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.util.*;
import java.io.*;

public class constructarr {
    static class seg implements Comparable<seg> {
        int l, r;
        public seg(int l, int r) {
            this.l = l;
            this.r = r;
        }

        @Override
        public int compareTo(seg seg) {
            if(r - l + 1 == seg.r - seg.l + 1) {
                if(this.l < seg.l) {
                    return -1;
                } else {
                    return 1;
                }
            }
            return -1*((r-l+1) - (seg.r - seg.l + 1));
        }
    }
    public static void main(String[] args) throws IOException {
        FastReader sc = new FastReader();
        PrintWriter pw = new PrintWriter(System.out);


        int t = sc.nextInt();
        while(t-- > 0) {
            int n = sc.nextInt();
            int a[] = new int[n+1];

            int curr = 0;
            PriorityQueue<seg> q = new PriorityQueue<>();
            q.add(new seg(1,n));
            while(!q.isEmpty()) {
                seg p = q.poll();
                int mid = 0;
                int r = p.r;
                int l = p.l;
                if(r - l + 1 == 0) continue;
                if((r - l + 1) % 2 == 1) {
                    mid = (l + r) / 2;
                } else {
                    mid = (l + r - 1) / 2;
                }
                if(mid <= 0 || mid > n || a[mid] != 0) continue;
                curr++;
                a[mid] = curr;
                q.add(new seg(mid+1,r));
                q.add(new seg(l,mid-1));
            }
            for(int i = 1; i <= n; i++) {
                pw.print(a[i] + " ");
            }
            pw.println();
        }
        pw.close();
    }

    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;
        }
    }
}