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.math.*;
import java.util.*;


/**
 *
 * @author Saju
 *
 */

public class Main {

    private static int dx[] = { 1, 0, -1, 0 };
    private static int dy[] = { 0, -1, 0, 1 };

    private static final long INF = Long.MAX_VALUE;
    private static final int INT_INF = Integer.MAX_VALUE;
    private static final long NEG_INF = Long.MIN_VALUE;
    private static final int NEG_INT_INF = Integer.MIN_VALUE;
    private static final double EPSILON = 1e-10;

    private static final int MAX = 1000005;
    
    private static final long MOD = 1000000007;

    private static final int MAXN = 10000007;
    private static final int MAXA = 10000009;
    private static final int MAXLOG = 22;

	public static void main(String[] args) throws IOException {

		InputReader in = new InputReader(System.in);
//		Scanner in = new Scanner(System.in);
		PrintWriter out = new PrintWriter(System.out);

//         InputReader in = new InputReader(new FileInputStream("src/test.in"));
//         PrintWriter out = new PrintWriter(new BufferedWriter(new FileWriter("src/test.out")));

		
		
/*



*/
		int test = in.nextInt();
		StringBuilder sb = new StringBuilder();
		for (int t = 1; t <= test; t++) {
			
			int n = in.nextInt();
			
			PriorityQueue<Segment> segments = new PriorityQueue<>(new Comparator<Segment>() {

				@Override
				public int compare(Segment o1, Segment o2) {
					int val = Integer.compare(o2.len, o1.len);
					if(val == 0) {
						return o1.left - o2.left;
					}
					return val;
				}
			});
			
			segments.add(new Segment(1, n));
			int action = 1;
			int arr[] = new int[n + 1];
			while(!segments.isEmpty()) {
				Segment segment = segments.remove();
//				System.out.println(segment);
				if(segment.len % 2 == 0) {
					int id = (segment.left + segment.right - 1) / 2;
					arr[id] = action;
					
					if(id - 1 >= segment.left) {
						segments.add(new Segment(segment.left, id - 1));
					}
					
					if(id + 1 <= segment.right) {
						segments.add(new Segment(id + 1, segment.right));
					}
				}
				else {
					int id = (segment.left + segment.right) / 2;
					arr[id] = action;
					if(id - 1 >= segment.left) {
						segments.add(new Segment(segment.left, id - 1));
					}
					
					if(id + 1 <= segment.right) {
						segments.add(new Segment(id + 1, segment.right));
					}
				}
				
				action++;
			}
			
//			System.out.println(Arrays.toString(arr));
			for(int i = 1; i <= n; i++) {
				sb.append(arr[i]);
				if(i <= n - 1) {
					sb.append(" ");
				}
				else {
					sb.append("\n");
				}
			}
			
		}
		out.print(sb);
		
		in.close();
		out.flush();
		out.close();
		System.exit(0);
	}
	
	private static class Segment{
		int left;
		int right;
		int len = 0;
		public Segment(int left, int right){
			this.left = left;
			this.right = right;
			len = this.right - this.left + 1;
		}
		
		@Override
		public String toString() {
			return left + " " + right + " " + len;
		}
	}
	
	
	private static long bigMod(long n, long k, long m) {

        long ans = 1;
        while (k > 0) {
            if ((k & 1) == 1) {
                ans = (ans * n) % m;
            }
            n = (n * n) % m;
            k >>= 1;
        }
        return ans;
    }
    
	private static long ceil(long n, long x) {
		long div = n / x;
        if(div * x != n) {
            div++;
        }
        return div;
	}
	
    private static int ceil(int n, int x) {
        int div = n / x;
        if(div * x != n) {
            div++;
        }
        return div;
    }

    private static class Point {
        double x;
        double y;

        Point(double x, double y) {
            this.x = x;
            this.y = y;
        }

        double getDistance(Point p2) {
            Point p1 = this;
            double dx = p1.x - p2.x;
            double dy = p1.y - p2.y;

            return Math.sqrt((dx * dx) + (dy * dy));
        }
    }

    private static int abs(int x) {
        if (x < 0) {
            return -x;
        }
        return x;
    }

    private static long abs(long x) {
        if(x < 0) {
            return -x;
        }
        return x;
    }

    private static int lcm(int a, int b) {
        return (a * b) / gcd(a, b);
    }

    private static int gcd(int a, int b) {
        if (a == 0)
            return b;
        return gcd(b % a, a);
    }

    private static int log(long x, int base) {
        return (int) (Math.log(x) / Math.log(base));
    }

    private static long min(long a, long b) {
        if (a < b) {
            return a;
        }
        return b;
    }

    private static int min(int a, int b) {
        if (a < b) {
            return a;
        }
        return b;
    }

    private static long max(long a, long b) {
        if (a < b) {
            return b;
        }
        return a;
    }

    private static int max(int a, int b) {
        if (a < b) {
            return b;
        }
        return a;
    }

    private static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream));
            tokenizer = null;
        }

        public String next() {
            try {
                while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                    tokenizer = new StringTokenizer(reader.readLine());

                }
            } catch (IOException e) {
                return null;
            }
            return tokenizer.nextToken();
        }

        public String nextLine() {
            String line = null;
            try {
                tokenizer = null;
                line = reader.readLine();
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
            return line;
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

        public double nextDouble() {
            return Double.parseDouble(next());
        }

        public long nextLong() {
            return Long.parseLong(next());
        }

        public boolean hasNext() {
            try {
                while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                    tokenizer = new StringTokenizer(reader.readLine());
                }
            } catch (Exception e) {
                return false;
            }
            return true;
        }
        public void close() {
        	try {
        		if(reader != null) {
        			reader.close();
        		}
        	}
        	catch(Exception e) {
        		
        	}
        	
        	
        }
    }
    
}