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.util.*;

public class codeforces
{
    static int M = 1_000_000_007;
    static int INF = 2_000_000_000;
    static final FastScanner fs = new FastScanner();

    //variable
    static int[][] needs = new int[3][2];
    static int ans = 0;
    public static void main(String[] args) throws IOException {

        int T = fs.nextInt();
        while(T-- > 0) {
            int n = fs.nextInt();
            PriorityQueue<Array> q = new PriorityQueue<>();
            int[] ans = new int[n];
            q.add(new Array(-1,n));
            int i = 1;
            while(!q.isEmpty()) {
                //System.out.println("HI");
                Array a = q.remove();
                int x = a.l + (a.size+1)/2;
                ans[x] = i;
                i++;

                if(x > a.l+1) q.add(new Array(a.l,x-a.l-1));
                if(a.size-(x-a.l)> 0) q.add(new Array(x,a.size-x+a.l));

            }
            for(int a:ans) System.out.print(a+" ");
            System.out.println();
        }
    }
    //function
    public static class Array implements Comparable<Array> {
        int l,size;
        Array(int l, int size) {
            this.l = l;
            this.size = size;
        }

        @Override
        public int compareTo(Array o) {
            if(this.size != o.size)return -Integer.compare(this.size,o.size);
            return Integer.compare(this.l,o.l);
        }
    }
    static int lcm(int a, int b) {
        return (a / gcd(a, b)) * b;
    }

    static int gcd(int a, int b) {
        if(a==0) return b;

        return gcd(b%a,a);
    }
    static void premutation(int n, ArrayList<Integer> arr,boolean[] chosen) {
        if(arr.size() == n) {

        }else {
            for(int i=1; i<=n; i++) {
                if(chosen[i]) continue;
                arr.add(i);
                chosen[i] = true;
                premutation(n,arr,chosen);
                arr.remove(i);
                chosen[i] = false;
            }
        }
    }
    static boolean isPalindrome(char[] c) {
        int n = c.length;
        for(int i=0; i<n/2; i++) {
            if(c[i] != c[n-i-1]) return false;
        }
        return true;
    }
    // Template
    static long nCk(int n, int k) {
        return (modMult(fact(n),fastexp(modMult(fact(n-k),fact(k)),M-2)));
    }

    static long fact (long n) {

        long fact =1;
        for(int i=1; i<=n; i++) {
            fact = modMult(fact,i);
        }
        return fact%M;
    }

    static int modMult(long a,long b) {
        return (int) (a*b%M);
    }
    static int negMult(long a,long b) {
        return (int)((a*b)%M + M)%M;
    }
    static long fastexp(long x, int y){
        if(y==1) return x;

        long ans = fastexp(x,y/2);
        if(y%2 == 0) return modMult(ans,ans);
        else return modMult(ans,modMult(ans,x));
    }

    static final Random random = new Random();

    static void ruffleSort(int arr[])
    {
        int n = arr.length;
        for(int i=0; i<n; i++)
        {
            int j = random.nextInt(n),temp = arr[j];
            arr[j] = arr[i];
            arr[i] = temp;
        }
        Arrays.sort(arr);
    }


    public static class Pairs implements Comparable<Pairs>
    {
        int value,index;
        Pairs(int value, int index)
        {
            this.value = value;
            this.index = index;
        }
        public int compareTo(Pairs p)
        {
            return Integer.compare(this.value,p.value);
        }
    }
}
class FastScanner
{
    BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
    StringTokenizer str = new StringTokenizer("");

    String next() throws IOException
    {
        while(!str.hasMoreTokens())
            str = new StringTokenizer(br.readLine());

        return str.nextToken();
    }

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

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

    float nextfloat() throws IOException
    {
        return Float.parseFloat(next());
    }

    double nextDouble() throws IOException
    {
        return Double.parseDouble(next());
    }
    long nextLong() throws IOException
    {
        return Long.parseLong(next());
    }
    byte nextByte() throws IOException
    {
        return Byte.parseByte(next());
    }
    int [] arrayIn(int n) throws IOException
    {
        int  arr[] = new int[n];
        for(int i=0; i<n; i++)
        {
            arr[i] = nextInt();
        }
        return arr;
    }
}