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

public class Constructing_Array_CF
{
	class Pair
	{
		int l,r;
		public Pair(int l,int r)
		{
			this.l = l;
			this.r = r;
		}
	}
	InputReader in;PrintWriter pw;
	PriorityQueue<Pair> q;

	void solve(int test) throws Exception
	{
		int n = ni();
		q = new PriorityQueue<Pair>(1,new Comparator<Pair>()
			{
				public int compare(Pair a,Pair b)
				{
					if(a.r-a.l==b.r-b.l)
					{
						return a.l-b.l;
					}
					return (b.r-b.l)-(a.r-a.l);
				}
			});
		q.add(new Pair(1,n));
		int arr[] = new int[n+1],cnt=0;

		while(q.size()>0)
		{
			Pair pair = q.poll();
			int l = pair.l,r = pair.r,mid;
			if((l%2==1 && r%2==0)||(l%2==0 && r%2==1))
			{
				arr[(l+r-1)/2] = ++cnt;
				mid = (l+r-1)/2 - 1;
			}
			else
			{
				arr[(l+r)/2] = ++cnt;
				mid = (l+r)/2 - 1;
			}
			//pn(l+" "+r+" "+(mid+1));
			// if(mid-l>=r-mid-2)
			// {
			// 	if(l<=mid)
			// 	{
			// 		q.add(new Pair(l,mid));
			// 	}
			// 	if(mid+2<=r)
			// 	{
			// 		q.add(new Pair(mid+2,r));
			// 	}
			// }
			// else
			// {
			// 	if(mid+2<=r)
			// 	{
			// 		q.add(new Pair(mid+2,r));
			// 	}
			// 	if(l<=mid)
			// 	{
			// 		q.add(new Pair(l,mid));
			// 	}	
			// }
			if(l<=mid)
			{
				q.add(new Pair(l,mid));
			}
			if(mid+2<=r)
			{
				q.add(new Pair(mid+2,r));
			}
		}
		for(int i=1;i<=n;i++)
		{
			p(arr[i]+" ");
		}
		pn();
	}
	void run() throws Exception
	{
		in = new InputReader();
		pw = new PrintWriter(System.out);
		int test = ni();
		while(test--!=0){solve(test);}
		pw.close();
	}
	public static void main(String[] args) throws Exception
	{
		new Constructing_Array_CF().run();
	}

	void p(Object o){pw.print(o);}
	void pn(Object o){pw.println(o);}
	void pn(){pw.println();}
	void spn(Object o){System.out.println(o);};
	String nln() throws Exception {return in.nextLine();}
	int ni() throws Exception {return Integer.parseInt(in.next());}
	double nd() throws Exception {return Double.parseDouble(in.next());}
	long nl() throws Exception {return Long.parseLong(in.next());}
	class InputReader
	{
		BufferedReader br;
		StringTokenizer st;

		public InputReader()
		{
			br = new BufferedReader(new InputStreamReader(System.in));
		}
		public InputReader(String s) throws IOException
		{
			br = new BufferedReader(new FileReader(s));
		}

		String next() throws Exception
		{
			if(st==null || !st.hasMoreElements())
			{
				try
				{
					st = new StringTokenizer(br.readLine());
				}
				catch(IOException e)
				{
					throw new Exception(e.toString());
				}
			}
			return st.nextToken();
		}

		String nextLine() throws Exception
		{
			String str = "";
			try
			{
				str = br.readLine();
			}
			catch(IOException e)
			{
				throw new Exception(e.toString());
			}
			return str;
		}
	}
}