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.util.*;
import java.io.*;

public class tr0 {
	static PrintWriter out;
	static StringBuilder sb;
	static int mod = (int) 1e9 + 7;
	static long inf = (long) 1e16;
	static int[] col;
	static int n, m, a[];
	static ArrayList<Integer>[] ad;
	static int[][][] memo;
	static ArrayList<Integer> h;
	static int[] perm;
	static char[][] g;
	static boolean[] tak;
	static boolean f;

	public static void main(String[] args) throws Exception {
		Scanner sc = new Scanner(System.in);
		out = new PrintWriter(System.out);
		int t = sc.nextInt();
		while (t-- > 0) {
			int n = sc.nextInt();
			int[] a = new int[n];
			PriorityQueue<pair> pq = new PriorityQueue<>();
			pq.add(new pair(0, n - 1));
			int id = 1;
			while (!pq.isEmpty()) {
				pair cur = pq.poll();
				a[(cur.r + cur.l) / 2] = id++;
				if (cur.r != cur.l) {
					if ((cur.r - cur.l) % 2 == 1) {
						if(cur.r-cur.l!=1)
						   pq.add(new pair(cur.l, ((cur.r + cur.l) / 2)-1));
						pq.add(new pair(((cur.r + cur.l) / 2) + 1, cur.r));
					} else {
						pq.add(new pair(cur.l, ((cur.r + cur.l) / 2) - 1));
						pq.add(new pair(((cur.r + cur.l) / 2) + 1, cur.r));
					}
				}
			}
			for (int i = 0; i < n; i++)
				out.print(a[i] + " ");
			out.println();
		}
		out.flush();
	}

	static class pair implements Comparable<pair> {
		int l;
		int r;

		pair(int ll, int rr) {
			l = ll;
			r = rr;
		}

		public String toString() {
			return l + " " + r;
		}

		@Override
		public int compareTo(pair o) {
			int le = r - l;
			int le1 = o.r - o.l;
			if (le1 == le)
				return l - o.l;
			return le1 - le;
		}

	}

	static class Scanner {
		StringTokenizer st;
		BufferedReader br;

		public Scanner(InputStream system) {
			br = new BufferedReader(new InputStreamReader(system));
		}

		public Scanner(String file) throws Exception {
			br = new BufferedReader(new FileReader(file));
		}

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

		public String nextLine() throws IOException {
			return br.readLine();
		}

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

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

		public char nextChar() throws IOException {
			return next().charAt(0);
		}

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

		public int[] nextArrInt(int n) throws IOException {
			int[] a = new int[n];
			for (int i = 0; i < n; i++)
				a[i] = nextInt();
			return a;
		}

		public long[] nextArrLong(int n) throws IOException {
			long[] a = new long[n];
			for (int i = 0; i < n; i++)
				a[i] = nextLong();
			return a;
		}

		public boolean ready() throws IOException {
			return br.ready();
		}

		public void waitForInput() throws InterruptedException {
			Thread.sleep(3000);
		}
	}
}