\n                    tmp=heapq.heappop(q)\n                    if arr[pos]==tmp:\n                        pos+=1\n                        continue\n                    else:\n                        tpos=pos+arr[pos:].index(tmp)\n                        while tpos-pos>=2:\n                            cnt+=1\n                            tpos-=2\n                            ans.append(tpos+1)\n                            tmp=0\n                            if arr[tpos]>arr[tpos+1]:\n                                tmp+=1\n                            if arr[tpos]>arr[tpos+2]:\n                                tmp+=1\n                            if arr[tpos+1]>arr[tpos+2]:\n                                tmp+=1\n                            arr[tpos],arr[tpos+1],arr[tpos+2]=arr[tpos+2],arr[tpos],arr[tpos+1]\n                            if arr[tpos]>arr[tpos+1]:\n                                tmp-=1\n                            if arr[tpos]>arr[tpos+2]:\n                                tmp-=1\n                            if arr[tpos+1]>arr[tpos+2]:\n                                tmp-=1\n                            turned-=tmp\n                        if tpos-pos==1:\n                            cnt+=2\n                            tpos-=1\n                            ans.append(tpos+1)\n                            ans.append(tpos+1)\n                            tmp=0\n                            if arr[tpos]>arr[tpos+1]:\n                                tmp+=1\n                            if arr[tpos]>arr[tpos+2]:\n                                tmp+=1\n                            if arr[tpos+1]>arr[tpos+2]:\n                                tmp+=1\n                            arr[tpos],arr[tpos+1],arr[tpos+2]=arr[tpos+1],arr[tpos+2],arr[tpos]\n                            if arr[tpos]>arr[tpos+1]:\n                                tmp-=1\n                            if arr[tpos]>arr[tpos+2]:\n                                tmp-=1\n                            if arr[tpos+1]>arr[tpos+2]:\n                                tmp-=1\n                            turned-=tmp\n                        pos+=1\n                print(cnt)\n                print(*ans)\n        else:\n            cnt=0\n            pos=0\n            ans=[]\n            while pos<n-2:\n                tmp=heapq.heappop(q)\n                if arr[pos]==tmp:\n                    pos+=1\n                    continue\n                else:\n                    tpos=pos+arr[pos:].index(tmp)\n                    while tpos-pos>=2:\n                        cnt+=1\n                        tpos-=2\n                        ans.append(tpos+1)\n                        tmp=0\n                        if arr[tpos]>arr[tpos+1]:\n                            tmp+=1\n                        if arr[tpos]>arr[tpos+2]:\n                            tmp+=1\n                        if arr[tpos+1]>arr[tpos+2]:\n                            tmp+=1\n                        arr[tpos],arr[tpos+1],arr[tpos+2]=arr[tpos+2],arr[tpos],arr[tpos+1]\n                        if arr[tpos]>arr[tpos+1]:\n                            tmp-=1\n                        if arr[tpos]>arr[tpos+2]:\n                            tmp-=1\n                        if arr[tpos+1]>arr[tpos+2]:\n                            tmp-=1\n                        turned-=tmp\n                    if tpos-pos==1:\n                        cnt+=2\n                        tpos-=1\n                        ans.append(tpos+1)\n                        ans.append(tpos+1)\n                        tmp=0\n                        if arr[tpos]>arr[tpos+1]:\n                            tmp+=1\n                        if arr[tpos]>arr[tpos+2]:\n                            tmp+=1\n                        if arr[tpos+1]>arr[tpos+2]:\n                            tmp+=1\n                        arr[tpos],arr[tpos+1],arr[tpos+2]=arr[tpos+1],arr[tpos+2],arr[tpos]\n                        if arr[tpos]>arr[tpos+1]:\n                            tmp-=1\n                        if arr[tpos]>arr[tpos+2]:\n                            tmp-=1\n                        if arr[tpos+1]>arr[tpos+2]:\n                            tmp-=1\n                        turned-=tmp\n                    pos+=1\n            if turned==0:\n                print(cnt)\n                print(*ans)\n            else:\n                ttpos=-1\n                for i in range(n-2,-1,-1):\n                    if arr[i]==arr[i+1]:\n                        ttpos=i\n                        break\n                if ttpos==-1:\n                    cnt+=1\n                    ans.append(n-2)\n                    arr[n-3],arr[n-2],arr[n-1]=arr[n-1],arr[n-3],arr[n-2]\n                    if arr[n-3]<=arr[n-2]<=arr[n-1]:\n                        print(cnt)\n                        print(*ans)\n                    else:\n                        cnt+=1\n                        ans.append(n-3)\n                        print(cnt)\n                        print(*ans)\n                else:\n                    cnt+=2\n                    ans.append(ttpos+1)\n                    ans.append(ttpos+1)\n                    arr[ttpos],arr[ttpos+1],arr[ttpos+2]=arr[ttpos+1],arr[ttpos+2],arr[ttpos]\n                    turned+=1\n                    q=[]\n                    for i in range(n):\n                        heapq.heappush(q,arr[i])\n                    pos=0\n                    while pos<n-2:\n                        tmp=heapq.heappop(q)\n                        if arr[pos]==tmp:\n                            pos+=1\n                            continue\n                        else:\n                            tpos=pos+arr[pos:].index(tmp)\n                            while tpos-pos>=2:\n                                cnt+=1\n                                tpos-=2\n                                ans.append(tpos+1)\n                                arr[tpos],arr[tpos+1],arr[tpos+2]=arr[tpos+2],arr[tpos],arr[tpos+1]\n                            if tpos-pos==1:\n                                cnt+=2\n                                tpos-=1\n                                ans.append(tpos+1)\n                                ans.append(tpos+1)\n                                arr[tpos],arr[tpos+1],arr[tpos+2]=arr[tpos+1],arr[tpos+2],arr[tpos]\n                            pos+=1\n                    print(cnt)\n                    print(*ans)"
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 18085