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:
FAST_IO = 1
if FAST_IO:
    import io, sys, atexit
    rr = iter(sys.stdin.read().splitlines()).next
    sys.stdout = _OUTPUT_BUFFER = io.BytesIO()
    @atexit.register
    def write():
        sys.__stdout__.write(_OUTPUT_BUFFER.getvalue())
else:
    rr = raw_input
rri = lambda: int(rr())
rrm = lambda: map(int, rr().split())


from collections import Counter, defaultdict as ddic
def solve(N, K, A):
    # N even, all ai <= K
    # replace minimum elements so ai + a~i = x
    N2 = N // 2
    count = [0] * (2*K + 2)
    for i in xrange(N2):
        x = A[i]
        y = A[~i]
        if x>y:x,y=y,x
        s = x + y
        # all s  in [a+1, b+K] is 1
        # rest is 0
        # s == a+b is 2
        count[x+1] += 1  # 
        count[y+K+1] -= 1
        count[s] += 1
        count[s+1] -= 1
        
    for i in xrange(1,2*K+2):
        count[i] += count[i-1]
    #print("!", count)
    return 2 * N2 - max(count)
        
        
        

T = rri()
for t in xrange(1, T+1):
    N,K =rrm()
    A = rrm()
    ans= solve(N, K, A)
    print ans