Problem: You are given an array a consisting of n integers.

In one move, you can choose some index i (1 ≤ i ≤ 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 ≤ t ≤ 100) — the number of test cases. Then t test cases follow.

The first line of the test case contains one integer n (3 ≤ n ≤ 500) — the length of a. The second line of the test case contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 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, ..., idx_{ans} (1 ≤ idx_i ≤ 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 

Solution (in PYTHON):

Solution:
#   Author: yumtam
#   Created at: 2020-09-18 11:08

from __future__ import division, print_function
_interactive = False

def main():
    mx = 501
    for _ in range(int(input())):
        n = int(input())
        ar = [int(t) for t in input().split()]

        cnt = [0]*mx
        inv = 0
        sameelt = -1
        ar2 = []
        for x in ar:
            inv += sum(cnt[x+1:])
            ar2.append(x*mx+cnt[x])
            cnt[x] += 1
            if cnt[x] > 1:
                sameelt = x

        if inv % 2 == 1:
            if sameelt == -1:
                print(-1)
                continue
            else:
                idxs = [i for i, x in enumerate(ar) if x==sameelt]
                ar2[idxs[-2]] += 2

        ar = ar2
        ans = []
        def rotate(i):
            ans.append(i+1)
            ar[i], ar[i+1], ar[i+2] = ar[i+2], ar[i], ar[i+1]

        order = sorted(ar)
        for i, x in enumerate(order):
            pos = ar.index(x, i)
            while i < pos:
                if pos-i > 1:
                    rotate(pos-2)
                    pos -= 2
                else:
                    rotate(pos-1)
                    rotate(pos-1)
                    pos -= 1

        print(len(ans))
        print(*ans)


# Constants
INF = float('inf')
MOD = 10**9+7

# Python3 equivalent names
import os, sys, itertools
if sys.version_info[0] < 3:
    input = raw_input
    range = xrange

    filter = itertools.ifilter
    map = itertools.imap
    zip = itertools.izip

# print-flush in interactive problems
if _interactive:
    flush = sys.stdout.flush
    def printf(*args, **kwargs):
        print(*args, **kwargs)
        flush()

# Debug print, only works on local machine
LOCAL = "LOCAL_" in os.environ
debug_print = (print) if LOCAL else (lambda *x, **y: None)

# Fast IO
if (not LOCAL) and (not _interactive):
    from io import BytesIO
    from atexit import register
    sys.stdin = BytesIO(os.read(0, os.fstat(0).st_size))
    sys.stdout = BytesIO()
    register(lambda: os.write(1, sys.stdout.getvalue()))
    input = lambda: sys.stdin.readline().rstrip('\r\n')

# Some utility functions(Input, N-dimensional lists, ...)
def input_as_list():
    return [int(x) for x in input().split()]

def input_with_offset(o):
    return [int(x)+o for x in input().split()]

def input_as_matrix(n, m):
    return [input_as_list() for _ in range(n)]

def array_of(f, *dim):
    return [array_of(f, *dim[1:]) for _ in range(dim[0])] if dim else f()

# Start of external code templates...
# End of external code templates.

main()