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.*;
import java.io.*;
public class Task {
static int f(int[] a, int[] b){
    if((a[1]-a[0])==(b[1]-b[0])){
        return a[0]-b[0];
    }
    return (b[1]-b[0])-(a[1]-a[0]);
}
public static void main(String args[]) throws  IOException {
         assign();
              int t=int_v(read()),cn=1;

            while(t--!=0){
                int n=int_v(read());
                PriorityQueue<int[]> pq=new PriorityQueue<>((a,b)-> f(a,b));
                pq.add(new int[]{1,n});
                int[] a=new int[n+1]; int i=1;
                while(!pq.isEmpty()&&i<=n){
                    int[] x=pq.poll();
                    int j=(x[1]+x[0]);
                    if((x[1]-x[0]+1)%2==1){
                        a[j/2]=i;
                        int tmp=j/2;
                        if(tmp-1>=x[0]) pq.add(new int[]{x[0],tmp-1});
                        if(tmp+1<=x[1]) pq.add(new int[]{tmp+1,x[1]});                        
                    }
                    else{
                        a[(j-1)/2]=i;
                        int tmp=(j-1)/2;
                        if(tmp-1>=x[0]) pq.add(new int[]{x[0],tmp-1});
                        if(tmp+1<=x[1]) pq.add(new int[]{tmp+1,x[1]});
                    }
                    i++;
                }
                for(int x:a){if(x!=0) out.write(x+" ");}
                out.write("\n");
            }
                out.flush();
               
            }

static BufferedReader s1;
static BufferedWriter out;
static String read() throws IOException{String line="";while(line.length()==0){line=s1.readLine();continue;}return line;}
static int int_v (String s1){return Integer.parseInt(s1);}
static long long_v(String s1){return Long.parseLong(s1);}
static int[] int_arr() throws IOException{String[] a=read().split(" ");int[] b=new int[a.length];for(int i=0;i<a.length;i++){b[i]=int_v(a[i]);}return b;}
static long[] long_arr() throws IOException{String[] a=read().split(" ");long[] b=new long[a.length];for(int i=0;i<a.length;i++){b[i]=long_v(a[i]);}return b;}
static void assign(){s1=new BufferedReader(new InputStreamReader(System.in));out=new BufferedWriter(new OutputStreamWriter(System.out));}
static int gcd(int a,int b){if(b==0){return a;}return gcd(b,a%b);}

           
}