Problem: You are given an array a consisting of n integers (it is guaranteed that n is even, i.e. divisible by 2). All a_i does not exceed some integer k.

Your task is to replace the minimum number of elements (replacement is the following operation: choose some index i from 1 to n and replace a_i with some integer in range [1; k]) to satisfy the following conditions:

  * after all replacements, all a_i are positive integers not greater than k; 
  * for all i from 1 to n/2 the following equation is true: a_i + a_{n - i + 1} = x, where x should be the same for all n/2 pairs of elements. 



You have to answer t independent test cases.

Input

The first line of the input contains one integer t (1 ≤ t ≤ 10^4) — the number of test cases. Then t test cases follow.

The first line of the test case contains two integers n and k (2 ≤ n ≤ 2 ⋅ 10^5, 1 ≤ k ≤ 2 ⋅ 10^5) — the length of a and the maximum possible value of some a_i correspondingly. It is guratanteed that n is even (i.e. divisible by 2). The second line of the test case contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ k), where a_i is the i-th element of a.

It is guaranteed that the sum of n (as well as the sum of k) over all test cases does not exceed 2 ⋅ 10^5 (∑ n ≤ 2 ⋅ 10^5, ∑ k ≤ 2 ⋅ 10^5).

Output

For each test case, print the answer — the minimum number of elements you have to replace in a to satisfy the conditions from the problem statement.

Example

Input


4
4 2
1 2 1 2
4 3
1 2 2 1
8 7
6 1 1 7 6 3 4 6
6 6
5 2 6 1 3 4


Output


0
1
4
2

Solution (in PYTHON3):

Solution:
#!/usr/bin/env python3

import heapq
import sys
input=sys.stdin.readline

def shift(k,arr):
    arr[k],arr[k+1],arr[k+2]=arr[k+2],arr[k],arr[k+1]

def solve(pos,cnt,ans,arr):
    n=len(arr)
    q=[]
    for i in range(n):
        heapq.heappush(q,arr[i])
    while pos<n-2:
        tmp=heapq.heappop(q)
        if arr[pos]==tmp:
            pos+=1
            continue
        else:
            tpos=pos+arr[pos:].index(tmp)
            while tpos-pos>=2:
                cnt+=1
                tpos-=2
                ans.append(tpos+1)
                shift(tpos,arr)
            if tpos-pos==1:
                cnt+=2
                tpos-=1
                ans.append(tpos+1)
                ans.append(tpos+1)
                shift(tpos,arr)                
                shift(tpos,arr)
            pos+=1
    return cnt,ans

t=int(input())
for _ in range(t):
    n=int(input())
    arr=list(map(int,input().split()))
    cnt,ans=solve(0,0,[],arr)
    if arr[n-2]<=arr[n-1]:
        print(cnt)
        print(*ans)
    else:
        ttpos=-1
        for i in range(n-2,-1,-1):
            if arr[i]==arr[i+1]:
                ttpos=i
                break
        if ttpos!=-1:
            cnt+=2
            ans.append(ttpos+1)
            ans.append(ttpos+1)            
            shift(ttpos,arr)
            shift(ttpos,arr)
            cnt,ans=solve(0,cnt,ans,arr)
            print(cnt)
            print(*ans)
        else:
            cnt+=1
            ans.append(n-2)
            shift(n-3,arr)
            if arr[n-3]<=arr[n-2]<=arr[n-1]:
                print(cnt)
                print(*ans)
            else:
                cnt+=1
                ans.append(n-2)
                shift(n-3,arr)
                if arr[n-3]<=arr[n-2]<=arr[n-1]:
                    print(cnt)
                    print(*ans)
                else:
                    print(-1)