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 codechef; // don't place package name! */

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

/* Name of the class has to be "Main" only if the class is public. */
public class Main
{
    static class Pair implements Comparable<Pair>
    {
        int diff;
        int st;
        int end;
        public int compareTo(Pair p)
        {
            if(this.diff==p.diff)
               return (this.st-p.st);
            return -(this.diff - p.diff);
        }
        Pair(int diff, int st, int end)
        {
            this.diff=diff;
            this.st=st;
            this.end=end;
        }
    }
	public static void main (String[] args) throws java.lang.Exception
	{
	    Scanner sc = new Scanner(System.in);
		int test = sc.nextInt();
		while(test-->0)
		{
		    int n = sc.nextInt();
		    int []arr = new int[n];
		  //  for(int i=0;i<n;i++)
		  //     arr[i] = sc.nextInt();
		    PriorityQueue<Pair> queue = new PriorityQueue<>();   
		    queue.add(new Pair(n, 0, n-1));     
		    for(int i=1;i<=n;i++)
		    {
		        Pair p = queue.poll();
		        if(p!=null){
	                if(p.diff == 1){
	                    int j=0;
	                    while(j<n){
	                        if(arr[j]==0)
	                           arr[j]=i++;
	                        j++;    
	                    }
	                    break;
	                }
		            int mid = (p.st+p.end)/2;
		            arr[mid] = i;
		            int st=p.st;
		            int end = p.end;
		            
		            if(mid>st)
		               queue.add(new Pair(mid-st, st, mid-1));
		            if(mid<end)     
		               queue.add(new Pair(end-mid, mid+1, end));
		        }
		    }
		       
		    for(int i=0;i<n;i++)
		       System.out.print(arr[i]+" ");
		    System.out.println();     
		}
	}
}