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 Solve() {
  int t;
  cin >> t;
  while (t--) {
    int n;
    cin >> n;
    priority_queue<vector<int>, vector<vector<int>>> pq;
    pq.push({n, -1, n});
    vector<int> res(n);
    int cnt{1};
    while (!pq.empty()) {
      const auto curr{pq.top()};
      pq.pop();
      const int i{(-curr[1] + curr[2]) / 2};
      res[i - 1] = cnt;
      if (i + curr[1] > 0) {
        pq.push({i + curr[1], curr[1], i - 1});
      }
      if (curr[2] - i > 0) {
        pq.push({curr[2] - i, -i - 1, curr[2]});
      }
      ++cnt;
    }
    for (int x : res) {
      cout << x << ' ';
    }
    cout << endl;
  }
}
void Run() {
  ios::sync_with_stdio(false);
  cin.tie(nullptr);
  Solve();
  ;
}
int main() {
  Run();
  return 0;
}