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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.io.PrintWriter;
import java.util.StringTokenizer;*/
import java.io.*;
import java.util.*;

public class Main {

	static BufferedReader br;
	static PrintWriter out;
	static StringTokenizer st;

	static class Pair {
		int l, r;
		Pair(int l, int r) {
			this.l = l;
			this.r = r;
		}
	}

	static void solve() throws IOException {
		int n = readInt();
		int[] a = new int[n + 1];
		int[] b1 = new int[n + 1];
		PriorityQueue<Pair> pq = new PriorityQueue<>(new Comparator<Pair>() {
			public int compare(Pair a1, Pair b) {
				if ((a1.r - a1.l) == (b.r - b.l)) return a1.l - b.l;
				return (b.r - b.l) - (a1.r - a1.l);
			}
		});
		pq.add(new Pair(1, n));
		int x = 0;
		int y = 1;
		while (x < n) {

			Pair p1 = pq.poll();
			if ((p1.l + p1.r + 1) % 2 == 1) {
				int m = (p1.l + p1.r) / 2;
				b1[m] = y;

				pq.add(new Pair(p1.l, m - 1));
				pq.add(new Pair(m + 1, p1.r));
			} else {
				int m = (p1.l + p1.r - 1) / 2;
				b1[m] = y;

				pq.add(new Pair(p1.l, m - 1));
				pq.add(new Pair(m + 1, p1.r));
			}

			x++;
			y++;
		}
		for (int i = 1; i <= n; i++) {
			out.print(b1[i] + " ");
		}
		out.println();
	}

	public static void main(String[] args) throws IOException {
		br = new BufferedReader(new InputStreamReader(System.in));
		out = new PrintWriter(new OutputStreamWriter(System.out));
		// br = new BufferedReader(new FileReader("input"));
		// out = new PrintWriter(new FileWriter("output"));
		int t = readInt();
		while (t-- > 0) {
			solve();
		}
		out.close();
	}

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

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

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

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

	static char readCharacter() throws IOException {
		return next().charAt(0);
	}

	static String readLine() throws IOException {
		return br.readLine().trim();
	}
}