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.*;
import java.util.stream.*;


public class Main {
	static final PrintWriter out = new PrintWriter(System.out);

	static class ContestInputReader {
		BufferedReader reader;
		StringTokenizer tokenizer;

		ContestInputReader(Reader reader) {
			this.reader = new BufferedReader(reader);
		}

		ContestInputReader(){
			this(new InputStreamReader(System.in));
		}

		public static ContestInputReader get(String file){
			if("true".equalsIgnoreCase(System.getProperty("nojudge"))){
				try {
					return new ContestInputReader(new FileReader(file));
				} catch (IOException e) {
					throw new RuntimeException(e);
				}
			}
			return new ContestInputReader();
		}

		String readLine(){
			try {
				return reader.readLine();
			} catch (IOException e) {
				throw new RuntimeException("Couldn't read anything", e);
			}
		}

		String next(){
			while(tokenizer == null || ! tokenizer.hasMoreElements()){
				tokenizer = new StringTokenizer(readLine());
			}
			return tokenizer.nextToken();
		}

		int nextInt(){
			return Integer.parseInt(next());
		}

		int[] nextIntArray(){
			return Arrays.stream(readLine().split("\\s+"))
						.mapToInt(Integer::parseInt)
						.toArray();
		}
	}

	static class Segment implements Comparable<Segment>{
		int l, r;
		Segment(int l, int r){ this.l = l; this.r = r;}
		@Override
		public int compareTo(Segment that){
			int diff = (that.r - that.l) - (this.r - this.l);
			if( diff != 0) return diff;
			return this.l - that.l;
		}
	}

	static void solve(int[] A){
		int n = A.length;
		PriorityQueue<Segment> queue = new PriorityQueue<>(A.length);
		queue.add(new Segment(0, n - 1));
		int i = 1;
		while( !queue.isEmpty() ){
			Segment next = queue.remove();
			int p = (next.r + next.l) >>> 1;
			A[p] = i++;
			if(p > next.l) queue.add(new Segment(next.l, p - 1));
			if(p < next.r) queue.add(new Segment(p + 1, next.r));
		}
	}

	public static void main(String[] args){
		ContestInputReader reader = new ContestInputReader();
		int tc = reader.nextInt();
		while(tc --> 0){
			int n = reader.nextInt();
			int[] A = new int[n];
			solve(A);
			out.println(Arrays.stream(A).mapToObj(String::valueOf)
										.collect(Collectors.joining(" ")));
		}

		out.close();
	}
}