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:

import java.util.*;

public class codeforce {

	public static class Pair {
		int st;
		int end;

		Pair(int st, int end) {
			this.st = st;
			this.end = end;
		}
	}

	public static class Combine {
		int len;
		Pair p;

		Combine(int len, Pair p) {
			this.len = len;
			this.p = p;
		}
	}

	public static class ComComparator implements Comparator<Combine>{ 
        
        // Overriding compare()method of Comparator  
                    // for descending order of cgpa 
        public int compare(Combine s1, Combine s2) { 
            if (s1.len < s2.len) 
                return 1; 
            else if (s1.len > s2.len) 
                return -1; 
            else 
            {
            	int st1 = s1.p.st;
            	int st2 = s2.p.st;
            	
            	if(st1<st2)
            		return -1; 
            	else
            		return 1;
            }
        }              
       
    } 
	public static void main(String[] args)
	{
   
	  Scanner s = new Scanner(System.in); 
	int t=s.nextInt();
	for(int i=0;i<t;i++)
	{
	  int n =s.nextInt();
	  int[] res= new int[n];
	  PriorityQueue<Combine> pq = new 
	             PriorityQueue<Combine>(5, new ComComparator()); 
	  Pair p = new Pair(1,n);
	  Combine c1 = new Combine(n,p);
	  pq.add(c1);
	  int count=1;
      while(!pq.isEmpty())
      {
    	  
    	  Combine c2 = pq.remove();
    	  Pair p1 = c2.p;
    	  int mid = p1.st + (p1.end-p1.st)/2;
    	  res[mid-1]=count;
    	  count++;      

    	  Pair np1 = new Pair(p1.st,mid-1);
    	  Combine nc1 = new Combine(mid-p1.st,np1);
    	  
    	  Pair np2 = new Pair(mid+1,p1.end);
    	  Combine nc2 = new Combine(p1.end-mid,np2);
    	  
    	  if(nc1.len>0)
    	  pq.add(nc1);
    	  if(nc2.len>0)
    	  pq.add(nc2);
      }
      
      
      for(int j=0;j<res.length;j++)
    	  System.out.print(res[j]+" ");
      System.out.println();
	}
	}
	
}