For his birthday, Kevin received the set of pairwise distinct numbers $1, 2, 3, \ldots, n$ as a gift.

He is going to arrange these numbers in a way such that the minimum absolute difference between two consecutive numbers be maximum possible. More formally, if he arranges numbers in order $p_1, p_2, \ldots, p_n$, he wants to maximize the value $$\min \limits_{i=1}^{n - 1} \lvert p_{i + 1} - p_i \rvert,$$ where $|x|$ denotes the absolute value of $x$.

Help Kevin to do that.


-----Input-----

Each test consists of multiple test cases. The first line contains a single integer $t$ ($1 \le t \le 100$) — the number of test cases. Description of the test cases follows.

The only line of each test case contains an integer $n$ ($2 \le n \leq 1000$) — the size of the set.


-----Output-----

For each test case print a single line containing $n$ distinct integers $p_1, p_2, \ldots, p_n$ ($1 \le p_i \le n$) describing the arrangement that maximizes the minimum absolute difference of consecutive elements.

Formally, you have to print a permutation $p$ which maximizes the value $\min \limits_{i=1}^{n - 1} \lvert p_{i + 1} - p_i \rvert$.

If there are multiple optimal solutions, print any of them.


-----Examples-----

Input
2
4
3
Output
2 4 1 3
1 2 3


-----Note-----

In the first test case the minimum absolute difference of consecutive elements equals $\min \{\lvert 4 - 2 \rvert, \lvert 1 - 4 \rvert, \lvert 3 - 1 \rvert \} = \min \{2, 3, 2\} = 2$. It's easy to prove that this answer is optimal.

In the second test case each permutation of numbers $1, 2, 3$ is an optimal answer. The minimum absolute difference of consecutive elements equals to $1$.

Difficulty: EASY

Solutions:
t = int(input())
for i in range(t):
	n = int(input())
	mid = n // 2
	j = 1
	k = mid + 1
	ret = ''
	for a in range(mid):
		ret += f'{k} {j} '
		k += 1
		j += 1
	if n % 2 != 0:
		ret += str(n)
	print(ret)


def solve(n):
	i = 1
	j = n // 2 + 1
	s = ''
	while i < n // 2 + 1:
		s += f'{j} {i} '
		i += 1
		j += 1
	if n % 2 == 1:
		s += f'{n}'
	return s
t = int(input())
while t > 0:
	t -= 1
	n = int(input())
	print(solve(n))


for _ in range(int(input())):
	n = int(input())
	r = ''
	l = n // 2 + 1
	for i in range(n // 2):
		r += f'{i + l} {i + 1} '
	if n % 2 != 0:
		r += f'{n}'
	print(r)


n = int(input())
for i in range(n):
	m = int(input())
	k = (m + 1) // 2
	l = abs(k - m)
	s = ''
	if m % 2 == 1:
		for j in range(1, m // 2 + 1):
			x = j + l
			s = s + str(x) + ' '
			s += str(j) + ' '
		s += str(m)
		print(s)
	else:
		for j in range(1, m // 2 + 1):
			x = j + l
			s = s + str(x) + ' '
			s += str(j) + ' '
		print(s)


t = int(input())
for _ in range(t):
	n = int(input())
	x = 1
	a = [0] * n
	for i in range(1, n, 2):
		a[i] = x
		x += 1
	for i in range(0, n, 2):
		a[i] = x
		x += 1
	_str = ''
	for i in a:
		_str += str(i) + ' '
	print(_str)