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 egaeus
 * @mail sebegaeusprogram@gmail.com
 * @veredict
 * @url
 * @category
 * @date
 **/

import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.util.Arrays;
import java.util.TreeSet;
import java.util.stream.Collectors;
import java.util.stream.IntStream;

import static java.lang.Integer.parseInt;

public class CFD {
    public static void main(String args[]) throws Throwable {
        BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
        int T = parseInt(in.readLine());
        StringBuilder sb = new StringBuilder();
        for (int t = 0; t < T; t++) {
            int N = parseInt(in.readLine());
            int[] result = new int[N];
            TreeSet<int[]> set = new TreeSet<>((a, b) -> a[1] - a[0] < b[1] - b[0] ? 1 : a[1] - a[0] > b[1] - b[0] ? -1 : a[0] - b[0]);
            set.add(new int[]{0, N});
            int i = 1;
            while (!set.isEmpty()) {
                int[] first = set.pollFirst();
                int v = first[0] + (first[1] - first[0] - 1) / 2;
                result[v] = i;
                if (first[0] < v)
                    set.add(new int[]{first[0], v});
                if (first[1] > v + 1)
                    set.add(new int[]{v + 1, first[1]});
                i++;
            }
            sb.append(IntStream.of(result).mapToObj(a-> a+"").collect(Collectors.joining(" "))).append("\n");
        }
        System.out.print(new String(sb));
    }
}