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.lang.*;

public class ranjan{

    //public static Read cin;
    public static InputReader cin;
    public static PrintWriter cout;
    public static boolean[] visited;
    public static int node=-1;
    public static boolean flag;
    public static final long b = (long)1e9+7;
    public static int fileread = 0; 
    
    public static void main(String ...arg) throws IOException
    {
        /*console writer*/
        cout = new PrintWriter(new BufferedOutputStream(System.out));
        /*Debug Reader*/
        //Scan cin =new Scan();
        if(fileread == 1)
        {
            try
            {
            //cin = new Read(new FileInputStream(new File("in1.txt")));
            cin = new InputReader(new FileInputStream(new File("in1.txt")));
            }
            catch (IOException error){}
        }
        else{
            //cin = new Read(System.in);
            cin = new InputReader(System.in);
        }

        int t = cin.nextInt();
        PriorityQueue<Range> pq = new PriorityQueue<>(new Comparator<Range>(){
                @Override
                public int compare(Range a,Range b)
                {
                    if(a.len - b.len != 0)
                    {
                        return b.len - a.len;
                    }
                    else
                        return a.l-b.l;
                }
            });
        while(t-->0)
        {
            int n = cin.nextInt();
            int[] ans = new int[n];
            pq.clear();
            pq.add(new Range(0,n-1));
            for(int i=1;i<=n;i++)
            {
                Range top = pq.peek();
                pq.remove();
                int index = (int)(top.l + top.r)/2;
                pq.add(new Range(top.l,index-1));
                pq.add(new Range(index+1,top.r));
                ans[index] = i;
            }
            for(int val:ans) cout.print(val+" ");
            cout.print("\n");
        }
           
        cout.close();
    }

    static class Range{
        public int l;
        public int r;
        public int len;

        public Range(int a,int b)
        {
            this.l = a;
            this.r = b;
            this.len = b-a+1;
        }
    }

    public static <K, V> V getOrDefault(HashMap<K,V> map, K key, V defaultValue) {
        return map.containsKey(key) ? map.get(key) : defaultValue;
    }
    

    public static long mod_pow(long x,long n,long mod) {
		long res=1;
		while(n>0) {
			if((n&1)==1)res=res*x%mod;
			x=x*x%mod;
			n>>=1;
		}
		return res;
    }
    public static int gcd(int n1, int n2) 
	{
		int r;
		while (n2 != 0) 
		{
			r = n1 % n2;
			n1 = n2;
			n2 = r;
		}
		return n1;
	}
 
	/*public static long lcm(long n1, long n2) 
	{
		long answer = (n1 * n2) / (gcd(n1, n2));
		return answer;
	}*/


    static class InputReader {
        final InputStream is;
        final byte[] buf = new byte[1024];
        int pos;
        int size;
 
        public InputReader(InputStream is) {
            this.is = is;
        }
 
        public int nextInt() {
            int c = read();
            while (isWhitespace(c))
                c = read();
            int sign = 1;
            if (c == '-') {
                sign = -1;
                c = read();
            }
            int res = 0;
            do {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res = res * 10 + c - '0';
                c = read();
            } while (!isWhitespace(c));
            return res * sign;
        }
 
        int read() {
            if (size == -1)
                throw new InputMismatchException();
            if (pos >= size) {
                pos = 0;
                try {
                    size = is.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (size <= 0)
                    return -1;
            }
            return buf[pos++] & 255;
        }
 
        static boolean isWhitespace(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }
 
    }

static class RecursionLimiter {
    public static long maxLevel = 1549;

    public static void emerge() {
        if (maxLevel == 0)
            return;
        try {
            throw new IllegalStateException("Too deep, emerging");
        } catch (IllegalStateException e) {
            if (e.getStackTrace().length > maxLevel + 1)
                throw e;
        }
    }
}


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

}

class Read
{
    private BufferedReader br;
    private StringTokenizer st;

    public Read(InputStream is)
    { br = new BufferedReader(new InputStreamReader(is)); }

    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;
    }
}