Problem: You are given a positive integer n, it is guaranteed that n is even (i.e. divisible by 2).

You want to construct the array a of length n such that: 

  * The first n/2 elements of a are even (divisible by 2); 
  * the second n/2 elements of a are odd (not divisible by 2); 
  * all elements of a are distinct and positive; 
  * the sum of the first half equals to the sum of the second half (∑_{i=1}^{n/2} a_i = ∑_{i=n/2 + 1}^{n} a_i). 



If there are multiple answers, you can print any. It is not guaranteed that the answer exists.

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 only line of the test case contains one integer n (2 ≤ n ≤ 2 ⋅ 10^5) — the length of the array. It is guaranteed that that n is even (i.e. divisible by 2).

It is guaranteed that the sum of n over all test cases does not exceed 2 ⋅ 10^5 (∑ n ≤ 2 ⋅ 10^5).

Output

For each test case, print the answer — "NO" (without quotes), if there is no suitable answer for the given test case or "YES" in the first line and any suitable array a_1, a_2, ..., a_n (1 ≤ a_i ≤ 10^9) satisfying conditions from the problem statement on the second line.

Example

Input


5
2
4
6
8
10


Output


NO
YES
2 4 1 5
NO
YES
2 4 6 8 1 3 5 11
NO

Solution (in PYTHON3):

Solution:
from sys import stdin


def inp():
    return stdin.buffer.readline().rstrip().decode("utf8")


def itg():
    return int(stdin.buffer.readline())


def mpint():
    return map(int, stdin.buffer.readline().split())

# ############################## import
# from pyrival.data_structures.LazySegmentTree import *
class LazySegmentTree:
    def __init__(self, data, default=0, func=max):
        """initialize the lazy segment tree with data"""
        self._default = default
        self._func = func

        self._len = len(data)
        self._size = _size = 1 << (self._len - 1).bit_length()
        self._lazy = [0] * (2 * _size)

        self.data = [default] * (2 * _size)
        self.data[_size:_size + self._len] = data
        for i in reversed(range(_size)):
            self.data[i] = func(self.data[i + i], self.data[i + i + 1])

    def __len__(self):
        return self._len

    def _push(self, idx):
        """push query on idx to its children"""
        # Let the children know of the queries
        q, self._lazy[idx] = self._lazy[idx], 0

        self._lazy[2 * idx] += q
        self._lazy[2 * idx + 1] += q
        self.data[2 * idx] += q
        self.data[2 * idx + 1] += q

    def _update(self, idx):
        """updates the node idx to know of all queries applied to it via its ancestors"""
        for i in reversed(range(1, idx.bit_length())):
            self._push(idx >> i)

    def _build(self, idx):
        """make the changes to idx be known to its ancestors"""
        idx >>= 1
        while idx:
            self.data[idx] = self._func(self.data[2 * idx], self.data[2 * idx + 1]) + self._lazy[idx]
            idx >>= 1

    def add(self, start, stop, value):
        """lazily add value to [start, stop)"""
        start = start_copy = start + self._size
        stop = stop_copy = stop + self._size
        while start < stop:
            if start & 1:
                self._lazy[start] += value
                self.data[start] += value
                start += 1
            if stop & 1:
                stop -= 1
                self._lazy[stop] += value
                self.data[stop] += value
            start >>= 1
            stop >>= 1

        # Tell all nodes above of the updated area of the updates
        self._build(start_copy)
        self._build(stop_copy - 1)

    def query(self, start, stop, default=0):
        """func of data[start, stop)"""
        start += self._size
        stop += self._size

        # Apply all the lazily stored queries
        self._update(start)
        self._update(stop - 1)

        res = default
        while start < stop:
            if start & 1:
                res = self._func(res, self.data[start])
                start += 1
            if stop & 1:
                stop -= 1
                res = self._func(res, self.data[stop])
            start >>= 1
            stop >>= 1
        return res

    def __repr__(self):
        return "LazySegmentTree({0})".format(self.data)

INF = int(1e7)
# ############################## main

for case in range(itg()):
    n, k = mpint()
    arr = tuple(mpint())
    tree = LazySegmentTree([n]*(2*k+1), INF, min)
    for i in range(n >> 1):
        a, b = arr[i], arr[-i-1]
        mn = min(a, b) + 1
        mx = max(a, b) + k
        # [mn,a+b): -1, a+b:-2, (a+b,mx]:-1
        # -> [mn, mx]: -1 and a+b: -1
        tree.add(mn, mx+1, -1)
        tree.add(a+b, a+b+1, -1)
    print(tree.query(0, len(tree), INF))

# Please check!