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
	{
		// your code goes here
		Scanner input = new Scanner(System.in);
		int test = input.nextInt();
		while(test-->0){
		    int n = input.nextInt();
		    PriorityQueue<pair>q = new PriorityQueue<>(new comp());
		    int arr[] = new int[n];
		    q.add(new pair(0,n-1));
		    for(int i =1;i<=n;i++){
		        pair seg = q.remove();
		        int mid = (seg.l+seg.r)/2;
		        arr[mid] = i;
		        if(seg.l<mid)q.add(new pair(seg.l,mid-1));
		        if(mid<seg.r)q.add(new pair(mid+1,seg.r));
		        
		    }
		    for(int i =0;i<n;i++)System.out.print(arr[i]+" ");
		    System.out.println();
		}
	}
}
class pair{
        int l,r;
    public pair(int l,int r){
        this.l = l;
        this.r = r;
    }
}
class comp implements Comparator<pair>{

    public int compare(pair a,pair b){
        int seg1 = a.r-a.l+1;
        int seg2 = b.r - b.l+1;
        if(seg1<seg2)return 1;
        if(seg1 == seg2) return a.l>b.l?1:-1;
        return -1;
    }
}