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:
from sys import stdin
input=lambda : stdin.readline().strip()
from math import ceil,sqrt,factorial,gcd
from collections import deque
for _ in range(int(input())):
	n=int(input())
	ans=[0 for i in range(n+1)]
	stack=deque()
	stack.append((1,n))
	d={i:[] for i in range(1,n+1)}
	z=set()
	z.add(1)
	while stack:
		a=stack.pop()
		if a[0]<=a[1]:
			if a[0]==a[1]:
				d[1].append(a[0])
			else:
				d[a[1]-a[0]+1].append(a)
				z.add(a[1]-a[0]+1)
				if (a[1]-a[0]+1)%2!=0:
					# ans[(a[1]+a[0])//2]=t
					stack.append((a[0],(a[1]+a[0])//2-1))
					stack.append(((a[1]+a[0])//2+1,a[1]))
				else:
					# ans[(a[1]+a[0]-1)//2]=t
					stack.append(((a[1]+a[0]-1)//2+1,a[1]))
					stack.append((a[0],(a[1]+a[0]-1)//2-1))
	z=list(z)
	z.sort(reverse=True)
	t=1
	# print(z)
	for i in z:
		f=sorted(d[i])
		if i==1:
			for k in f:
				ans[k]=t
				t+=1
		else:
			for k in f:
				ans[(k[1]+k[0])//2]=t
				t+=1
	print(*ans[1:])