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:
//note: 0<=|int|<=2 * 10^9
//note: 0<=|long|<= 9 * 10^18

import java.io.*;
import java.util.*;
 
public class MyProgram{
    static ArrayList<Integer>[] adj;
    
    static StringTokenizer st;
    static BufferedReader br;
    
    static class Comp implements Comparator<int[]>{
        public int compare(int[] i1, int[] i2){
            if(i2[1] - i2[0] == i1[1] - i1[0]){
                return Integer.compare(i1[0], i2[0]);
            }
            else{
                return Integer.compare(i2[1]-i2[0],i1[1]-i1[0]);
            }
        }
    }
   
    public static void main(String[] args) throws IOException{
        MyScanner sc = new MyScanner();
        out = new PrintWriter(new BufferedOutputStream(System.out));
        
        int t = sc.nextInt();
        for(int i = 0; i < t; i++){
            int n = sc.nextInt();
            int[] arr = new int[n];
            
            PriorityQueue<int[]> pq = new PriorityQueue<>(new Comp());
            int[] start = {0,n-1};
            pq.add(start);
            
            int count = 1;
            while(!pq.isEmpty()){
                int[] k = pq.poll();
                
                int left = k[0];
                int mid = k[0] + (k[1] - k[0])/2;
                int right = k[1];
                
                if(right - left == 1){
                    int[] add = {k[1], k[1]};
                    pq.add(add);
                }
                else if(right - left != 0){
                    int[] add1 = {k[0], mid - 1};
                    int[] add2 = {mid+1, k[1]};
                    pq.add(add1);
                    pq.add(add2);
                }
                
                arr[mid] = count++;
            }
            
            for(int j : arr){
                System.out.print(j + " ");
            }
            System.out.println();
            
        }
        out.close();
   }
   
   //-----------PrintWriter for faster output---------------------------------
    public static PrintWriter out;
      
   //-----------MyScanner class for faster input----------
    public static class MyScanner {
 
      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;
      }

   }
   //--------------------------------------------------------
}