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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.HashMap;
import java.util.*;

public class Codeforces2 {
    public static void main(String[] args) throws IOException {
       BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
       int t=Integer.parseInt(br.readLine());
       while(t-->0)
       {
          int n=Integer.parseInt(br.readLine());
          PriorityQueue<int []> q=new PriorityQueue<>((a,b)->(a[1]-a[0])==(b[1]-b[0])?a[0]-b[0]:(b[1]-b[0])-(a[1]-a[0]));
          int c=1;
          int res[]=new int[n];
          q.add(new int[]{0,n-1});
          int count=n;
          while(!q.isEmpty() )
          {
              int arr[]=q.poll();
            //   System.out.println(Arrays.toString(arr));
              if(arr[0]>arr[1])
              continue;
              int mid=(arr[0]+arr[1])/2;
              res[mid] = c++;
              q.add(new int[]{arr[0],mid-1});
              q.add(new int[]{mid+1,arr[1]});
              
          }
         for(int i:res)
         System.out.print(i+" ");
                  System.out.println();

         
          
    }
    }
}