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.Comparator;
import java.util.PriorityQueue;

public class paritySummands {
	static class node {
		int l,r;
		node(int a ,int b)
		{
			l=a; r = b;
		}
	}
	static class cp implements Comparator<node>{
		public int compare (node n1  , node n2)
		{
			if (n1.r-n1.l > n2.r-n2.l)
				return -1;
			else if (n1.r-n1.l < n2.r-n2.l)
				return 1;
			else
			{
				if (n1.l<n2.l)
					return -1;
				else
					return 1;
			}
		}
	}
	public static void main(String[] args) throws IOException {
		BufferedReader br = new BufferedReader(new  InputStreamReader(System.in));
		int t = Integer.parseInt(br.readLine());
		StringBuilder res = new StringBuilder();
		while (t-->0)
		{
			int n = Integer.parseInt(br.readLine());
			int[] arr = new int[n+1];
			PriorityQueue<node> pq = new PriorityQueue<node>(new cp());
			pq.add(new node(1,n));
			for (int i=1;i<=n;i++)
			{
				node c = pq.remove();
				int m = 0;
				if ((c.r-c.l+1)%2==1)
				{
					arr[(c.l+c.r)/2]=i;
					m = (c.l+c.r)/2;
				}
				else
				{
					arr[(c.l+c.r-1)/2] = i;
					m = (c.l+c.r-1)/2;
				}
				if (c.l<=m-1)
				pq.add(new node(c.l , m-1));
				if (c.r>=m+1)
				pq.add(new node(m+1,c.r));
			}
			for(int i=1;i<=n;i++)
				res.append(arr[i]+" ");
			res.append("\n");
		}
		System.out.println(res);
	}
}