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.math.BigInteger;
import java.util.*;

public class SolutionC {
    static BufferedReader input;
    static StringTokenizer _stk;

    static String readln() throws IOException {
        String l = input.readLine();
        if (l != null)
            _stk = new StringTokenizer(l, " ");
        return l;
    }

    static String next() {
        return _stk.nextToken();
    }

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

    static long nextLong() {
        return Long.parseLong(next());
    }


    static void dbg(Object... o) {
        System.out.println(Arrays.deepToString(o));
    }

    static PrintWriter output = new PrintWriter(new BufferedWriter(
            new OutputStreamWriter(System.out)));

    public static void main(String[] args) throws IOException {
        Locale.setDefault(Locale.US);
        input = new BufferedReader(new InputStreamReader(System.in));
        readln();
        int t = nextInt();
        PriorityQueue<Segment> queue = new PriorityQueue<>(Comparator.comparing(Segment::getLen).reversed().thenComparing(Segment::getStart));
        for (int testI = 0; testI < t; testI++) {
            queue.clear();
            readln();
            int n = nextInt();
            int[] a = new int[n];
            int cur = 1;
            queue.add(new Segment(0, n));
            while(!queue.isEmpty()) {
                Segment segment = queue.poll();
                if (segment.len == 1) {
                    a[segment.start] = cur++;
                    continue;
                }

                int l = segment.start;
                int r = l + segment.len;
                int mid;
                if ((r - l) % 2 == 1) {
                    mid = l + (r - l) / 2;
                } else {
                    mid = l + (r - l - 1) / 2;
                }

                a[mid] = cur++;
                if (mid != l) {
                    queue.add(new Segment(l, mid - l));
                }

                if (mid != r) {
                    queue.add(new Segment(mid + 1, r - mid - 1));
                }
            }

            for (int i = 0; i < n; i++) {
                output.print(a[i]);
                if (i < n - 1) {
                    output.print(" ");
                }
            }

            if (testI < t - 1) {
                output.println();
            }
        }


        output.close();
    }

    private static class Segment {
        private int start;
        private int len;

        public Segment(int start, int len) {
            this.start = start;
            this.len = len;
        }

        public int getStart() {
            return start;
        }

        public Segment setStart(int start) {
            this.start = start;
            return this;
        }

        public int getLen() {
            return len;
        }

        public Segment setLen(int len) {
            this.len = len;
            return this;
        }
    }
}