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:
# import sys 
# sys.stdin = open('input.txt', 'r')
# sys.stdout = open('output.txt', 'w')
mod = int(1e9)+7
import heapq
def ip():
	return int(input())
def Ip():
	return map(int, input().split())

for _ in range (0, int(input())):
	n = int(input())
	if n==1:
		print ("1")
	elif n==2:
		print ("1 2")
	else:
		l = [0]*(n)
		t = (n//2)-(n%2==0)
		l[t] = 1
		t -= 1
		x = []
		c = 2
		heapq.heapify(x)
		heapq.heappush(x,[-(t+1),0,t])
		heapq.heappush(x,[-(n-t-2),t+2,n-1])
		# print (x)
		while c<=n:
			el = heapq.heappop(x)
			i,j = el[1],el[2]
			if (j-i+1)%2==1:
				t = (i+j)//2
				l[t] = c
			else:
				t = (i+j-1)//2
				l[t] = c
			if (j-i)>1:
				heapq.heappush(x,[i-t,i,t-1])
				heapq.heappush(x,[t-j,t+1,j])
			else:
				if (j-i)==1:
					heapq.heappush(x,[-1,j,j])
			c += 1
		for i in l:
			print (i, end = " ")
		print()