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.util.Map.Entry;


import java.io.*;
/*
-> Written by <-
  -----------
 |J_O_B_E_E_L|
 |___________|
 |    ___    |
 |   (^_^)   |
 |  /( | )\  |
 |____|_|____|
*/

public class Main {
	
	public static void main(String[] args) throws Exception {
		int t=sc.nextInt();
		while(t-->0) {
			int x=sc.nextInt(); 
			int [] arr=new int [x+1];
			PriorityQueue<pair> pq=new PriorityQueue<>();
			pq.add(new pair(1, x));
			int i=1;
			while(!pq.isEmpty()) {
				pair p=pq.poll();
				int mid=(p.l+p.r)>>1;
				arr[mid]=i++;
				pair p1 = new pair(p.l, mid - 1);
				if (p1.length > 0) pq.add(p1);
				p1 = new pair(mid + 1, p.r);
				if (p1.length > 0) pq.add(p1);
			}
			for(int j=1;j<=x;j++) pw.print(arr[j]+" ");
			pw.println();
		}
		pw.flush();
		pw.close();
	}
	
	static class pair implements Comparable<pair>{
		int l,r,length;
		 public pair(int l , int r) {
			this.l=l; this.r=r;
			length=r-l+1;
		}
		@Override
		public int compareTo(pair o) {
			if(o.length!=length) return o.length-length;
			return l-o.l;
		}
		public String toString() {return l+" "+r+" "+length;}
		
	}
    static class Scanner {
    	 
        private InputStream in;
        private byte[] buffer = new byte[1024];
        private int curbuf;
        private int lenbuf;
 
        public Scanner(InputStream in) {
            this.in = in;
            this.curbuf = this.lenbuf = 0;
        }
 
        public boolean hasNextByte() {
            if (curbuf >= lenbuf) {
                curbuf = 0;
                try {
                    lenbuf = in.read(buffer);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (lenbuf <= 0)
                    return false;
            }
            return true;
        }
 
        private int readByte() {
            if (hasNextByte())
                return buffer[curbuf++];
            else
                return -1;
        }
 
        private boolean isSpaceChar(int c) {
            return !(c >= 33 && c <= 126);
        }
 
        private void skip() {
            while (hasNextByte() && isSpaceChar(buffer[curbuf]))
                curbuf++;
        }
 
        public boolean hasNext() {
            skip();
            return hasNextByte();
        }
 
        public String next() {
            if (!hasNext())
                throw new NoSuchElementException();
            StringBuilder sb = new StringBuilder();
            int b = readByte();
            while (!isSpaceChar(b)) {
                sb.appendCodePoint(b);
                b = readByte();
            }
            return sb.toString();
        }
 
        public int nextInt() {
            if (!hasNext())
                throw new NoSuchElementException();
            int c = readByte();
            while (isSpaceChar(c))
                c = readByte();
            boolean minus = false;
            if (c == '-') {
                minus = true;
                c = readByte();
            }
            int res = 0;
            do {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res = res * 10 + c - '0';
                c = readByte();
            } while (!isSpaceChar(c));
            return (minus) ? -res : res;
        }
 
        public long nextLong() {
            if (!hasNext())
                throw new NoSuchElementException();
            int c = readByte();
            while (isSpaceChar(c))
                c = readByte();
            boolean minus = false;
            if (c == '-') {
                minus = true;
                c = readByte();
            }
            long res = 0;
            do {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res = res * 10 + c - '0';
                c = readByte();
            } while (!isSpaceChar(c));
            return (minus) ? -res : res;
        }
 
        public double nextDouble() {
            return Double.parseDouble(next());
        }
 
        public int[] nextIntArray(int n) {
            int[] a = new int[n];
            for (int i = 0; i < n; i++)
                a[i] = nextInt();
            return a;
        }
 
        public long[] nextLongArray(int n) {
            long[] a = new long[n];
            for (int i = 0; i < n; i++)
                a[i] = nextLong();
            return a;
        }
 
    }
	static Scanner sc = new Scanner(System.in);
	static PrintWriter pw = new PrintWriter(System.out);
}