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 ConstructingtheArray {

	// https://codeforces.com/problemset/problem/1353/D
	
	public static void main(String[] args) throws IOException, FileNotFoundException {
		BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
		//BufferedReader in = new BufferedReader(new FileReader("ConstructingtheArray"));

		int t = Integer.parseInt(in.readLine());
		while (t --> 0) {
			int n = Integer.parseInt(in.readLine());
			PriorityQueue<int[]> a = new PriorityQueue<>(
		    		new Comparator<int[]>() {
		    			public int compare(int[] x, int[] y) {
		    				if (y[0] != x[0]) return y[0]-x[0]; // sort by largest first
		    				else return x[1] - y[1]; // if same large, sort by leftmost
		    			}
		    });
			
			int[] ans = new int[n];
			a.add(new int[] {n, 0, n-1});
				// length, l, r
			int curnum=1;
			while (a.size() > 0) {
				int[] cur = a.poll();
				if (cur[0] <= 0 || cur[1] < 0 || cur[2] < 0) continue;
				ans[(cur[1] + cur[2])/2] = curnum;
				curnum++;
				if (cur[1] == cur[2]) continue;
				a.add(new int[] {(cur[1] + cur[2])/2 - cur[1], cur[1], (cur[1] + cur[2])/2 -1});
				a.add(new int[] {cur[2] - (cur[2] + cur[1])/2, (cur[2] + cur[1])/2 + 1, cur[2]});
			}
			for (int i=0; i<n; i++) {
				System.out.print(ans[i] + " ");
			}
			System.out.println();
		}
	}
}