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 arr
{
    static class seg{
        int len,a,b;
        seg(int x,int y){
            a=x;
            b=y;
            len=y-x+1;
        }
    }
	public static void main (String[] args) throws java.lang.Exception
	{
		// your code goes here
		Scanner sc=new Scanner(System.in);
		int tt=sc.nextInt();
		while(tt-->0){
		    int n=sc.nextInt();
		    int[] arr=new int[n];
		    PriorityQueue<seg> q=new PriorityQueue<>(new Comparator<seg>(){
		        public int compare(seg fir,seg sec){
		            if(fir.len==sec.len){
		                return fir.a-sec.a;
		            }
		            else return sec.len-fir.len;
		        }});
		        int idx=1;
		        q.add(new seg(0,n-1));
		        while(q.size()>0){
		            seg t=q.poll();
		            int s=t.a;
		            int e=t.b;
		            int diff=t.len;
		            int id=0;
		            if(diff%2==1){
		                id=(s+e)/2;
		            }
		            else{
		                id=(s+e-1)/2;
		            }
		            arr[id]=idx++;
		            if(s<=id-1) q.add(new seg(s,id-1));
		            if(e>=id+1) q.add(new seg(id+1,e));
		            
		            
		        }
		        for(int ii:arr){
		            System.out.print(ii+" ");
		        }
		        System.out.println();
		        
		    }
		}
	}