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:
import sys
# sys.setrecursionlimit(10**6)
input = sys.stdin.buffer.readline
# arr = [[int(el) for el in input().split()] for i in range(n)]

import collections

def solve(n, k, arr):
    d = collections.defaultdict(int)
    
    for i in range(n // 2):
        t = arr[i] + arr[n - 1 - i]
        d[t] += 1

    count_list = sorted( set(d.values()) )

    # print ('###', count_list, d)

    ans = float('inf')

    for i in count_list:

        upper_near_mid_v = float('inf')
        v1 = 0

        lower_near_mid_v = float('inf')
        v2 = 0

        for j in d:
            if d[j] == i:

                if j > k:
                    if j - k < upper_near_mid_v:
                        upper_near_mid_v = j - k
                        v1 = j

                else:
                    if k - j < lower_near_mid_v:
                        lower_near_mid_v = k - j
                        v2 = j
                # if abs(j - k) < near_mid_v:
                #     near_mid_v = abs(j - k)
                #     v = j

        # print (v)
        def chk(v):
            if not v:
                return float('inf')

            t = 0
            # for j in d:
            #     if j != v:
            #         if abs(j - v) <= k:
            #             t += d[j]
            #         else:
            #             t += 2 * d[j]

            for i in range(n // 2):
                temp = arr[i] + arr[n - 1 - i]
                if temp != v:
                    max_v = max(arr[i], arr[n - 1 - i])
                    min_v = min(arr[i], arr[n - 1 - i])
                    
                    if temp > v:
                        if max_v - 1 >= temp - v:
                            t += 1
                        else:
                            t += 2
                    elif temp < v:
                        if k - min_v >= v - temp:
                            t += 1
                        else:
                            t += 2

            return t

        # print ('#v1', v1, chk(v1), '#v2', v2, chk(v2))
        ans = min(ans, chk(v1), chk(v2))

    return min(ans, n//2)


t = int( input() )

for _ in range(t):

    n, k = map(int, input().split())

    arr = list(map(int, input().split()))

    ans = solve(n, k, arr)

    print (ans)