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 PYTHON3):

Solution:
#!/usr/bin/env python
import os
import sys
from io import BytesIO, IOBase
from bisect import bisect_left,bisect_right
import threading 
from collections import Counter,defaultdict  
arr=[]




def main():
    for _ in range(int(input())):
        n=int(input())
        arr=list(map(int,input().split()))
        a=arr.copy()
        a.sort()
        mis=0
        cnt=[0]*501
        for i in arr:
            cnt[i]+=1
        b=True
        for i in cnt:
            if i>1:
                b=False
        
        for i in range(n):
            for j in range(i+1,n):
                if arr[j]<arr[i]:
                    mis+=1
        
        if mis%2==1 and b:
            print(-1)
        else:
            ans=[]
            st=n-1
            while st>1:
                ma_=max(arr)
                ind=arr.index(ma_)
                # print(st,ind,ma_,arr)
                for i in range(ind,st-1):
                    arr[i],arr[i+1],arr[i+2]=arr[i+2],arr[i],arr[i+1]
                    # print(arr)
                    ans.append(i)
                if arr[st]!=ma_:
                    arr[st-2],arr[st-1],arr[st]=arr[st],arr[st-2],arr[st-1]
                    ans.append(st-2)
                arr[st]=-1
                st-=1
            # print(ans)
            # print(arr)
            if arr[0]>arr[1]:
                i=1
                while i+2<len(a) and a[i]!=a[i-1]:
                    ans.append(i)
                    ans.append(i-1)
                    a[i+1],a[i+2]=a[i+2],a[i+1]
                    i+=2
                    if i<n-1 and  a[i+1]==a[i-1]:
                        ans.append(i-1)
                        ans.append(i-1)
                        break
            # print("i:",i)

            for i in range(len(ans)):
                ans[i]+=1
            print(len(ans))
            print(*ans)






            









       
 
 
BUFSIZE = 8192
 
 
class FastIO(IOBase):
    newlines = 0
 
    def __init__(self, file):
        self._fd = file.fileno()
        self.buffer = BytesIO()
        self.writable = "x" in file.mode or "r" not in file.mode
        self.write = self.buffer.write if self.writable else None
 
    def read(self):
        while True:
            b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
            if not b:
                break
            ptr = self.buffer.tell()
            self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
        self.newlines = 0
        return self.buffer.read()
 
    def readline(self):
        while self.newlines == 0:
            b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
            self.newlines = b.count(b"\n") + (not b)
            ptr = self.buffer.tell()
            self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
        self.newlines -= 1
        return self.buffer.readline()
 
    def flush(self):
        if self.writable:
            os.write(self._fd, self.buffer.getvalue())
            self.buffer.truncate(0), self.buffer.seek(0)
 
 
class IOWrapper(IOBase):
    def __init__(self, file):
        self.buffer = FastIO(file)
        self.flush = self.buffer.flush
        self.writable = self.buffer.writable
        self.write = lambda s: self.buffer.write(s.encode("ascii"))
        self.read = lambda: self.buffer.read().decode("ascii")
        self.readline = lambda: self.buffer.readline().decode("ascii")
 
 
sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)
input = lambda: sys.stdin.readline().rstrip("\r\n")
 
# endregion
 
if __name__ == "__main__":
    main()