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 forces;

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayDeque;
import java.util.Arrays;
import java.util.HashMap;
import java.util.List;
import java.util.Map;
import java.util.NavigableSet;
import java.util.PriorityQueue;
import java.util.Queue;
import java.util.TreeSet;

public class P3_1353 {
	
	static class Bound implements Comparable<Bound>{
		int lo;
		int hi;
		
		Bound(int lo, int hi) {
			this.lo = lo;
			this.hi = hi;
		}

		@Override
		public int compareTo(Bound b) {
			return this.lo-b.lo;
		}
		
	}
	
	public static void main(String[] args) throws IOException {
		try( BufferedReader in = new BufferedReader(new InputStreamReader(System.in))  ) {
			int t = Integer.parseInt(in.readLine() );
			while(t-- > 0) {
				int n = Integer.parseInt(in.readLine());
				int[] ans = new int[n];
				Map<Integer, NavigableSet<Bound>> map = new HashMap<>();
				Queue<Integer> heap = new PriorityQueue<>(10, (i1, i2) -> i2.intValue()-i1.intValue() );
				
				int lo = 0;
				int hi = (n-1);
				int mid = mid(lo,hi);
				add(map, heap, lo, hi);
				int action = 0;

				while(!map.isEmpty()) {
					int maxlen = heap.peek().intValue();
					Bound b = map.get(maxlen).pollFirst();
					lo = b.lo;
					hi = b.hi;
					mid = mid(lo, hi);
					
					ans[mid] = (++action);
					
					// remove the key if no more bounds attached to it
					if( map.get(maxlen).isEmpty() ) {
						map.remove(maxlen);
						heap.poll();
					}
					
					//add child bounds
					//left child first
					if( lo <= (mid-1) ) {
						add(map, heap, lo, mid-1);
					}
					
					//right child next
					if( hi >= (mid+1) ) {
						add(map, heap, mid+1, hi);
					}
				}
				
				Arrays.stream( ans ).forEach(e -> System.out.print(e+" "));
				System.out.println();
			}
		}
	}
	
	private static void add(Map<Integer, NavigableSet<Bound>> map, Queue<Integer> heap, int lo, int hi) {
		int len = getlen(lo, hi);
		if(!map.containsKey(len)) {
			map.put(len, new TreeSet<Bound>());
			map.get(len).add(new Bound(lo, hi));
			heap.offer(len);
		} else {
			map.get(len).add(new Bound(lo, hi));
		}
	}
	
	private static Integer getlen(int lo, int hi) {
		return hi-lo+1;
	}

	public static int mid(int lo, int hi) {
		if( (hi-lo+1)%2 == 1  )
			return (hi+lo)/2;
		else
			return (hi+lo-1)/2;
	}
}