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 javafx.util.Pair;
    import java.util.TreeSet;
    import java.util.Scanner;
     
    public class ConstructingTheArray {
      public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        int T = in.nextInt();
        while(T-- > 0){
          int n = in.nextInt();
          TreeSet<Pair<Integer,Integer>> set = new TreeSet<>((pair1, pair2) -> {
            int lenA = pair2.getKey() - pair1.getKey() + 1;
            int lenB = pair2.getValue() - pair1.getValue() + 1;
            if (lenA == lenB)
              return pair1.getKey() - pair2.getKey();
            return lenB - lenA;
          });
          set.add(new Pair<>(0,n-1));
          int[] arr = new int[n];
          for(int i = 1 ; i <= n ;i++){
            Pair<Integer, Integer> pair = set.pollFirst();
            int idx = (pair.getKey() + pair.getValue()) / 2;
            arr[idx]=i;
            if(pair.getKey() < idx)
              set.add(new Pair<>(pair.getKey(),idx-1));
            if(idx < pair.getValue())
              set.add(new Pair<>(idx+1,pair.getValue()));
          }
          for(int a : arr)
            System.out.print(a + " ");
          System.out.println();
        }
      }
    }