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.PrintWriter;
import java.util.*;
public class code {
	public static void main(String[] args)throws IOException {
		FastReader sc = new FastReader();
		PrintWriter pw = new PrintWriter(System.out);
		int t = sc.nextInt();
		while (t-- > 0) {
			int n = sc.nextInt();
			PriorityQueue<Edge> pq = new PriorityQueue<>(new Edge());
			int arr[] = new int[n + 1];
			int mid = 0;

			pq.add(new Edge(n, 1, n));
			int i = 1;
			while (i <= n) {
				Edge e = pq.poll();
				if (e.size % 2 != 0)
					mid = (e.l + e.r) / 2;
				else
					mid = (e.l + e.r - 1) / 2;
				arr[mid] = i;
				i++;
				int size1 = 0, size2 = 0;
				if (e.size % 2 != 0) {
					size1 = e.size / 2;
					size2 = e.size / 2;
				} else {
					size1 = e.size / 2;
					size2 = e.size / 2 - 1;
				}
				pq.add(new Edge(size2, e.l, mid - 1));
				pq.add(new Edge(size1, mid + 1, e.r));
				//System.out.println("s");

			}
			for (int j = 1; j <= n; j++) {
				System.out.print(arr[j] + " ");
			}
			System.out.println();
		}




	}


	static int gcd(int a, int b) {
		if (b == 0)
			return a;
		return gcd(b, a % b);
	}
}
class Edge implements Comparator<Edge> {
	int size, l, r;
	public Edge() {}
	public Edge(int s, int ll, int rr) {
		size = s;
		l = ll;
		r = rr;
	}
	public int compare(Edge e1, Edge e2) {
		if (e1.size < e2.size)
			return 1;
		if (e1.size == e2.size) {
			if (e1.l > e2.l)
				return 1;
			return -1;
		}
		return -1;
	}
}



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