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
from collections import defaultdict


def solve():
    [n, k] = map(int, input().split(" "))
    a = list(map(int, input().split(" ")))
    assert len(a) == n and n % 2 == 0
    cnt = defaultdict(int)
    pref = [0] * (2 * k)
    for i in range(0, n // 2):
        x = a[i]
        y = a[n - i - 1]
        cnt[x + y] += 1
        lo = min(x, y) + 1
        hi = max(x, y) + k
        # print(">", x, y, lo, hi)
        # [lo, hi] is a segment for x, in which we have to change one of the numbers
        pref[hi - 1] += 1
        pref[lo - 2] -= 1
        # print("<", pref)

    # print("()", pref)
    for i in range(2 * k - 1 - 1, -1, -1):
        pref[i] += pref[i + 1]

    # print(pref, cnt)

    answer = float('inf')

    for x in range(2, 2 * k + 1):
        zeroes = cnt[x]
        ones = pref[x - 1] - cnt[x]
        twos = n // 2 - zeroes - ones
        # print("x: {0}".format(x), zeroes, ones, twos)
        answer = min(answer, 0 * zeroes + 1 * ones + 2 * twos)
    print(answer)


# https://codeforces.com/problemset/problem/1343/D
# TODO: note down verdict
def main():
    t = int(input())
    for _ in range(t):
        solve()


if __name__ == "__main__":
    main()