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.*;


public class Main {

    public static void main(String[] args) {

        int i;
        int j;
        int k;
        int n;
        int m;
        int t;
        int len;
        int f;
        int c=0;
        int d=0;
        int b;
        int p;
        int q;
        FastScanner fs = new FastScanner();

        PriorityQueue<State> pq = new PriorityQueue<>();

        t = fs.nextInt();

        while(t>0 ){
            t--;

            n = fs.nextInt();

            int[] ans = new int[n+5];

            pq.add(new State(1,n));
            j=0;

            while(! pq.isEmpty()){

                State a = pq.poll();

                if((a.l+a.r)%2==0)
                    c = (a.l+a.r)/2;
                else
                    c = (a.l+a.r-1)/2;

                ans[c] = ++j;

                if((c-1)>=(a.l))
                    pq.add(new State(a.l,c-1));

                if((c+1)<=(a.r))
                    pq.add(new State(c+1, a.r));
            }

            for(i=1;i<=n;i++){
                System.out.print(ans[i]+" ");
            }

            System.out.println();
        }
    }


    static void sort(int[] a) {
        ArrayList<Integer> l=new ArrayList<>();
        for (int i:a) l.add(i);
        Collections.sort(l);
        for (int i=0; i<a.length; i++) a[i]=l.get(i);
    }

    static class FastScanner {
        BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st=new StringTokenizer("");
        String next() {
            while (!st.hasMoreTokens())
                try {
                    st=new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            return st.nextToken();
        }

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

        int[] readArray(int n) {
            int[] a=new int[n];
            for (int i=0; i<n; i++) a[i]=nextInt();
            return a;
        }
        long nextLong() {
            return Long.parseLong(next());
        }
    }

    static class State implements Comparable<State> {
        int l, r;
        int len;
        public State(int l, int r) {
            this.l=l;
            this.r=r;
            this.len=r-l+1;
        }

        public int compareTo(State o) {
            if (len!=o.len) {
                return -Integer.compare(len, o.len);
            }
            else {
                return Integer.compare(l, o.l);
            }
        }
    }

}