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.util.*; 
import java.math.*; 
public class Constructing_the_Array 
{ 
    static class FastReader 
    { 
        BufferedReader br; 
        StringTokenizer st; 
  
        public FastReader() 
        { 
            br = new BufferedReader(new
                     InputStreamReader(System.in)); 
        } 
  
        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; 
        } 
    } 
    public static long binary(long x)
    {
        long left=0;
        long right=1000000;
        long ans=0;

        while(left<=right)
        {
            long mid=(left+right)/2;

            long temp=mid*(3*mid+1)/2;
            if(temp<=x)
            {
                ans=temp;
                left=mid+1;
            }
            else
            {
                right=mid-1;
            }
        }
        return ans;
    }
    static class Node
    {
        int len;
        int l;
        int r;
        public Node(int x,int y,int z)
        {
            len=x;
            l=y;
            r=z;
        }
    }
    public static void main(String[] args) 
    { 
        FastReader sc=new FastReader(); 
        
        PrintWriter pw=new PrintWriter(System.out);
 
        int t1=sc.nextInt();
 
        m:while(t1-->0)
        {
            
            int n=sc.nextInt();

            long arr[]=new long[n+1];

            PriorityQueue<Node> q=new PriorityQueue<Node>(2*n ,new Comparator<Node>()
            {
                @Override
                public int compare(Node a,Node b)
                {
                    if(a.len!=b.len)
                    {
                        return -a.len+b.len;
                    }
                    else
                    {
                        return a.l-b.l;
                    }
                }
            });
            
            q.add(new Node(n,1,n));
            Node temp;
            int i=0;
            while(!q.isEmpty())
            {
                temp=(Node)q.poll();

                //System.out.println(temp.len+" "+temp.l+" "+temp.r);
                if(temp.len%2==1)
                {
                    arr[(temp.l+temp.r)/2]=i+1;

                    int x=(temp.l+temp.r)/2;
                    if(temp.r!=temp.l)
                    {
                        if(x-temp.l>0)
                            q.add(new Node(x-temp.l,temp.l,x-1));
                        if(temp.r-x>0)
                            q.add(new Node(temp.r-x,x+1,temp.r));
                    }
                }
                else
                {
                    arr[(temp.l+temp.r-1)/2]=i+1;
                    int x=(temp.l+temp.r-1)/2;
                    if(temp.r!=temp.l)
                    {
                        if(x-temp.l>0)
                            q.add(new Node(x-temp.l,temp.l,x-1));
                        if(temp.r-x>0)
                            q.add(new Node(temp.r-x,x+1,temp.r));
                    }
                }

                i++;
            }
            for(int ia=1;ia<=n;ia++)
                pw.print(arr[ia]+" ");
            pw.println();
        }
        pw.flush();
        
    } 
}