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.IOException;
import java.io.InputStreamReader;
import java.util.Comparator;
import java.util.PriorityQueue;

public class D {
    public static void main(String[] args) throws IOException {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        int t = Integer.parseInt(br.readLine());
        StringBuilder sb = new StringBuilder();
        while (t-- > 0) {
            int n = Integer.parseInt(br.readLine());
            int[] arr = new int[n];
            PriorityQueue<Data> pq = new PriorityQueue<>(new Sort());
            pq.add(new Data(1, arr.length));
            int current = 1;
            while (!pq.isEmpty()){
                Data data = pq.poll();
                int mid = (data.l + data.r)/2 - 1;
                if((data.r - data.l + 1) % 2 == 0){
                    mid = (data.l + data.r - 1)/2;
                    mid--;
                }
                arr[mid] = current;
                current++;
                mid++;
                if(data.l <= mid - 1)
                pq.add(new Data(data.l, mid - 1));
                if(mid +1 <= data.r)
                pq.add(new Data(mid + 1, data.r));
            }
            for(Integer val : arr){
                sb.append(val).append(" ");
            }
            sb.append("\n");
        }
        System.out.println(sb.toString());
    }
    static class Data{
        int l,r;
        public Data(int l, int r){
            this.l = l;
            this.r = r;
        }
    }
    static class Sort implements Comparator<Data>{

        @Override
        public int compare(Data o1, Data o2) {
            int s1 = o1.r - o1.l;
            int s2 = o2.r - o2.l;
            if(s2 > s1) return s2 - s1;
            else if(s2 < s1) return s2 - s1;
            else {
                return o1.l - o2.l;
            }
        }
    }
}