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.*;
import java.util.*;

public class Main {
    private static FastReader f = new FastReader();

    public static void main(String[] args) {
        int t = f.nextInt();
        while (t-- > 0) {
            solve();
        }
    }

    static void solve() {
        int n = f.nextInt();
        int[] ans = new int[n];
        PriorityQueue<Pair> que = new PriorityQueue<>();
        que.add(new Pair(0,n-1));

        int cnt = 1;
        while (!que.isEmpty()) {
            Pair now = que.poll();
            //System.out.println(now.left+" "+now.right);
            int place = now.left + (now.right-now.left)/2;

            ans[place] = cnt;
            cnt++;

            if(now.left != place) {
                que.add(new Pair(now.left, place-1));
            }

            if(now.right != place) {
                que.add(new Pair(place+1, now.right));
            }

        }

        StringBuilder sb = new StringBuilder();
        for(int i=0;i<n;i++) {
            sb.append(ans[i]);
            sb.append(' ');
        }
        System.out.println(sb.toString());

    }

    static class Pair implements Comparable<Pair>{
        int left;
        int right;
        int diff;

        Pair(int left, int right) {
            this.left = left;
            this.right = right;
            diff = right - left;
        }


        @Override
        public int compareTo(Pair o) {
            if(diff == o.diff) {
                return left - o.left;
            }
            return o.diff - diff;
        }
    }

    //fast input reader
    static class FastReader
    {
        BufferedReader br;
        StringTokenizer st;

        public FastReader()
        {
            br = new BufferedReader(new
                    InputStreamReader(System.in));
        }

        String next()
        {
            while (st == null || !st.hasMoreElements())
            {
                try
                {
                    st = new StringTokenizer(br.readLine());
                }
                catch (IOException e)
                {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        int nextInt()
        {
            return Integer.parseInt(next());
        }

        long nextLong()
        {
            return Long.parseLong(next());
        }

        double nextDouble()
        {
            return Double.parseDouble(next());
        }

        String nextLine()
        {
            String str = "";
            try
            {
                str = br.readLine();
            }
            catch (IOException e)
            {
                e.printStackTrace();
            }
            return str;
        }
    }
}