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 = '#!/usr/bin/env python3\n\nimport heapq\nimport sys\ninput=sys.stdin.readline\n\ndef shift(k,arr):\n    arr[k],arr[k+1],arr[k+2]=arr[k+2],arr[k],arr[k+1]\n\ndef solve(pos,cnt,ans,arr):\n    n=len(arr)\n    q=[]\n    for i in range(n):\n        heapq.heappush(q,arr[i])\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                shift(tpos,arr)\n            if tpos-pos==1:\n                cnt+=2\n                tpos-=1\n                ans.append(tpos+1)\n                ans.append(tpos+1)\n                shift(tpos,arr)                \n                shift(tpos,arr)\n            pos+=1\n    return cnt,ans\n\nt=int(input())\nfor _ in range(t):\n    n=int(input())\n    arr=list(map(int,input().split()))\n    cnt,ans=solve(0,0,[],arr)\n    if arr[n-2]<=arr[n-1]:\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+=2\n            ans.append(ttpos+1)\n            ans.append(ttpos+1)            \n            shift(ttpos,arr)\n            shift(ttpos,arr)\n            cnt,ans=solve(0,cnt,ans,arr)\n            print(cnt)\n            print(*ans)\n        else:\n            cnt+=1\n            ans.append(n-2)\n            shift(n-3,arr)\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-2)\n                shift(n-3,arr)\n                if arr[n-3]<=arr[n-2]<=arr[n-1]:\n                    print(cnt)\n                    print(*ans)\n                else:\n                    print(-1)'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 14255