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 JAVA):

Solution:
//package CodeForces;

import java.io.*;
import java.util.*;

public class ConstructingTheArray {
	
	static class node
	{
		int x;int y;
		node(int a,int b)
		{
			this.x=a;
			this.y=b;
		}
	}

	public static void main(String[] args) throws IOException{
		// TODO Auto-generated method stub
		BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
		int t=Integer.parseInt(br.readLine());
		StringBuilder small=new StringBuilder();
		while(t>0)
		{
			int n=Integer.parseInt(br.readLine());
			PriorityQueue<node> arr=new PriorityQueue<node>(new Comparator<node>(){
				public int compare(node a,node b)
				{
					int temp1=a.y-a.x+1;
					int temp2=b.y-b.x+1;
					if(temp1!=temp2)
					{
						return temp2-temp1;
					}
					else
					{
						return a.x-b.x;
					}
				}
			});
			node root=new node(0,n-1);
			arr.add(root);
			int ans[]=new int[n];int count=1;
			while(arr.size()>0)
			{
				    node temp=arr.remove();
					int x=temp.x;
					int y=temp.y;
					
						int mid=(x+y)/2;
						ans[mid]=count++;
						node newnode1=new node(x,mid-1);
						node newnode2=new node(mid+1,y);
						if(mid-1>=x)
						{
							arr.add(newnode1);
						}
						if(mid+1<=y)
						{
							arr.add(newnode2);
						}
					
				
			}
			
			
			for(int i=0;i<n;i++)
				small.append(ans[i]+" ");
			small.append("\n");
			
			
			t--;
		}
		System.out.println(small);

	}

}