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:
/**
 * Author: Nirav Talaviya
 */

import java.io.*;
import java.util.*;

public class D1353 {
    static BufferedReader br;
    static PrintWriter out;
    static class pair{
        int i;
        int j;
        pair(int ii, int jj){
            i = ii;
            j = jj;
        }
    }

    static void solve() throws IOException {
        int t = readInt();
        while(t-->0){
            int n = readInt();
            int []a = new int[n + 1];
            PriorityQueue<pair> pq = new PriorityQueue<>(new Comparator<pair>() {
                @Override
                public int compare(pair o1, pair o2) {
                    if(Math.abs(o1.j - o1.i) !=Math.abs(o2.j - o2.i)){
                        return - Math.abs(o1.j - o1.i) + Math.abs(o2.j - o2.i) ;
                    }
                    return o1.i - o2.i;
                }
            });
            pq.add(new pair(1, n));
            int i = 1;
            while(!pq.isEmpty()){
                pair temp = pq.poll();
                int l = temp.i;
                int r = temp.j;
                int mid = (l + r)/2;
                if((temp.j - temp.i + 1)%2==0) {
                    mid = (l + r - 1) / 2;
                }
                a[mid] = i;
                if(l<=mid - 1){
                    pq.add(new pair(l, mid - 1));
                }
                if(mid + 1<=r){
                    pq.add(new pair(mid + 1, r));
                }

                i++;
            }
            for(i=1; i<=n; i++){
                System.out.print(a[i]+" ");
            }
            System.out.println();
        }

    }

    public static void main(String[] args) throws IOException {
        br = new BufferedReader(new InputStreamReader(System.in));
        out = new PrintWriter(System.out);
        solve();
        out.close();
    }

    static int readInt() throws IOException {
        return Integer.parseInt(br.readLine());
    }

    static long readLong() throws IOException {
        return Long.parseLong(br.readLine());
    }

    static int[] readintarr() throws IOException {
        String[] ___str___ = br.readLine().split(" ");
        int[] ___arr___ = new int[___str___.length];
        for (int i = 0; i < ___str___.length; i++) {
            ___arr___[i] = Integer.parseInt(___str___[i]);
        }
        return ___arr___;
    }

    static long[] readlongarr() throws IOException {
        String[] ___str___ = br.readLine().split(" ");
        long[] ___arr___ = new long[___str___.length];
        for (int i = 0; i < ___str___.length; i++) {
            ___arr___[i] = Long.parseLong(___str___[i]);
        }
        return ___arr___;
    }
}