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;
void Main();
int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  int x;
  cin >> x;
  while (~cin.peek()) Main(), cin.get();
  return 0;
}
void Main() {
  int n;
  cin >> n;
  set<pair<int, pair<int, int>>> s;
  s.insert({-n, {1, n}});
  vector<int> a(n + 1);
  int cnt = 1;
  while (s.size()) {
    0;
    auto it = s.begin();
    a[(it->second.first + it->second.second) / 2] = cnt;
    cnt++;
    int len = it->second.second - it->second.first + 1;
    if (len > 2)
      s.insert({-((len - 1) / 2),
                {it->second.first, it->second.first + (len - 1) / 2 - 1}});
    if (len > 1)
      s.insert({-(len - 1 - (len - 1) / 2),
                {it->second.first + (len - 1) / 2 + 1, it->second.second}});
    s.erase(it);
  }
  for (int i = 1; i <= n; i++) {
    cout << a[i] << " \n"[i == n];
  }
}