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.*;

public class Main {


    public static void main(String[] args) throws IOException {
//        br = new BufferedReader(new FileReader(new File("input.txt")));
//        out = new PrintWriter(new File("cutting.out"));
        br = new BufferedReader(new InputStreamReader(System.in));
        out = new PrintWriter(System.out);
        int Putin = nextInt();
        for (int POMOG = 0; POMOG < Putin; POMOG++) {
            int n = nextInt();
            int[] a = new int[n];
            TreeSet<f> s = new TreeSet<>(new Comparator<f>() {
                @Override
                public int compare(f o1, f o2) {
                    if (o1.size != o2.size)
                        return -Integer.compare(o1.size, o2.size);
                    return Integer.compare(o1.l, o2.l);
                }
            });
            s.add(new f(0, n - 1, n));
            for (int i = 1; i <= n; i++) {
                int l = s.first().l;
                int r = s.first().r;
                int size = s.first().size;
                s.pollFirst();
                int m = 0;
                if (size % 2 == 1) {
                    m = (l + r) / 2;
                    a[m] = i;
                } else {
                    m = (l + r - 1) / 2;
                    a[m] = i;
                }
                if (l != m)
                    s.add(new f(l, m - 1, m - l));
                if (r != m)
                    s.add(new f(m + 1, r, r - m));
            }
            for (int i = 0; i < n; i++) {
                out.print(a[i] + " ");
            }
            out.println();
        }
        out.close();
    }

    static BufferedReader br;
    static PrintWriter out;
    static StringTokenizer in = new StringTokenizer("");

    static String next() throws IOException {
        while (!in.hasMoreTokens()) {
            in = new StringTokenizer(br.readLine());
        }
        return in.nextToken();
    }

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

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

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

    static int gcd(int a, int b) {
        if (b == 0) return a;
        return gcd(b, a % b);
    }
}

class f {
    int l, r, size;

    public f(int v, int x, int y) {
        this.l = v;
        this.r = x;
        this.size = y;
    }
}