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 whatever; // 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 Ideone
{
	public static void main (String[] args) throws java.lang.Exception
	{

		MyScanner sc = new MyScanner();
		out = new PrintWriter(new BufferedOutputStream(System.out));
		int t = sc.nextInt();
		while(t-- > 0) {
			int n = sc.nextInt();
			int[] ans = new int[n+1];
			
			TreeSet<int[]> tSet = new TreeSet<int[]>((i1, i2) -> {
				if(i2[1]-i2[0] != i1[1]-i1[0])
					return i2[1]-i2[0] - (i1[1]-i1[0]);
				else {
					return i1[0] - i2[0];
				}
			});
			
			tSet.add(new int[]{1, n});
			int count = 1;
			while(count <= n && !tSet.isEmpty()) {
				int[] first = tSet.first();
				int len = first[1] - first[0] + 1;
				if(len%2==1) {
					int mid = (first[1] + first[0])/2;
					ans[mid] = count;
					tSet.remove(first);
					if(mid-1-first[0] + 1 > 0)
						tSet.add(new int[]{first[0], mid-1});
					if(first[1] - mid > 0)
						tSet.add(new int[]{mid+1, first[1]});
				} else {
					int mid = (first[1] + first[0] - 1)/2;
					ans[mid] = count;
					tSet.remove(first);
					if(mid-1-first[0] + 1 > 0)
						tSet.add(new int[]{first[0], mid-1});
					if(first[1] - mid > 0)
						tSet.add(new int[]{mid+1, first[1]});
				}
				count++;
			}
			
			for(int i=1; i<=n; i++) {
				System.out.print(ans[i] + " ");
			}
			System.out.println();
		}
	}
	
	
	public static PrintWriter out;
      
   //-----------MyScanner class for faster input----------
   public static class MyScanner {
      BufferedReader br;
      StringTokenizer st;
 
      public MyScanner() {
         br = new BufferedReader(new InputStreamReader(System.in));
      }
 
      String next() {
          while (st == null || !st.hasMoreElements()) {
              try {
                  st = new StringTokenizer(br.readLine());
              } catch (IOException e) {
                  e.printStackTrace();
              }
          }
          return st.nextToken();
      }
 
      int nextInt() {
          return Integer.parseInt(next());
      }
 
      long nextLong() {
          return Long.parseLong(next());
      }
 
      double nextDouble() {
          return Double.parseDouble(next());
      }
 
      String nextLine(){
          String str = "";
	  try {
	     str = br.readLine();
	  } catch (IOException e) {
	     e.printStackTrace();
	  }
	  return str;
      }

   }
}