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 CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
int main() {
  int t;
  cin >> t;
  while (t--) {
    int n;
    cin >> n;
    int a[n + 1];
    fill(a, a + n + 1, 0);
    priority_queue<pair<int, int>> q;
    priority_queue<pair<int, int>, vector<pair<int, int>>,
                   greater<pair<int, int>>>
        temp;
    q.push(make_pair(n, (n % 2 == 0) ? n / 2 - 1 : n / 2));
    int r = 1;
    while (q.top().first != 1 || (r > 1 && !temp.empty())) {
      int idx, y;
      if (!temp.empty()) {
        y = temp.top().first;
        idx = temp.top().second;
        temp.pop();
      } else {
        idx = q.top().second;
        y = q.top().first;
        q.pop();
        while (q.top().first == y && idx > q.top().second) {
          int x = q.top().second;
          q.pop();
          temp.push(make_pair(y, idx));
          idx = x;
        }
      }
      a[idx] = r;
      if (y % 2 == 1) {
        if ((y / 2) % 2 == 1) {
          q.push(make_pair(y / 2, idx - y / 4 - 1));
          q.push(make_pair(y / 2, idx + y / 4 + 1));
        } else {
          q.push(make_pair(y / 2, idx - y / 4 - 1));
          q.push(make_pair(y / 2, idx + y / 4));
        }
      } else {
        if ((y / 2) % 2 == 1) {
          if (y == 2) {
            if (idx - 1 < 0 || a[idx - 1] != 0)
              q.push(make_pair(1, idx + 1));
            else {
              q.push(make_pair(1, idx - 1));
            }
          } else {
            q.push(make_pair(y / 2 - 1, idx - (y / 2 - 1) / 2 - 1));
            q.push(make_pair(y / 2, idx + y / 4 + 1));
          }
        } else {
          q.push(make_pair(y / 2 - 1, idx - (y / 2 - 1) / 2 - 1));
          q.push(make_pair(y / 2, idx + y / 4));
        }
      }
      r++;
    }
    for (int i = 0; i < n; i++) {
      if (a[i] > 0)
        cout << a[i] << ' ';
      else {
        cout << r << ' ';
        r++;
      }
    }
    cout << endl;
  }
  return 0;
}