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 Codechef
{
	public static void main (String[] args) throws java.lang.Exception
	{
	
	BufferedReader bf = new BufferedReader(new InputStreamReader(System.in));
	int t=Integer.parseInt(bf.readLine());
	while(t-->0)
	{
	    int n=Integer.parseInt(bf.readLine());
	    int ans[]=new int[n];
	    PriorityQueue<pair> pq=new PriorityQueue<>();
	    pq.add(new pair(0,n-1));
	    int count=0;
	    
	    while(count<n && pq.size()>0)
	    {
	        count++;
	        pair p=pq.poll();
	        int mid=(p.l +p.r)/2;
	        ans[mid]=count;
	        if(p.l<p.r)
	        {
	            pq.add(new pair(p.l,mid-1));
	            pq.add(new pair(mid+1,p.r));
	        }
	    }
	    for(int i=0;i<n;i++)
	    {
	        System.out.print(ans[i]+" ");
	    }
	    System.out.println();
	}
	
	}
	
//  public static class pair
//  {
//      int l;
//      int r;
//       pair(int a,int b)
//       {
//           this.l=a;
//           this.r=b;
//       }
//  }
public static class pair implements Comparable<pair> {
		int l;
		int r;
		int len;
 
		pair(int a, int b) {
			this.l = a;
			this.r = b;
			this.len = b - a + 1;
		}
 
	//	@Override
		public int compareTo(pair o) {
			// TODO Auto-generated method stub
			return (o.len == this.len) ? this.l - o.l : o.len - this.len;
		}
 
	}
}