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:
/*  
 *  created on : Thu May 14 2020
 */

import java.io.*;
import java.util.*;

public class D{

    public static void main(String[] args) throws IOException {
        int t = in.nextInt();
        while(t-->0){
            int n = in.nextInt();
            PriorityQueue<Interval> pq = new PriorityQueue<>(new Comparator<Interval>() {
                public int compare(Interval a, Interval b){
                    int diff1 = a.r - a.l;
                    int diff2 = b.r - b.l;

                    if(diff1 == diff2){
                        return a.l - b.l;
                    }

                    return diff2 - diff1;
                }
            });
            int ans[] = new int[n];
            pq.add(new Interval(1, n));
            for(int i = 0; i < n; i++){
                Interval iv = pq.poll(); 
                int mid = iv.l + (iv.r - iv.l)/2;
                ans[mid - 1] = i + 1;

                if(iv.l == iv.r){
                    continue;
                }
                else if(iv.l + 1 == iv.r){
                    pq.add(new Interval(iv.r, iv.r));
                }
                else{
                    pq.add(new Interval(iv.l, mid - 1));
                    pq.add(new Interval(mid + 1, iv.r));
                }
            }

            println(ans);
        }
        
        in.close();
        out.close();
    }

    static class Interval{
        int l;
        int r;

        Interval(int l, int r){
            this.l = l;
            this.r = r;
        }
    }

    static int MIN = Integer.MIN_VALUE;
    static int MAX = Integer.MAX_VALUE;
    static Reader in = new Reader();
    static PrintWriter out = new PrintWriter(System.out);

    static int[] readInt(int N) throws IOException { 
    	int arr[] = new int[N];
    	for(int i = 0; i < N; i++){ 
    		arr[i] = in.nextInt(); 
    	} 
    	return arr;
    }
    
    static long[] readLong(int N) throws IOException { 
    	long arr[] = new long[N];
    	for(int i = 0; i < N; i++){ 
    		arr[i] = in.nextLong(); 
    	} 
    	return arr;
    }
    
    static String[] readString(int N) throws IOException { 
    	String arr[] = new String[N];
    	for(int i = 0; i < N; i++){ 
    		arr[i] = in.next(); 
    	} 
    	return arr;
    }
    
    static void print(Object O) {  
    	out.print(O); 
    }
    
    static void println(Object O) { 
    	out.println(O); 
    }
    
    static void println(int arr[]) { 
    	for(int i = 0; i < arr.length; i++){ 
    		print(arr[i] + " "); 
    	} 
    	println(""); 
    }
    
    static void debug(Object ... O) { 
    	for(Object obj: O){
    		System.out.print(obj + " ");
    	}
    	System.out.println();
    }
}

class Reader {
    BufferedReader reader;
    StringTokenizer tokenizer;

    Reader() {
        reader = new BufferedReader(new InputStreamReader(System.in));
        tokenizer = new StringTokenizer("");
    }

    String next() throws IOException {
        while (!tokenizer.hasMoreTokens() ) { 
            tokenizer = new StringTokenizer(reader.readLine()); 
        }
        return tokenizer.nextToken();
    }

    int nextInt() throws IOException { 
        return Integer.parseInt(next()); 
    }
    
    double nextDouble() throws IOException { 
        return Double.parseDouble(next());
    }
    
    long nextLong() throws IOException { 
        return Long.parseLong(next()); 
    }
    
    String nextLine() throws IOException { 
        return reader.readLine(); 
    }
    
    void close() throws IOException { 
        reader.close(); 
    }
}