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.BufferedReader;
import java.io.BufferedWriter;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.util.*;

public class psykibaek {
    public static class aTree implements Comparable<aTree>{
        public int start;
        public int end;
        public int dist;
        public aTree(int start, int end){
            this.start = start;
            this.end = end;
            this.dist = end-start;
        }
        public int getDist(){
            return dist;
        }

        // dist가 큰게 먼저와야 함
        // dist가 같다면, start가 작은게 먼저 와야함
        @Override
        public int compareTo(aTree b){
            if(this.getDist() > b.getDist())
                return -1;
            else if(this.getDist() == b.getDist()){
                if(this.start < b.start)
                    return -1;
                else
                    return 1;
            }
            else
                return 1;
        }
    }
    public static void main(String[] args) throws Exception{
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        BufferedWriter bw = new BufferedWriter(new OutputStreamWriter(System.out));
        int totCase =  Integer.parseInt(br.readLine());
        while(totCase-- > 0){
            int n = Integer.parseInt(br.readLine());
            int[] result = new int[n+1];
            PriorityQueue<aTree> pq = new PriorityQueue<>();

            pq.add(new aTree(1, n));
            int k = 1;
            while(!pq.isEmpty()){
                aTree a = pq.peek();
                pq.poll();

                int newPoint = (a.end + a.start)/2;

                if(a.start <= newPoint-1)
                    pq.add(new aTree(a.start, newPoint-1));
                if(newPoint+1 <= a.end)
                    pq.add(new aTree(newPoint+1, a.end));

                result[newPoint] = k;
                k++;


                if(isDebug){
                    System.out.println("start,end: " + a.start + " " + a.end);
                    for (int i = 1; i <= n; i++) {
                        System.out.print(result[i] + " ");
                    }
                    System.out.println();
                    System.out.println();
                }
            }

            if(isDebug){
                System.out.println("답");
            }
            for (int i = 1; i <= n ; i++) {
                bw.write(result[i] + " ");
            }
            bw.newLine();
        }
        bw.close();
    }
    public static boolean isDebug = false;
}