Given a sequence of N elements, Chef defines a function F(i) (1 ≤ i ≤ N) as the median of the first i elements of the sequence.

Chef wants to get a *permutation* P of length N such that P_{i} = F(i) \forall 1 ≤ i ≤ N. Can you help Chef in achieving this?

Note that:
The *median* of a sequence is the middle element in the sorted order of the sequence. If N is even, choose the element at \frac{N}{2} position in the sorted order. If N is odd, choose the middle element.
A *permutation* of length N is an array of N integers P = [P_{1}, P_{2}, \ldots, P_{N}] such that every integer from 1 to N (inclusive) appears in it exactly once. For example, [2,5,4,1,3] is a permutation of length 5 while [2, 5, 2, 1, 3] is not.

------ Input Format ------ 

- First line will contain T, number of test cases. Then the test cases follows.
- Each test case consists of a single line of input, an integer N, the length of the required permutation.

------ Output Format ------ 

For each test case, output in a new line, N space-separated integers, denoting a *permutation* satisfying the condition.

------ Constraints ------ 

$1 ≤ T ≤ 700$
$1 ≤ N ≤ 10^{5}$
- Sum of $N$ over all test cases does not exceed $2 \cdot 10^{5}$.

----- Sample Input 1 ------ 
3
1
2
3

----- Sample Output 1 ------ 
1
2 1 
3 1 2
----- explanation 1 ------ 
Test Case $1$: $[1]$ is the only permutation and it satisfies the condition as the median of the sequence $[1]$ is $1$.

Test Case $2$: The possible permutations of length $2$ are $[1, 2]$ and $[2, 1]$. The only permutation that satisfies the condition is $[2, 1]$. Here, $P_{1} = 2 = median([2])$ and $P_{2} = 1 = median([2, 1])$.

Test Case $3$: There are $6$ possible permutations out of which only $[3,1,2]$ satisfies the above condition.  Here, $P_{1} = 3 = median([3]), P_{2} = 1 = median([3, 1]),$ and $P_{3} = 2 = median([3, 1, 2])$.

Difficulty: EASY

Solutions:
def solve():
	n = int(input())
	p = n // 2 + 1
	k = n - p
	if n % 2:
		for i in range(k, 0, -1):
			print(p + i, p - i, end=' ')
		print(p)
	else:
		for i in range(k, -1, -1):
			print(p + i, p - i - 1, end=' ')
		print()
for _ in range(int(input())):
	solve()


t = int(input())
while t > 0:
	n = int(input())
	i = 1
	while n >= i:
		if n != i:
			print(n, end=' ')
			print(i, end=' ')
		if n == i:
			print(n, end='')
		n -= 1
		i += 1
	print('')
	t -= 1


t = int(input())
for _ in range(t):
	length = int(input())
	max_val = length
	start = 1
	while start <= max_val:
		if start == max_val:
			print(start, end='')
			break
		print(f'{max_val} {start} ', end='')
		max_val -= 1
		start += 1
	print()


T = int(input())
while T:
	n = int(input())
	if n == 1:
		print(n)
	else:
		first = n
		sec = 1
		for i in range(n):
			if i % 2 == 1:
				print(sec, end=' ')
				sec += 1
			else:
				print(first, end=' ')
				first -= 1
		print()
	T = T - 1


for _ in range(int(input())):
	n = int(input())
	if n == 1:
		print(1)
	else:
		first = n
		sec = 1
		for i in range(n):
			if i % 2 == 0:
				print(first, end=' ')
				first -= 1
			else:
				print(sec, end=' ')
				sec += 1
		print()


T = int(input())
ans = []
for i in range(0, T):
	a = int(input())
	li = []
	for j in range(1, a + 1):
		li.append(j)
	ab = ''
	for j in range(0, a // 2):
		ab = ab + str(li[a - j - 1]) + ' ' + str(li[j]) + ' '
	if a % 2 == 1:
		ab += str(li[a // 2])
	print(ab)