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.BufferedOutputStream;
import java.io.PrintWriter;
import java.util.Comparator;
import java.util.PriorityQueue;
import java.util.Scanner;

public class D1353 {
    static PrintWriter out;

    public static void main(String[] args) {
        Scanner s = new Scanner(System.in);
        out = new PrintWriter(new BufferedOutputStream(System.out));
        int t = s.nextInt();
        for (int i = 0; i < t; i++) {
            int n = s.nextInt();
            process(n);
        }
    }

    static class Bounds {
        int l;
        int r;

        public Bounds(int l, int r) {
            this.l = l;
            this.r = r;
        }
    }

    private static void process(int n) {
        int[] arr = new int[n + 1];

        PriorityQueue<Bounds> queue = new PriorityQueue<>((o1, o2) -> {
            int i1 = o1.r - o1.l;
            int i2 = o2.r - o2.l;

            int compare = Integer.compare(i2, i1);
            return compare != 0 ? compare : Integer.compare(o1.l, o2.l);
        });
        queue.add(new Bounds(1, n));
        int idx = 1;
        while (!queue.isEmpty()) {
            Bounds poll = queue.poll();
            int pos;
            if ((poll.r - poll.l + 1) % 2 == 1) {
                pos = (poll.r + poll.l) / 2;
            } else {
                pos = (poll.r + poll.l - 1) / 2;
            }
            arr[pos] = idx++;
            if (poll.l <= pos - 1) queue.add(new Bounds(poll.l, pos - 1));
            if (poll.r >= pos + 1) queue.add(new Bounds(pos + 1, poll.r));
        }
        for (int i = 1; i < arr.length; i++) {
            out.print(arr[i] + " ");
        }
        out.println();
        out.flush();
    }

}