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:
''' Constant Palindrome Sum
'''

def search(cumurange, target, lwr=0, upr=False):
    if not upr:
        upr = len(cumurange) - 1
    if upr - lwr == 1:
        if cumurange[upr][0] < target:
            return cumurange[upr]
        else:
            return cumurange[lwr] 

    avg = (upr + lwr) // 2
    test = cumurange[avg]
    if test[0] > target:
        return search(cumurange, target, lwr, avg)
    else:
        return search(cumurange, target, avg, upr)

''' routine '''

T = int(input())

for test in range(T):
    N , K = list(map(int, input().split()))
    array = list(map(int, input().split()))

    totalpairs = N // 2
    pairsum = {}
    exceed2 = 0
    exceed1 = 0
    bounds = {}

    for n in range(totalpairs):
        a1 = array[n]
        a2 = array[N - 1 - n]
        sm = a1 + a2
        if a1 > K and a2 > K:
            exceed2 += 1
            continue
        elif a1 > K or a2 > K:
            a = min(a1, a2)
            minsum = a + 1
            maxsum = a + K + 1
        else:
            minsum = min(a1, a2) + 1
            maxsum = max(a1, a2) + K + 1
            asum = a1 + a2
            if asum in pairsum.keys():
                pairsum[asum] += 1
            else:
                pairsum[asum] = 1

        if minsum in bounds.keys():
                bounds[minsum] += 1
        else:
            bounds[minsum] = 1
        if maxsum in bounds.keys():
            bounds[maxsum] -= 1
        else:
            bounds[maxsum] = -1

    boundorder = sorted(bounds.items(), key=lambda x:x[0])
    # print(boundorder)
    cumulativerange = [boundorder[0]]
    for n in range(1, len(boundorder)):
        pos, qty = boundorder[n]
        prevqty = cumulativerange[n - 1][1]
        cumulativerange.append((pos, qty + prevqty))

    pairsum = list(pairsum.items())

    changes = []
    for cumu in cumulativerange:
        changes.append(N - cumu[1])
    for pair in pairsum:
        pos, val = pair
        cumu = search(cumulativerange, pos)
        # print(cumu, pair)
        changes.append((N - cumu[1] - val))

    minchanges = min(changes)
    # print(cumulativerange)
    # print(pairsum)
    # print(changes)
    print(minchanges)