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
# -*- coding: utf-8 -*-
##################################
# University of Wisconsin-Madison
# Author: Yaqi Zhang
##################################

# standard library
import sys


def main():
    T = int(input())
    for _ in range(T):
        n, k = map(int, input().split())
        nums = list(map(int, input().split()))
        # x <= 2k
        # a <= k
        # make them same
        dp = [0] * (2 * k + 2)
        for i in range(n // 2):
            a, b = nums[i], nums[n - 1 - i]
            if a > b:
                a, b = b, a
            s = a + b
            lo = s - (b - 1)
            hi = s + (k - a)
            # print(lo, s, hi)
            dp[lo] -= 1
            dp[s] -= 1
            dp[s + 1] += 1
            dp[hi + 1] += 1
        mn = n
        cur = n
        for i in range(2, 2 * k + 1):
            cur += dp[i]
            mn = min(cur, mn)
        print(mn)


if __name__ == "__main__":
    main()