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:
from sys import *
input = stdin.readline

for _ in range(int(input())):
    
    n,k = map(int,input().split())
    a = list(map(int,input().split()))
    b = [0]*(2*k+1)
    c = [0]*(2*k+1)
    mn = 1e18
    for i in range(n//2):
        x,y = a[i],a[n-i-1]
        x,y = min(x,y),max(x,y)
        sn = x + y
        if(sn+1<=2*k):
            b[sn+1] += 1
        if(sn-1>=0):
            c[sn-1] += 1
        if(sn-(y)>=0):
            c[sn-y] += 1
        if(sn+(k-x)+1<=2*k):
            b[sn+(k-x)+1] += 1
    
    for i in range(1,2*k+1):
        b[i] += b[i-1]
    for i in range(2*k-1,-1,-1):
        c[i] += c[i+1]
        
    for i in range(2*k+1):
        mn = min(mn,b[i]+c[i])
    
    stdout.write(str(mn)+'\n')