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 PYTHON):

Solution:
from collections import defaultdict
from bisect import bisect_left
import sys

t = int(sys.stdin.readline())
for _ in xrange(t):
    n, k = map(int, sys.stdin.readline().split())
    arr = map(int, sys.stdin.readline().split())

    points = defaultdict(int)

    pref = [0] * (2 * k + 2)

    for i in xrange(len(arr) / 2):
        a, b = arr[i], arr[n - i - 1]

        points[a + b] += 1

        min_v = min(1 + b, a + 1)
        max_v = max(k + b, a + k)
        pref[min_v] += 1
        pref[max_v + 1] -= 1

    for i in xrange(1, 2 * k + 1):
        pref[i] += pref[i - 1]

    print min((pref[x] - points[x]) + (n / 2 - pref[x]) * 2 for x in
              xrange(2, 2 * k + 1))