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.lang.*;
import java.io.*;

//           THIS TEMPLATE MADE BY AKSH BANSAL.

public class Solution {
    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;
        }
    }
    private static boolean[] isPrime;
    private static void primes(){
        int num = (int)1e6; // PRIMES FROM 1 TO NUM
        isPrime = new boolean[num];
     
        for (int i = 2; i< isPrime.length; i++) {
           isPrime[i] = true;
        }
        for (int i = 2; i< Math.sqrt(num); i++) {
           if(isPrime[i] == true) {
              for(int j = (i*i); j<num; j = j+i) {
                 isPrime[j] = false;
              }
           }
        }
    }
    private static long gcd(long a, long b){
        if(b==0)return a;
        return gcd(b,a%b);
    }
    private static long pow(long x,long y){
        if(y==0)return 1;
        long temp = pow(x, y/2);
        if(y%2==1){
            return x*temp*temp;
        }
        else{
            return temp*temp;
        }
    }
    // static ArrayList<Integer>[] adj;
    // static void getAdj(int n,int q, FastReader sc){
    //     adj = new ArrayList[n+1];
    //     for(int i=1;i<=n;i++){
    //         adj[i] = new ArrayList<>();
    //     }
    //     for(int i=0;i<q;i++){
    //         int a = sc.nextInt();
    //         int b = sc.nextInt();

    //         adj[a].add(b);
    //         adj[b].add(a);
    //     }
    // }
    public static void main(String[] args) throws IOException {
        FastReader sc = new FastReader();
        PrintWriter out = new PrintWriter(System.out);
        // primes();
        // ________________________________

        int t = sc.nextInt();
        StringBuilder output = new StringBuilder();

        while (t-- > 0) {
            int n = sc.nextInt();
            // output.append().append("\n");
            solver(n, out);
        }

        out.println(output);
        // _______________________________

        // int n = sc.nextInt();
        // out.println(solver());
        // ________________________________
        out.flush();
    }

    public static void solver(int n, PrintWriter out) {
        int[] res =new int[n];
        PriorityQueue<int[]> q = new PriorityQueue<>(
            (a,b)->b[1]-b[0]==a[1]-a[0]?a[0]-b[0]:b[1]-b[0]-a[1]+a[0]
        );
        // q.offer(0);
        // q.offer(n-1);
        q.offer(new int[]{0,n-1});
        int cur = 1;
        while(!q.isEmpty()){
            int pair[] = q.poll();
            int start = pair[0];
            int end = pair[1];

            int mid = start + (end-start)/2;
            res[mid] = cur++;

            // System.out.println(start+"__"+ end);

            if(start==end){
                continue;
            }

            if(end-mid>mid-start){
                // q.offer(mid+1);
                // q.offer(end);
                q.offer(new int[]{mid+1, end});
                if(mid-1>=start){
                    q.offer(new int[]{start, mid-1});
                    // q.offer(start);
                    // q.offer(mid-1);
                }
            }
            else{
                if(mid-1>=start){
                    q.offer(new int[]{start, mid-1});
                    // q.offer(start);
                    // q.offer(mid-1);
                }
                q.offer(new int[]{mid+1, end});
                // q.offer(mid+1);
                // q.offer(end);
            }
        }

        for(int i=0;i<n;i++){
            out.print(res[i]+" ");
        }
        out.println();
    }
}