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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;

public class ar {

    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 (final 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 (final IOException e) {
                e.printStackTrace();
            }
            return str;
        }
    }

    // static boolean[] seen;
    // static Map<Integer, Integer> map;
    // static Map<Long, Long> lmap;
    // static Set<Character> charset;
    // static Set<Integer> set;
    // static int[] arr;
    // static int[][] dp;
    // static int rem = (int) 1e9 + 7;
    // static List<List<Integer>> graph;
    // static int[][] kmv = { { 2, 1 }, { 1, 2 }, { 2, -1 }, { -1, 2 }, { -2, 1 }, {
    // 1, -2 }, { -1, -2 }, { -2, -1 } };
    // static char[] car;
    // static boolean[] primes;
    // static int MAX = (int) 1e4 + 1;
    // static double[] dar;
    static long[] lar;
    // static long[][] dlar;

    // static void Sieve() {
    // primes = new boolean[MAX];
    // primes[0] = true;
    // primes[1] = true;
    // for (int i = 2; i * i < MAX; i++) {
    // if (!primes[i]) {
    // for (int j = i * i; j < MAX; j += i) {
    // primes[j] = true;
    // }
    // }
    // }
    // }

    // static int[] t;
static int func(int[] a, int[] b){
    int len1=a[1]-a[0]+1;
    int len2=b[1]-b[0]+1;
    if(len1>len2||len2>len1){
        return len2-len1;
    }
return a[0]-b[0];
}
    public static void main(String[] args) throws java.lang.Exception {
        FastReader scn = new FastReader();
        int T = scn.nextInt();

        for(int t=0;t<T;t++){
            int n=scn.nextInt();
            PriorityQueue<int[]> pq = new PriorityQueue<>((a,b)->func(a,b)); 
            pq.add(new int[]{0,n-1});
            int[] arr = new int[n];
            for(int i=1;i<=n;i++){
              int[] sub=pq.poll();
              if(sub[0]<0||sub[1]<0||sub[0]>=n||sub[1]>=n)continue;
              
              int ind=(sub[0]+sub[1])/2;
              arr[ind]=i;
              pq.add(new int[]{sub[0],ind-1});
              pq.add(new int[]{ind+1,sub[1]});
            }
            for(int k:arr){
                System.out.print(k+" ");
            }
            System.out.print("\n");
        }
    }
}