Problem: You are given an array a of length n consisting of zeros. You perform n actions with this array: during the i-th action, the following sequence of operations appears:

  1. Choose the maximum by length subarray (continuous subsegment) consisting only of zeros, among all such segments choose the leftmost one; 
  2. Let this segment be [l; r]. If r-l+1 is odd (not divisible by 2) then assign (set) a[(l+r)/(2)] := i (where i is the number of the current action), otherwise (if r-l+1 is even) assign (set) a[(l+r-1)/(2)] := i. 



Consider the array a of length 5 (initially a=[0, 0, 0, 0, 0]). Then it changes as follows:

  1. Firstly, we choose the segment [1; 5] and assign a[3] := 1, so a becomes [0, 0, 1, 0, 0]; 
  2. then we choose the segment [1; 2] and assign a[1] := 2, so a becomes [2, 0, 1, 0, 0]; 
  3. then we choose the segment [4; 5] and assign a[4] := 3, so a becomes [2, 0, 1, 3, 0]; 
  4. then we choose the segment [2; 2] and assign a[2] := 4, so a becomes [2, 4, 1, 3, 0]; 
  5. and at last we choose the segment [5; 5] and assign a[5] := 5, so a becomes [2, 4, 1, 3, 5]. 



Your task is to find the array a of length n after performing all n actions. Note that the answer exists and unique.

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 (1 ≤ n ≤ 2 ⋅ 10^5) — the length of a.

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 — the array a of length n after performing n actions described in the problem statement. Note that the answer exists and unique.

Example

Input


6
1
2
3
4
5
6


Output


1 
1 2 
2 1 3 
3 1 2 4 
2 4 1 3 5 
3 4 1 5 2 6 

Solution (in PYTHON3):

Solution:
# d1.py

t = int(input())
answers = []
for _ in range(t):
	n = int(input())	
	a = [0 for i in range(n)]

	store = [[]]
	store += [[] for i in range(n)]
	#store[i] has i consecutive zeros stored at the following locations	
	store[n].append((0,n-1))
	iter_num = 1
	for i in range(n):
		if iter_num == n+1:
			break
		num_zeros = n -i

		store[num_zeros].sort()
		for l,r in store[num_zeros]:
			if (r-l)%2 == 0:
				center = int((r+l)/2) 
				# a[int(r+l)/2] = 1
			else:
				center = int((r+l-1)/2)
				# a[int(r+l-1)/2] = 1
				# store[]
			a[center] = iter_num #iter number
			iter_num += 1
			# store[centre]
			if center -l > 0 :
				store[center-l].append((l,center-1))
			if r - center > 0:
				store[r - center].append((center + 1, r))
	a = [str(i)+' ' for i in a]
	answers.append(''.join(a))

print(*answers, sep = '\n')