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.InputStreamReader;
import java.io.PrintWriter;
import java.util.PriorityQueue;
import java.util.StringTokenizer;

public class TaskD {
    public static void main(String[] args) throws Exception {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st;
        PrintWriter pw = new PrintWriter(System.out);
        
        try {
            int t = Integer.parseInt(br.readLine());
            while(t-->0) {
                int n = Integer.parseInt(br.readLine());
                int[] a = new int[n+1];
                PriorityQueue<Pair> pq  =new PriorityQueue<>(16, (o1, o2) -> o1.c == o2.c ? o1.l - o2.l : o2.c - o1.c);
                pq.add(new Pair(1, n, n));

                for(int i=0 ; i<n ; i++) {
                    Pair p = pq.poll();
                    if(p.c%2 == 0) {
                        int ind =  ( p.l + p.r - 1 )/2;
                        a[ind] = (i+1);
                        pq.add(new Pair(p.l, ind-1, (ind-1-p.l+1)));
                        pq.add(new Pair(ind+1, p.r, (p.r-ind)));
                    }
                    else {
                        int ind = (p.l + p.r)/2;
                        a[ind] = (i+1);
                        pq.add(new Pair(p.l, ind-1, (ind-1-p.l+1)));
                        pq.add(new Pair(ind+1, p.r, (p.r-ind)));
                    }
                }

                for(int i=1 ; i<=n ; i++) {
                    pw.print(a[i] + " ");
                }
                pw.println();
            }
        }
        finally {
            pw.flush();
            pw.close();
        }
    }
}

class Pair {
    int l;
    int r;
    int c;
    Pair(int x, int y, int z) {
        l = x;
        r = y;
        c = z;
    }
}