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.util.PriorityQueue;

public class Main {
    public static int stoi(String s) {
        return Integer.parseInt(s);
    }

    public static class Segment implements Comparable<Segment>{
        int low;
        int high;
        int length;

        public Segment(int a, int b){
            low = a;
            high = b;
            length = b-a+1;
        }

        @Override
        public int compareTo(Segment segment) {
            if(length != segment.length){
                return segment.length - length;
            } else {
                return low - segment.low;
            }
        }
    }

    public static void main(String[] args) throws IOException {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        BufferedWriter bw = new BufferedWriter(new OutputStreamWriter(System.out));
        StringBuilder sb = new StringBuilder();

        int T = stoi(br.readLine());

        for(int i = 0 ; i < T; i++){
            int n = stoi(br.readLine());
            PriorityQueue<Segment> pq= new PriorityQueue<>();
            int arr[] = new int[n+1];
            pq.add(new Segment(1,n));
            int j = 1;

            while(!pq.isEmpty()){
                Segment now = pq.poll();
                if(now.low > now.high) continue;
                if(now.length%2 == 0){
                    arr[(now.low+now.high-1) / 2] = j;
                    if(now.length > 1){
                        pq.add(new Segment(now.low,(now.low+now.high-1)/2 - 1));
                        pq.add(new Segment((now.low+now.high-1)/2 + 1, now.high));
                    }
                    j++;
                } else {
                    arr[(now.low + now.high)/2] = j;
                    if(now.length > 1){
                        pq.add(new Segment(now.low,(now.low + now.high)/2 - 1));
                        pq.add(new Segment((now.low + now.high)/2 + 1, now.high));
                    }
                    j++;
                }

            }

            for(int k = 1; k <= n; k++){
                sb.append(arr[k]);
                sb.append(" ");
            }
            sb.append("\n");
        }
        bw.write(sb.toString());
        bw.flush();
        bw.close();

    }
}