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.lang.*;
import java.util.*;
public class Main{
    public static class S implements Comparable<S>{
        int start;int end;
        public S(int a,int b){ start=a;end=b;}
        public int compareTo(S a){
            if((this.end-this.start)==(a.end-a.start)) return Integer.compare(a.start,this.start);
            else return Integer.compare((this.end-this.start),(a.end-a.start));
        }
    }
    public static void main(String[] args) throws IOException{
        BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
        int t=Integer.parseInt(br.readLine());
        StringBuffer sb=new StringBuffer();
        while(t-->0){
            int n=Integer.parseInt(br.readLine());
            int arr[]=new int[n];
            PriorityQueue<S> pq=new PriorityQueue<S>(n,Collections.reverseOrder());
            pq.add(new S(0,n-1));
            for(int i=1;i<=n;i++){
                S a=pq.poll();
                int mid=(a.start+a.end)/2;
                arr[mid]=i;
                if(a.start<mid) pq.add(new S(a.start,mid-1));
                if(a.end>mid) pq.add(new S(mid+1,a.end));
            }
            for(int i=0;i<n;i++) sb.append(arr[i]+" ");
            sb.append("\n");
        }
        System.out.print(sb);
    }
}