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:
/*
    Author: Anthony Ngene
    Created: 07/08/2020 - 06:51
*/

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

public class D {
// He who angers you conquers you. - Elizabeth Kenny
public static void main(String[] args) throws IOException {
    in = new FastScanner();

    int cases = in.intNext();
    for (int t = 1; t <= cases; t++) {
        int n = in.intNext();
        int[] arr = new int[n];
        TreeSet<Tuple> treeSet = new TreeSet<>();
        treeSet.add(new Tuple(0, n - 1));
        int selected = 0;
        while (selected < n) {
            selected++;
            Tuple node = treeSet.pollLast();
            int idx = (node.a + node.b) / 2;
            arr[idx] = selected;
            if (idx > node.a) treeSet.add(new Tuple(node.a, idx - 1));
            if (idx < node.b) treeSet.add(new Tuple(idx + 1, node.b));
        }
        for (int i: arr) out.p(i).p(" ");
        out.println("");
    }

    out.close();
}


    static class Tuple implements Comparable<Tuple> {
        int a;
        int b;
        public Tuple(int a, int b) {
            this.a = a;
            this.b = b;
        }
        public int getA() { return a; }
        public int getB() { return b; }
        public int size() {
            return this.b - this.a + 1;
        }
        public int compareTo(Tuple other) {
            if (this.size() == other.size()) return Integer.compare(other.b, this.b);
            return Integer.compare(this.size(), other.size());
        }
        @Override
        public int hashCode() { return Arrays.deepHashCode(new Integer[]{a, b}); }
        @Override
        public boolean equals(Object o) {
            if (!(o instanceof Tuple)) return false;
            Tuple pairo = (Tuple) o;
            return (this.a == pairo.a && this.b == pairo.b);
        }
        @Override
        public String toString() { return String.format("(%d, %d) ", this.a, this.b); }
    }


private static final FastWriter out = new FastWriter();
private static FastScanner in;
static ArrayList<Integer>[] adj;
private static long e97 = (long)1e9 + 7;
static class FastWriter {
    private static final int IO_BUFFERS = 128 * 1024;
    private final StringBuilder out;
    public FastWriter() {
        out = new StringBuilder(IO_BUFFERS);
    }
    public FastWriter p(Object object) {
        out.append(object);
        return this;
    }
    public FastWriter p(String format, Object... args) {
        out.append(String.format(format, args));
        return this;
    }
    public FastWriter pp(Object... args) {
        for (Object ob : args) {
            out.append(ob).append(" ");
        }
        out.append("\n");
        return this;
    }
    public FastWriter println(Object object) {
        out.append(object).append("\n");
        return this;
    }
    public void toFile(String fileName) throws IOException {
        BufferedWriter writer = new BufferedWriter(new FileWriter(fileName));
        writer.write(out.toString());
        writer.close();
    }
    public void close() throws IOException {
        System.out.print(out);
    }
}
static class FastScanner {
    private InputStream sin = System.in;
    private final byte[] buffer = new byte[1024];
    private int ptr = 0;
    private int buflen = 0;
    public FastScanner(){}
    public FastScanner(String filename) throws FileNotFoundException {
        File file = new File(filename);
        sin = new FileInputStream(file);
    }
    private boolean hasNextByte() {
        if (ptr < buflen) {
            return true;
        }else{
            ptr = 0;
            try {
                buflen = sin.read(buffer);
            } catch (IOException e) {
                e.printStackTrace();
            }
            if (buflen <= 0) {
                return false;
            }
        }
        return true;
    }
    private int readByte() { if (hasNextByte()) return buffer[ptr++]; else return -1;}
    private static boolean isPrintableChar(int c) { return 33 <= c && c <= 126;}
    public boolean hasNext() { while(hasNextByte() && !isPrintableChar(buffer[ptr])) ptr++; return hasNextByte();}
    public String next() {
        if (!hasNext()) throw new NoSuchElementException();
        StringBuilder sb = new StringBuilder();
        int b = readByte();
        while(isPrintableChar(b)) {
            sb.appendCodePoint(b);
            b = readByte();
        }
        return sb.toString();
    }
    public long longNext() {
        if (!hasNext()) throw new NoSuchElementException();
        long n = 0;
        boolean minus = false;
        int b = readByte();
        if (b == '-') {
            minus = true;
            b = readByte();
        }
        if (b < '0' || '9' < b) {
            throw new NumberFormatException();
        }
        while(true){
            if ('0' <= b && b <= '9') {
                n *= 10;
                n += b - '0';
            }else if(b == -1 || !isPrintableChar(b) || b == ':'){
                return minus ? -n : n;
            }else{
                throw new NumberFormatException();
            }
            b = readByte();
        }
    }
    public int intNext() {
        long nl = longNext();
        if (nl < Integer.MIN_VALUE || nl > Integer.MAX_VALUE) throw new NumberFormatException();
        return (int) nl;
    }
    public double doubleNext() { return Double.parseDouble(next());}
    public long[] nextLongArray(final int n){
        final long[] a = new long[n];
        for (int i = 0; i < n; i++)
            a[i] = longNext();
        return a;
    }
    public int[] nextIntArray(final int n){
        final int[] a = new int[n];
        for (int i = 0; i < n; i++)
            a[i] = intNext();
        return a;
    }
    public ArrayList<Integer>[] getAdj(int n) {
        ArrayList<Integer>[] adj = new ArrayList[n + 1];
        for (int i = 1; i <= n; i++) adj[i] = new ArrayList<>();
        return adj;
    }

    public ArrayList<Integer>[] adjacencyList(int n, int m) throws IOException {
        adj = getAdj(n);
        for (int i = 0; i < m; i++) {
            int a = intNext(), b = intNext();
            adj[a].add(b);
            adj[b].add(a);
        }
        return adj;
    }
}
}