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.*;

public class ConstructingTheArray {
  public static void main(String[] args) {
    Scanner in = new Scanner(System.in);
    int T = in.nextInt();
    while(T-- > 0){
      int n = in.nextInt();
      TreeSet<Segment> set = new TreeSet<>((o1, o2) -> {
        int lenA = o2.x - o1.x + 1;
        int lenB = o2.y - o1.y + 1;
        if (lenA == lenB)
          return o1.x - o2.x;
        return lenB - lenA;
      });
      set.add(new Segment(0,n-1));
      int[] arr = new int[n];
      for(int i = 1 ; i <= n ;i++){
        Segment segment = set.pollFirst();
        int idx = (segment.x + segment.y) / 2;
        arr[idx]=i;
        if(segment.x < idx)
          set.add(new Segment(segment.x,idx-1));
        if(idx < segment.y)
          set.add(new Segment(idx+1,segment.y));
      }
      for(int a : arr)
        System.out.print(a + " ");
      System.out.println();
    }
  }
}

class Segment{
  public int x , y;

  public Segment(int x, int y) {
    this.x = x;
    this.y = y;
  }
}