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.InputStream;
import java.io.BufferedReader;
import java.io.PrintWriter;
import java.io.InputStreamReader;
import java.io.IOException;
import java.util.*;

public class ConstructArr {
  static int[] arr;

  public static void main(String[] args) throws IOException {
    InputReader in = new InputReader(System.in);
    PrintWriter pw = new PrintWriter(System.out);
    int t, n, cnt, mid;
    int[] tmp, tmp1, tmp2;
    Comparator<int[]> cmp = new Comparator<int[]>(){
    
      @Override
      public int compare(int[] arg0, int[] arg1) {
        if (arg0[0] == arg1[0])
          return arg0[1] - arg1[1];
        return arg1[0] - arg0[0];  
      }
    };
    PriorityQueue<int[]> qu = new PriorityQueue<>(cmp);

    t = in.nextInt();
    while(t-- > 0) {
      n = in.nextInt();
      arr = new int[n];
      qu.clear();
      cnt = 1;
      tmp = new int[] { n, 1, n};
      qu.add(tmp);
      while(!qu.isEmpty()) {
        tmp = qu.poll();
        mid = (tmp[2] + tmp[1]) / 2;
        arr[mid - 1] = cnt++;
        if (tmp[2] != tmp[1]) {
          if (mid - tmp[1] > 0) qu.add(new int[] { mid - tmp[1], tmp[1], mid - 1});
          if (tmp[2] - mid > 0) qu.add(new int[] { tmp[2] - mid, mid + 1, tmp[2]});
        }
      }
      for (int i = 0; i < arr.length; i++) pw.print(arr[i] + " ");
      pw.println();
    }
    pw.close();
  }

  static class InputReader {
    BufferedReader br;
    StringTokenizer st;
    public InputReader(InputStream inputStream) {
      br = new BufferedReader(new InputStreamReader(inputStream));
      st = null;
    }

    String next() {
      while (st == null || !st.hasMoreElements()) {
        try {
          st = new StringTokenizer(br.readLine());
        } catch (IOException e) {
          e.printStackTrace();
        }
      }
      return st.nextToken();
    }

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

    long nextLong() {
      return Long.parseLong(next());
    }

    double nextDouble() {
      return Double.parseDouble(next());
    }

    String nextLine() {
      String str = "";
      try {
        str = br.readLine();
      } catch (IOException e) {
        e.printStackTrace();
      }
      return str;
    }
  }
}