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.*;
	import java.math.*;
	
	 
	 public class Main	{
	   static class Pair implements Comparable<Pair>{
	   int a;
	   int b;
	   public Pair(int x,int y){a=x;b=y;}
	   public Pair(){}
	   public int compareTo(Pair p){
		  
		   int lena = b - a + 1;
		   int lenb = p.b - p.a + 1;
		   if(lena == lenb) {
			   if(a < p.a)return -1;
			   return 1;
		   }
		   else {
			   if(lena < lenb) {
				   return 1;
			   }
			   return -1;
		   }
		   
	   }
	  
//	@Override
//	public int hashCode() {
//		final int prime = 31;
//		int result = 1;
//		result = prime * result + a;
//		result = prime * result + b;
//	//	out.println("hashcode = "+result);
//		return result;
//	}
	@Override
	public boolean equals(Object obj) {
		Pair cur = (Pair)obj;
		if((a==cur.a && b==cur.b) || (a==cur.b && b==cur.a))return true;
		return false;
	}
	 }

	  
	   static class cell implements Comparable<cell>{
		   int a,b;
		   long dis;
		   public cell(int x,int y,long z) {a=x;b=y;dis=z;}
		   public int compareTo(cell c) {
			   return Long.compare(dis,c.dis);
		   }
	   }
	static class TrieNode{
		TrieNode left;
		TrieNode right;
		int op;
		int data;
		public TrieNode() {}
	}
	  public static int gcd(int a,int b)
	  {
	    if(a<b)
	
	      return gcd(b,a);
	    if(b==0)
	      return a;
	    return gcd(b,a%b);
	    
	  }
	  static int lcm(int a,int b) {
		  return  a*b / gcd(a,b);
	  }
	  //static long ans = 0;
	  static long mod = (long)(1e9+7); //998244353;//
	   
	    public static void main(String[] args) throws Exception {
	       new Thread(null, null, "Anshum Gupta", 99999999) {
	            public void run() {
	                try {
	                    solve();
	                } catch(Exception e) {
	                    e.printStackTrace();
	                    System.exit(1);
	                }
	            }
	        }.start();
	    }
	
	static long pow(long x,long y){
	    if(y == 0)return 1;
	    if(y==1)return x;
	    long a = pow(x,y/2);
	    a = (a*a)%mod;
	    if(y%2==0){
	        return a;
	    }
	    return (a*x)%mod;
	}
	
	static long mxx;
	static int mxN = (int)(2e6+5);
	static long[]fact,inv_fact;
	static long my_inv(long a) {
		return pow(a,mod-2);
	}
	static long bin(int a,int b) {
		if(a < b || a<0 || b<0)return 0;
	    return ((fact[a]*inv_fact[a-b])%mod * inv_fact[b])%mod;
	}
	static ArrayList<ArrayList<Integer>>adj;
	static boolean[]vis;
	static void make_facts() {
	  fact=new long[mxN];
	  inv_fact = new long[mxN];
	  fact[0]=inv_fact[0]=1L;
	  for(int i=1;i<mxN;i++) {
		   fact[i] = (i*fact[i-1])%mod;
		   inv_fact[i] = my_inv(fact[i]);
	  }
	}
	//static int[]bfs(int a){
	//	Queue<Integer> q = new  LinkedList<Integer>();
	//	
	//	vis = new boolean[n+1];
	//	int[]dis = new int[n+1];
	//	q.add(a);
	//	dis[a] = 0;
	//	vis[a] = true;
	//	while(!q.isEmpty()) {
	//		int cur = q.poll();
	//	//	vis[cur] = true;
	//	//	if(cur == b)break;
	//		for(int x : adj.get(cur)) {
	//			if(vis[x])continue;
	//			q.add(x);
	//			dis[x] = dis[cur]+1;
	//			vis[x] = true;
	//		}
	//	}
	//	return dis;
	//}
	
	 public static void solve() throws Exception {
	   // solve the problem here
	   MyScanner s = new MyScanner();
	        out = new PrintWriter(new BufferedOutputStream(System.out), true);
	        int tc = s.nextInt();
	        mxx = (long)(1e18+5);
	//        make_facts(); 
	        while(tc-->0){
	        	int n = s.nextInt();
	        	int[]a=new int[n];
	        	PriorityQueue<Pair> pq = new PriorityQueue<Main.Pair>();
	        	pq.add(new Pair(0, n-1));
	        	for(int i=0;i<n;i++) {
	        		Pair cur = pq.poll();
	        		int mid = (cur.a + cur.b) / 2;
	        		a[mid] = i+1;
	        		if(cur.a < mid) {
	        			pq.add(new Pair(cur.a, mid - 1));
	        		}
	        		 if(mid < cur.b) {
	        			pq.add(new Pair(mid+1, cur.b));
	        		}
	        	}
	        	for(int i=0;i<n;i++) {
	        		out.print(a[i] + " ");
	        	}out.println();
	        }
	        	
	           
	        out.flush();
	}
	 
	     
	 
	 
	 
	    //-----------PrintWriter for faster output---------------------------------
	    public static PrintWriter out;
	 
	    //-----------MyScanner class for faster input----------
	    public static class MyScanner {
	        BufferedReader br;
	        StringTokenizer st;
	 
	        public MyScanner() {
	            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;
	        }
	    }
	    //--------------------------------------------------------
	}