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 {
    private static InputReader in;
    private static PrintWriter out;

    public static void main(String[] args) {
        in = new InputReader();
        out = new PrintWriter(System.out);
        int t = 1;
        t = in.nextInt();
//        long start = System.currentTimeMillis();
        for (int i = 0; i < t; ++i) {
            solve();
        }
//        out.println(System.currentTimeMillis() - start);
        out.close();
    }

    private static void solve() {
        int n = in.nextInt();
        PriorityQueue<Pair> q = new PriorityQueue<>(new Comparator<Pair>() {
            @Override
            public int compare(Pair A, Pair B) {
                int sz1 = A.getSize(), sz2 = B.getSize();
                if (sz1 == sz2) {
                    return Integer.compare(A.l, B.l);
                }
                return -Integer.compare(sz1, sz2);
            }
        });
        int[] result = new int[n];
        int move = 1;
        q.add(new Pair(0, n - 1));
        while (q.size() > 0 && q.peek().getSize() > 1) {
            Pair current = q.remove();
            int mid = current.getMid();
            result[mid] = move++;
            if (current.l <= mid - 1) {
                q.add(new Pair(current.l, mid - 1));
            }
            if (current.r >= mid + 1) {
                q.add(new Pair(mid + 1, current.r));
            }
        }
        while (q.size() > 0) {
            Pair current = q.remove();
            result[current.l] = move++;
        }
//        out.println(Arrays.toString(result));
        for (int e : result) out.print(e + " ");
        out.println();
    }

    static class Pair {
        int l, r;

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

        public int getSize() {
            return r - l + 1;
        }

        @Override
        public String toString() {
            return "Pair{" +
                    "l=" + l +
                    ", r=" + r +
                    '}';
        }

        public int getMid() {
            return (l + r) / 2;
        }
    }

    static class InputReader {
        BufferedReader br;
        StringTokenizer st;

        public InputReader() {
            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;
        }
    }
}