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 change(i,j,k):\n\tnonlocal a\n\ta[i],a[j],a[k] = a[k],a[i],a[j]\n\nfor nt in range(int(input())):\n\tn = int(input())\n\ta = list(map(int,input().split()))\n\tarr = a[::]\n\tb = sorted(a)\n\tif a==b:\n\t\tprint (0)\n\t\tprint ()\n\t\tcontinue\n\ti = 0\n\tans = []\n\tflag = 0\n\twhile i<n:\n\t\tif a[i]==b[i]:\n\t\t\ti += 1\n\t\t\tcontinue\n\t\tind = a[i:].index(b[i])+i\n\t\t# print (ind)\n\t\twhile a[i]!=b[i]:\n\t\t\tif ind==i+1:\n\t\t\t\tif ind+1>=len(a):\n\t\t\t\t\tflag = 1\n\t\t\t\t\tbreak\n\t\t\t\tans.append((i,ind,ind+1))\n\t\t\t\tchange(i,ind,ind+1)\n\t\t\t\tans.append((i,ind,ind+1))\n\t\t\t\tchange(i,ind,ind+1)\n\t\t\t\tbreak\n\t\t\telse:\n\t\t\t\tans.append((ind-2,ind-1,ind))\n\t\t\t\tchange(ind-2,ind-1,ind)\n\t\t\t\tind -= 2\n\t\tif flag:\n\t\t\tbreak\n\t\ti += 1\n\t\t# print (a)\n\tif flag:\n\t\tif len(set(a))==n:\n\t\t\tprint (-1)\n\t\t\tcontinue\n\t\telse:\n\t\t\tif a[-3]==a[-1]:\n\t\t\t\tans.append((n-3,n-2,n-1))\n\t\t\telse:\n\t\t\t\tans = []\n\t\t\t\ta = arr[::]\n\t\t\t\tflag2 = 0\n\t\t\t\ttemp = sorted(a,reverse=True)\n\t\t\t\tfor i in range(1,n):\n\t\t\t\t\tif temp[i]==temp[i-1]:\n\t\t\t\t\t\tnumber = temp[i]\n\t\t\t\t\t\tbreak\n\t\t\t\ti = 0\n\t\t\t\twhile i<n:\n\t\t\t\t\tif a[i]==b[i] and (i==0 or a[i]!=a[i-1] or flag2):\n\t\t\t\t\t\ti += 1\n\t\t\t\t\t\tcontinue\n\t\t\t\t\telif i!=0 and a[i]==a[i-1]:\n\t\t\t\t\t\tif not flag2 and a[i]==number:\n\t\t\t\t\t\t\tans.append((i-1,i,i+1))\n\t\t\t\t\t\t\tchange(i-1,i,i+1)\n\t\t\t\t\t\t\tans.append((i-1,i,i+1))\n\t\t\t\t\t\t\tchange(i-1,i,i+1)\n\t\t\t\t\t\t\tans.append((i,i+1,i+1))\n\t\t\t\t\t\t\tchange(i,i+1,i+2)\n\t\t\t\t\t\t\tans.append((i,i+1,i+2))\n\t\t\t\t\t\t\tchange(i,i+1,i+2)\n\t\t\t\t\t\t\tflag2 = 1\n\t\t\t\t\t\ti += 1\n\t\t\t\t\t\tcontinue\n\t\t\t\t\t# print (i,a,b)\n\t\t\t\t\tind = a[i:].index(b[i])+i\n\t\t\t\t\t# print (ind)\n\t\t\t\t\twhile a[i]!=b[i]:\n\t\t\t\t\t\tif ind==i+1:\n\t\t\t\t\t\t\tans.append((i,ind,ind+1))\n\t\t\t\t\t\t\tchange(i,ind,ind+1)\n\t\t\t\t\t\t\tans.append((i,ind,ind+1))\n\t\t\t\t\t\t\tchange(i,ind,ind+1)\n\t\t\t\t\t\t\tbreak\n\t\t\t\t\t\telse:\n\t\t\t\t\t\t\tans.append((ind-2,ind-1,ind))\n\t\t\t\t\t\t\tchange(ind-2,ind-1,ind)\n\t\t\t\t\t\t\tind -= 2\n\t\t\t\t\t# print (a,i)\n\t\t\t\t\tif i!=0 and a[i]==a[i-1] and flag2==0 and a[i]==number:\n\t\t\t\t\t\tans.append((i-1,i,i+1))\n\t\t\t\t\t\tchange(i-1,i,i+1)\n\t\t\t\t\t\tans.append((i-1,i,i+1))\n\t\t\t\t\t\tchange(i-1,i,i+1)\n\t\t\t\t\t\tans.append((i,i+1,i+1))\n\t\t\t\t\t\tchange(i,i+1,i+2)\n\t\t\t\t\t\tans.append((i,i+1,i+2))\n\t\t\t\t\t\tchange(i,i+1,i+2)\n\t\t\t\t\t\tflag2 = 1\n\t\t\t\t\ti += 1\n\t\t\t\t\t# print (a)\n\t\n\tprint (len(ans))\n\tfor i in ans:\n\t\tprint (i[0]+1,end=" ")\n\tprint ()'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: