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

public class Solution {

	static class Pair {
		int z,s,e;
		Pair(int zz,int ss,int ee) {
			s = ss; e = ee; z = zz;
		}
	}
	public static void main(String[] args) {
		Scanner scn = new Scanner(System.in);
		PrintWriter pw = new PrintWriter(System.out);
		int t = scn.nextInt();
		while(t-- > 0) {
			int n = scn.nextInt();
			int a[] = new int[n];
			PriorityQueue<Pair> q = new PriorityQueue<>(new Comparator<Pair>() {
				public int compare(Pair a,Pair b) {
					if(a.z == b.z) return Integer.compare(a.s, b.s);
					return -Integer.compare(a.z, b.z);
				}
			});
			
			q.add(new Pair(n, 0, n-1));
			int i = 1;
			while(!q.isEmpty()) {
				Pair rem = q.remove();
				if(rem.z%2 == 1) {
					int m = (rem.s + rem.e)/2;
					a[m] = i++;
					if(rem.s != rem.e) {
						q.add(new Pair(rem.z/2, rem.s, m-1));
						q.add(new Pair(rem.z/2, m+1, rem.e));
					}
				}
				else {
					int m = (rem.s + rem.e - 1)/2; 
					a[m] = i++;
					if(rem.s < m) q.add(new Pair(rem.z/2-1, rem.s, m-1));
					if(m < rem.e) q.add(new Pair(rem.z/2, m+1, rem.e));
				}
			}
			for(int x : a) pw.print(x + " ");
			pw.println();
		}
		pw.flush();
	}
}