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.*;

 // Compiler version JDK 11.0.2

public class Dcoder
 {
   public static void main(String args[])
   { 
    Scanner sc=new Scanner(System.in);
    int t=sc.nextInt();
    while(t-->0){
      int n=sc.nextInt();
      Solution sol=new Solution();
      
      sol.solve(n);
      sol.getAns();
      System.out.println();
    }
   }
   static class Solution{
     static int arr[];
     static int itr=1;
     int dp[];
     static Map<Integer,SortedSet<Integer>> m=new TreeMap<>();
     public void solve(int n){
       arr=new int[n];
       itr=1;
       dp=new int[n+1];
       createArray(0,n-1);
     }
     public void createArray(int left,int right){
       
       if(right-left+1==0)
       return;
         
       
       
       
       SortedSet<Integer> set=new TreeSet<>();
       set.add(left);
       dp[left]=right;
       m.put(right-left+1,set);
       while(!m.isEmpty()){
         
        Set<Integer> s=m.keySet();
        int k=0;
        for(int r:s){
          k=r;
        }
        SortedSet<Integer> u=m.get(k);
        
        int kk=0;
        for(int r:u){
          kk=r;
          break;
        }
        u.remove(kk);
        
        if(u.isEmpty())
         m.remove(k);
        
        
        int x=kk;
        
        int y=dp[x];
        
         
         int len=y-x+1;
         int mid=(x+y)/2;
         if(len%2==0)
         mid=(x+y-1)/2;
           
         
         arr[mid]=itr++;
         
         if(x<=mid-1)
         add(x,mid-1);
         
         if(y>=mid+1)
         add(mid+1,y);
         
        
         
         
         }
         
         
       }
       public void add(int x,int y)
       {
         int ind=y-x+1;
         if(m.get(ind)==null){
           SortedSet<Integer> temp=new TreeSet<>();
           temp.add(x);
           dp[x]=y;
           m.put(ind,temp);
         }
         else{
           SortedSet<Integer> temp=m.get(ind);
           temp.add(x);
           dp[x]=y;
           m.put(ind,temp);
         }
         
         
       }
       
       
     
     public void getAns(){
      
      for(int i=0;i<arr.length;i++)
      System.out.print(arr[i]+" ");
      return ;
     }
   }
   
 }