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.*;
import java.math.BigInteger;
 public class Solution
{
     static class Pair<A,B>
     {
        A parent;
        B rank;
        Pair(A parent,B rank)
        {
            this.rank=rank;
            this.parent=parent;
        }
    }
     static class Node{
         int left;
         int right;
         Node(int l,int r)
         {
             left=l;
             right=r;
         }
     }
     static int m=1000000007;
    public static void main (String[] args) throws IOException
    {
        StringBuilder sb = new StringBuilder();
        FastReader s1 = new FastReader();
        int t=s1.I();
        while(t--!=0)
        {
            int n=s1.I();
            int ar[] = new int[n];
            PriorityQueue<Node> que = new PriorityQueue<Node>(new Comparator<Node>() {

                @Override
                public int compare(Node o1, Node o2) {
                    int size1=o1.right-o1.left+1;
                    int size2=o2.right-o2.left+1;
                    if(size2!=size1)
                        return size2-size1;
                    else
                    {
                        return o1.left-o2.left;
                    }
                }
            });
            que.add(new Node(0,n-1));
            int count=1;
            while(!que.isEmpty())
            {
                Node temp=que.poll();
                int left=temp.left;
                int right=temp.right;
                int len=right-left+1;
                if(len%2==0)
                {
                    int mid=(left+right-1)/2;
                    ar[mid]=count;
                    if(right>=mid+1)
                    que.add(new Node(mid+1,right));
                    if(left<=mid-1)
                    que.add(new Node(left,mid-1));
                }
                else
                {
                    int mid=(left+right)/2;
                    ar[mid]=count;
                    if(left<=mid-1)
                    que.add(new Node(left,mid-1));
                    if(right>=mid+1)
                    que.add(new Node(mid+1,right));
                }
                count++;
            }
            for(int i:ar)
                sb.append(i+" ");
            sb.append("\n");
        }
        System.out.println(sb);
    }
       static long computeXOR(long n) 
    {
        if (n % 4 == 0) 
            return n;
        if (n % 4 == 1) 
            return 1; 
        if (n % 4 == 2) 
            return n + 1;
        return 0; 
    }
    static ArrayList<Integer> primeFactor(int n)
    {
        ArrayList<Integer> ans = new ArrayList<>();
        if(n%2==0)
            ans.add(2);
        while (n%2==0)
        {   
            n /= 2;
        }
        for (int i = 3; i <= Math.sqrt(n); i+= 2)
        {
            if(n%i==0)
                ans.add(i);
            while (n%i == 0)
            {
                n /= i;
            }
        }
        if (n > 2)
            ans.add(n);
        return ans;
    }
    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 I()
        {
            return Integer.parseInt(next());
        }
        
        long L()
        {
            return Long.parseLong(next());
        }
        
        double D()
        {
            return Double.parseDouble(next());
        }
        
        String nextLine()
        {
            String str = "";
            try
            {
                str = br.readLine();
            }
            catch (IOException e)
            {
                e.printStackTrace();
            }
            return str;
        }
    }
    static long gcd(long a,long b)
    {
        if(a%b==0)
            return b;
        return gcd(b,a%b);
    }
    static float power(float x, int y)
    {
        float temp;
        if( y == 0)
            return 1;
        temp = power(x, y/2);
        
        if (y%2 == 0)
            return temp*temp;
        else
        {
            if(y > 0)
                return x * temp * temp;
            else
                return (temp * temp) / x;
        }
    }
    static long pow(long x, long y)
    {
        int p =  1000000007;
        long res = 1;
        x = x % p;
        if(x<0)
            x+=p;
        while (y > 0)
        {
            if((y & 1)==1){
                res = (res * x) % p;
                if(res<0)
                    res+=p;
            }
            y = y >> 1;
            x = (x * x) % p;
        }
        return res;
    }
    static void sieveOfEratosthenes(int n)
    {
        ArrayList<Integer> prime=new ArrayList<Integer>();
        boolean Prime[] = new boolean[n+1];
        for(int i=2;i<n;i++)
            Prime[i] = true;
        
        for(int p = 2; p*p <=n; p++)
        {
            if(Prime[p] == true)
            {
                prime.add(p);
                for(int i = p*p; i <= n; i += p)
                    Prime[i] = false;
            }
        }
    }
}