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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.stream.IntStream;
import java.util.Arrays;
import java.util.PriorityQueue;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.AbstractCollection;
import java.util.StringTokenizer;
import java.io.BufferedReader;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author El Mehdi ASSALI
 */
public class Main {
  public static void main(String[] args) {
    InputStream inputStream = System.in;
    OutputStream outputStream = System.out;
    InputReader in = new InputReader(inputStream);
    PrintWriter out = new PrintWriter(outputStream);
    DConstructingTheArray solver = new DConstructingTheArray();
    int testCount = Integer.parseInt(in.next());
    for (int i = 1; i <= testCount; i++)
      solver.solve(i, in, out);
    out.close();
  }

  static class DConstructingTheArray {
    public void solve(int testNumber, InputReader in, PrintWriter out) {
      int n = in.nextInt();
      int[] answer = new int[n];
      PriorityQueue<Interval> pq = new PriorityQueue<>();
      pq.add(new Interval(0, n - 1));
      int op = 1;
      while (!pq.isEmpty()) {
        Interval cur = pq.poll();
        if (cur.l <= cur.r) {
          answer[cur.mid] = op++;
          pq.add(new Interval(cur.l, cur.mid - 1));
          pq.add(new Interval(cur.mid + 1, cur.r));
        }
      }
      Arrays.stream(answer).forEach(e -> out.print(e + " "));
      out.println();
    }

    class Interval implements Comparable<Interval> {
      int l;
      int r;
      int size;
      int mid;

      Interval(int l, int r) {
        this.l = l;
        this.r = r;
        size = r - l + 1;
        mid = l + (size - 1) / 2;
      }

      public int compareTo(Interval interval) {
        if (size != interval.size) {
          return interval.size - size;
        }
        return l - interval.l;
      }

    }

  }

  static class InputReader {
    private BufferedReader reader;
    private StringTokenizer tokenizer;

    public InputReader(InputStream inputStream) {
      reader = new BufferedReader(new InputStreamReader(inputStream));
    }

    public String next() {
      while (tokenizer == null || !tokenizer.hasMoreTokens()) {
        try {
          tokenizer = new StringTokenizer(reader.readLine());
        } catch (IOException e) {
          e.printStackTrace();
        }
      }
      return tokenizer.nextToken();
    }

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

  }
}