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 ConstructingArray642D{
	static class FastReader {

        BufferedReader br;
        StringTokenizer st;

        private 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());
        }

	 int[] nextIntArray(int n) {
			int[] a = new int[n];
			for (int i = 0; i < n; i++)
				a[i] = nextInt();
			return a;
	}

	int[] nextIntArrayOne(int n) {
				int[] a = new int[n+1];
				for (int i = 1; i < n+1; i++)
					a[i] = nextInt();
				return a;
	}

        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;
        }
    }

	public static void main(String[] args) {
		FastReader s =new FastReader();
		int t = s.nextInt();
		StringBuilder str = new StringBuilder();
		while(t-- >0) {
				int n = s.nextInt();
				int arr[] = new int[n+1];
				PriorityQueue<Pair> heap = new PriorityQueue<>();
				heap.add(new Pair(1, n, 0));
				
				int i =1;
				while(!heap.isEmpty()) {
					 Pair p =heap.remove();
					 if(p.l==p.r || p.l>p.r||p.r<p.l) continue;
					 int param = p.r-p.l+1;
					 int mid = 0;
					 if(param%2==0) {
						 mid = (p.l+p.r-1)/2;
						 arr[mid] = i++;
						 }else {
						  mid = (p.l+p.r)/2;
						  arr[mid] =i++;
						 
					 }
					 
					 	
						 heap.add(new Pair(p.l, mid-1, 0));
					 	
						 heap.add(new Pair(mid+1, p.r, 1));
					 
				}
				
				for(int j=1;j<=n;j++) {
					if(arr[j]==0) arr[j] = i++;
				}
				for(int j=1;j<=n;j++) {
					str.append(arr[j]).append(" ");
				}
				str.append("\n");
				
			
		}
		System.out.println(str);
	}

	static class Pair implements Comparable<Pair>{
		int l,r,f;
		 // f = 0 = left &  f = 1 = right
		 
		public Pair(int l,int r,int f) {
			this.l = l;
			this.r = r;
			this.f = f;
			
		}
		
		@Override
		public String toString() {
			// TODO Auto-generated method stub
			return "["+l+" "+r+":"+f+"]";
		}

		@Override
		public int compareTo(Pair o) {
			int cur = this.r-this.l; 
			int other = o.r - o.l;
			
			if(cur == other) {
				if(this.l < o.l) {
					return -1;
				}else return 1;
			}
			
			if(cur>other){
				return -1;
			}
			
			
			return 1;
		}
		
	}

}