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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.AbstractCollection;
import java.util.PriorityQueue;
import java.util.Scanner;
import java.util.Comparator;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main
{
    public static void main(String[] args)
    {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        Scanner in = new Scanner(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskD solver = new TaskD();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskD
    {
        public void solve(int testNumber, Scanner in, PrintWriter out)
        {
            int T = in.nextInt();
            while (T-- > 0)
            {
                CPUtils.printIntArray(solve(in, out), out);
                out.println();
            }
        }

        private int[] solve(Scanner in, PrintWriter out)
        {
            int N = in.nextInt();
            if (N == 1) return new int[]{1};
            int[] array = new int[N];

            Comparator<Range> comparator = (range1, range2) -> {
                int s1 = range1.end - range1.start;
                int s2 = range2.end - range2.start;
                if (s1 != s2)
                {
                    return Integer.compare(s2, s1);
                }
                return Integer.compare(range1.start, range2.start);
            };

            PriorityQueue<Range> q = new PriorityQueue<>(comparator);
            q.add(new Range(1, N));
            int cnt = 1;
            while (!q.isEmpty())
            {
                Range range = q.poll();
                int mid;
                if ((range.end - range.start + 1) % 2 == 1)
                {
                    mid = (range.start + range.end) / 2;
                } else
                {
                    mid = (range.start + range.end - 1) / 2;
                }
                array[mid - 1] = cnt;
                cnt++;
                if (range.start <= mid - 1)
                    q.add(new Range(range.start, mid - 1));
                if (mid + 1 <= range.end)
                    q.add(new Range(mid + 1, range.end));
            }
            return array;
        }

    }

    static class CPUtils
    {
        public static void printIntArray(int[] array, PrintWriter out)
        {
            StringBuilder stringBuilder = new StringBuilder();
            for (int i = 0; i < array.length; i++)
            {
                stringBuilder.append(array[i] + " ");
            }
            out.print(stringBuilder.toString());
        }

    }

    static class Range
    {
        int start;
        int end;

        Range(int start, int end)
        {
            this.start = start;
            this.end = end;
        }

    }
}