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:

// Imports
import java.util.*;
import java.io.*;

public class D642 {

    static class Segment {
        public int start;
        public int end;
        public int size;
        
        public Segment(int s, int e) {
            start = s;
            end = e;
            size = e - s;
        }
        
        @Override
        public String toString() {
            return start + "/" + end;
        }
        
    }
    
    /**
     * @param args the command line arguments
     * @throws IOException, FileNotFoundException 
     */
    public static void main(String[] args) throws IOException, FileNotFoundException {
        
        // TODO UNCOMMENT WHEN ALGORITHM CORRECT
        BufferedReader f = new BufferedReader(new InputStreamReader(System.in));
        
        /* BufferedReader f = new BufferedReader(new StringReader("6\n" +
"1\n" +
"2\n" +
"3\n" +
"4\n" +
"5\n" +
"6")); */
        
        // TODO code application logic here
        int T = Integer.parseInt(f.readLine());
        for(int i = 0; i < T; i++) {
            int N = Integer.parseInt(f.readLine());
            PriorityQueue<Segment> pq = new PriorityQueue<>((Segment o1, Segment o2) -> {
                if(o2.size == o1.size) {
                    return o1.start - o2.start;
                }
                else {
                    return o2.size - o1.size;
                }
            });
            
            pq.add(new Segment(0, N - 1));
            int[] arr = new int[N];
            int val = 1;
            
            while(!pq.isEmpty()) {
                Segment s = pq.remove();
                // System.out.println(s);
                arr[(s.start + s.end)/2] = val;
                val++;
                
                if(s.size > 1) {
                    pq.add(new Segment(s.start, (s.start + s.end)/2 - 1));
                    pq.add(new Segment((s.start + s.end)/2 + 1, s.end));
                }
                else if(s.size == 1) {
                    pq.add(new Segment(s.end, s.end));
                }
            }
            
            StringBuilder sb = new StringBuilder();
            for(int j = 0; j < arr.length; j++) {
                sb.append(arr[j]);
                sb.append(" ");
            }
            System.out.println(sb.substring(0, sb.length() - 1));
        }
    }

}