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 sys\ndef rs(): return sys.stdin.readline().rstrip()\ndef ri(): return int(sys.stdin.readline())\ndef ria(): return list(map(int, sys.stdin.readline().split()))\ndef ws(s): sys.stdout.write(s + '\\n')\ndef wi(n): sys.stdout.write(str(n) + '\\n')\ndef wia(a): sys.stdout.write(' '.join([str(x) for x in a]) + '\\n')\n\n\ndef rotate(a, i):\n    t = a[i+2]\n    a[i + 2] = a[i + 1]\n    a[i + 1] = a[i]\n    a[i] = t\n\n\ndef solve(n, a):\n    sa = sorted(a)\n    s = []\n\n    rolled = False\n    i = 0\n    while i < n:\n        for j in range(i, n):\n            if a[j] == sa[i]:\n                break\n        while j - i >= 2:\n            j -= 2\n            rotate(a, j)\n            s.append(j+1)\n        if i+1 == j:\n            if i+2 < n:\n                rotate(a, i)\n                rotate(a, i)\n                s.append(i+1)\n                s.append(i+1)\n            else:\n                if rolled:\n                    wi(-1)\n                    return\n\n                found = False\n                for k in range(n-2, 0, -1):\n                    if len(set(a[k-1:k+2])) == 2:\n                        found = True\n                        break\n                if found:\n                    if a[k-1] == a[k]:\n                        rotate(a, k - 1)\n                        rotate(a, k - 1)\n                        s.append(k)\n                        s.append(k)\n                    else:\n                        rotate(a, k - 1)\n                        s.append(k)\n                    rolled = True\n                    i = k-2\n                else:\n                    wi(-1)\n                    return\n\n        i += 1\n\n    if len(s) <= n*n:\n        wi(len(s))\n        wia(s)\n    else:\n        wi(-1)\n\n\ndef main():\n    for _ in range(ri()):\n        n = ri()\n        a = ria()\n        solve(n, a)\n\n\ndef __starting_point():\n    main()\n\n__starting_point()"
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 15167