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 static java.lang.Math.*;

public class Main {

    static void run() throws IOException {
        file("", "");

        int t = nextInt();
        while (t-- > 0)
            solution();
        end();
    }


    static void solution() throws IOException {
        int n = nextInt();
        PriorityQueue<mem> pq = new PriorityQueue<>((o1, o2) -> {
            int diff = (o2.r - o2.l) - (o1.r - o1.l);
            if (diff == 0)
                return o1.l - o2.l;
            return diff;
        });
        pq.add(create_mem(0, n - 1));
        int[] arr = new int[n];
        for (int i = 0; i < n; i++) {
            mem next = pq.poll();
            int l = next.l;
            int r = next.r;
            arr[(r + l) / 2] = i + 1;
            if (l == r)
                continue;
            if (l <= (r + l) / 2 - 1)
                pq.add(create_mem(l, (r + l) / 2 - 1));
            pq.add(create_mem((r + l) / 2 + 1, r));
        }
        for (int i = 0; i < n; i++) {
            out.print(arr[i] + " ");
        }
        out.println();
    }

    static mem create_mem(int l, int r) {
        mem y = new mem();
        y.l = l;
        y.r = r;

        return y;
    }

    static class mem {
        int l, r;

    }


    static void Z_function() throws IOException {
        char[] s = nextToken().toCharArray();
        int[] z = new int[s.length];
        for (int i = 1, l = 0, r = 0; i < s.length; i++) {
            if (i <= r)
                z[i] = min(r - i + 1, z[i - l]);
            while (z[i] + i < s.length && s[z[i] + i] == s[z[i]])
                ++z[i];
            if (i + z[i] - 1 > r) {
                l = i;
                r = i + z[i] - 1;
            }
        }
        for (int i = 0; i < z.length; i++) {
            out.print(z[i] + " ");
        }
    }

    static long Pow(long a, long b) {
        long h = 1;
        while (b > 0) {
            if (b % 2 != 0) {
                h *= a;
                b--;
            }
            b /= 2;
            a *= a;
        }
        return h;
    }

    static long lcm(long a, long b) {
        return a * b / gcd(a, b);
    }

    static long gcd(long a, long b) {
        return b == 0 ? a : gcd(b, a % b);
    }

    static void end() {
        out.flush();
        out.close();
    }

    static BufferedReader br;
    static PrintWriter out;

    static void file(String input, String output) {
        if (input.equals("")) {
            br = new BufferedReader(new InputStreamReader(System.in));
            out = new PrintWriter(System.out);
        } else {
            try {
                br = new BufferedReader(new FileReader(input));
            } catch (FileNotFoundException e) {
                e.printStackTrace();
            }
            try {
                out = new PrintWriter(output);
            } catch (FileNotFoundException e) {
                e.printStackTrace();
            }
        }
    }

    static StringTokenizer in = new StringTokenizer("");

    public static String nextToken() throws IOException {
        while (in == null || !in.hasMoreTokens()) {
            String s = br.readLine();
            if (s == null) return null;
            in = new StringTokenizer(s);
        }
        return in.nextToken();
    }


    public static int nextInt() throws IOException {
        return Integer.parseInt(nextToken());
    }

    public static double nextDouble() throws IOException {
        return Double.parseDouble(nextToken());
    }

    public static long nextLong() throws IOException {
        return Long.parseLong(nextToken());
    }


    public static void main(String[] args) throws IOException {
        run();
    }
}