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.BufferedInputStream;
import java.io.InputStream;
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.io.OutputStream;
import java.io.OutputStreamWriter;
import java.io.BufferedWriter;
import java.io.IOException;
import java.util.InputMismatchException;
import java.util.TreeSet;

public class CF642DIV3D{
    public static void main(String [] args) throws IOException {
        final Scan sc = new Scan();
        final Print print = new Print();
        int t = sc.scanInt();

        while(t-- >0){
            int n = sc.scanInt();
            int [] arr = new int[n];
            TreeSet<Pair> seq = new TreeSet<>();
            seq.add(new Pair(0, n-1));

            for (int i=1; i<=n; i++) {
                Pair pair = seq.first();
                seq.remove(pair);
                int id = (pair.s + pair.e)/2;
                arr[id] = i;
                if(pair.s < id) seq.add(new Pair(pair.s, id-1));
                if(pair.e > id) seq.add(new Pair(id+1, pair.e));
            }

            for(int i=0;i<n; i++) print.print(arr[i]+" ");
            print.println("");
        }
        print.close();
    }

    static class Pair implements Comparable<Pair>{
        int s, e;  
        Pair(int s, int e){
            this.s = s;
            this.e = e;
        }
        public int compareTo(Pair o){
            int lenA = this.e - this.s + 1;
            int lenB = o.e - o.s + 1;
            if(lenA == lenB) return Integer.compare(this.s, o.s);
            return Integer.compare(lenB, lenA);
        }
    }

}

class Scan{
    private byte[] buf=new byte[1024];
    private int index;
    private InputStream in;
    private int total;
    public Scan(){
        in=System.in;
    }
    public int scan()throws IOException
    {
        if(total<0)
        throw new InputMismatchException();
        if(index>=total)
        {
            index=0;
            total=in.read(buf);
            if(total<=0)
            return -1;
        }
        return buf[index++];
    }
    public int scanInt()throws IOException
    {
        int integer=0;
        int n=scan();
        while(isWhiteSpace(n))
        n=scan();
        int neg=1;
        if(n=='-')
        {
            neg=-1;
            n=scan();
        }
        while(!isWhiteSpace(n))
        {
            if(n>='0'&&n<='9')
            {
                integer*=10;
                integer+=n-'0';
                n=scan();
            }
            else throw new InputMismatchException();
        }
        return neg*integer;
    }


    public long scanLong()throws IOException
    {
        long integer=0;
        int n=scan();
        while(isWhiteSpace(n))
        n=scan();
        long neg=1;
        if(n=='-')
        {
            neg=-1;
            n=scan();
        }
        while(!isWhiteSpace(n))
        {
            if(n>='0'&&n<='9')
            {
                integer*=10;
                integer+=n-'0';
                n=scan();
            }
            else throw new InputMismatchException();
        }
        return neg*integer;
    }

    public double scanDouble()throws IOException
    {
        double doub=0;
        int n=scan();
        while(isWhiteSpace(n))
        n=scan();
        int neg=1;
        if(n=='-')
        {
            neg=-1;
            n=scan();
        }
        while(!isWhiteSpace(n)&&n!='.')
        {
            if(n>='0'&&n<='9')
            {
                doub*=10;
                doub+=n-'0';
                n=scan();
            }
            else throw new InputMismatchException();
        }
        if(n=='.')
        {
            n=scan();
            double temp=1;
            while(!isWhiteSpace(n))
            {
                if(n>='0'&&n<='9')
                {
                    temp/=10;
                    doub+=(n-'0')*temp;
                    n=scan();
                }
                else throw new InputMismatchException();
            }
        }
        return doub*neg;
    }

    public String scanString()throws IOException
    {
        StringBuilder sb=new StringBuilder();
        int n=scan();
        while(isWhiteSpace(n))
        n=scan();
        while(!isWhiteSpace(n))
        {
            sb.append((char)n);
            n=scan();
        }
        return sb.toString();
    }

    public int [] scanIntArray(int n)throws IOException{
        int [] arr = new int[n];
        for (int i=0; i<n; ++i) {
            arr[i] = scanInt();
        }

        return arr;
    }

    public long [] scanLongArray(int n)throws IOException{
        long [] arr = new long[n];
        for (int i=0; i<n; ++i) {
            arr[i] = scanLong();
        }

        return arr;
    }

    private boolean isWhiteSpace(int n)
    {
        if(n==' '||n=='\n'||n=='\r'||n=='\t'||n==-1)
        return true;
        return false;
    }

}


class Print{
    private final BufferedWriter bw;
    public Print()
    {
        this.bw=new BufferedWriter(new OutputStreamWriter(System.out));
    }
    public void print(Object object)throws IOException
    {
        bw.append(""+object);
    }
    public void println(Object object)throws IOException
    {
        print(object);
        bw.append("\n");
    }
    public void close()throws IOException
    {
        bw.close();
    }
}