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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.PriorityQueue;
import java.io.BufferedWriter;
import java.util.InputMismatchException;
import java.io.IOException;
import java.util.AbstractCollection;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author unknown
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        OutputWriter out = new OutputWriter(outputStream);
        DConstructingTheArray solver = new DConstructingTheArray();
        solver.solve(1, in, out);
        out.close();
    }

    static class DConstructingTheArray {
        PriorityQueue<_C.Pair<Integer, Integer>> pq = new PriorityQueue<>(200005, (o1, o2) -> {
            int dist = (o2.s - o2.f) - (o1.s - o1.f);
            if (dist != 0) {
                return dist;
            }
            return (Integer) o1.f - (Integer) o2.f;
        });

        public void solve(int testNumber, InputReader in, OutputWriter out) {
            int ntc = in.nextInt();
            while ((ntc--) > 0) {
                int n = in.nextInt();
                if (n == 1) {
                    out.println(1);
                    continue;
                }
                int[] arr = new int[n];
                partition(0, n - 1);
                int x = 1;
                while (!pq.isEmpty()) {
                    _C.Pair<Integer, Integer> p = pq.poll();
                    arr[p.f + (p.s - p.f) / 2] = x;
                    x++;
                }
                StringBuilder ans = new StringBuilder();
                for (int i = 0; i < n; i++) {
                    if (arr[i] == 0) {
                        ans.append(x++).append(" ");
                    } else {
                        ans.append(arr[i]).append(" ");
                    }
                }
                pq.clear();
                out.println(ans);
            }
        }

        public void partition(int l, int r) {
            if (l >= r) {
                return;
            }
            pq.add(new _C.Pair<Integer, Integer>(l, r));
            int mid = l + (r - l) / 2;
            partition(l, mid - 1);
            partition(mid + 1, r);
        }

    }

    static class OutputWriter {
        private final PrintWriter writer;

        public OutputWriter(OutputStream outputStream) {
            writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
        }

        public OutputWriter(Writer writer) {
            this.writer = new PrintWriter(writer);
        }

        public void print(Object... objects) {
            for (int i = 0; i < objects.length; ++i) {
                if (i != 0) {
                    writer.print(' ');
                }
                writer.print(objects[i]);
            }
        }

        public void println(Object... objects) {
            print(objects);
            writer.println();
        }

        public void close() {
            writer.close();
        }

        public void println(long i) {
            writer.println(i);
        }

    }

    static class _C {
        static public class Pair<F extends Comparable<F>, S extends Comparable<S>> implements Comparable<_C.Pair<F, S>> {
            public F f;
            public S s;

            public Pair(F f, S s) {
                this.f = f;
                this.s = s;
            }

            public int compareTo(_C.Pair<F, S> o) {
                int t = f.compareTo(o.f);
                if (t == 0) return s.compareTo(o.s);
                return t;
            }

            public int hashCode() {
                return (31 + f.hashCode()) * 31 + s.hashCode();
            }

            public boolean equals(Object o) {
                if (!(o instanceof _C.Pair)) return false;
                if (o == this) return true;
                _C.Pair p = (_C.Pair) o;
                return f.equals(p.f) && s.equals(p.s);
            }

            public String toString() {
                return "{" + f + ", " + s + "}";
            }

        }

    }

    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private InputReader.SpaceCharFilter filter;

        public InputReader(InputStream stream) {
            this.stream = stream;
        }

        public int read() {
            if (numChars == -1) {
                throw new InputMismatchException();
            }
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 0) {
                    return -1;
                }
            }
            return buf[curChar++];
        }

        public int nextInt() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            int res = 0;
            do {
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public boolean isSpaceChar(int c) {
            if (filter != null) {
                return filter.isSpaceChar(c);
            }
            return isWhitespace(c);
        }

        public static boolean isWhitespace(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);

        }

    }
}