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;
const double pi = acos(-1.0);
const double eps = 1e-8;
const int mod = 1e9 + 7;
const int inf = 1e9;
const long long INF = 1e18;
const int N = 1e5 + 5;
struct data {
  int l, r, len;
  data(int l, int r, int len) : l(l), r(r), len(len) {}
  bool operator<(const data &q) const {
    return len == q.len ? l > q.l : len < q.len;
  }
};
void solve() {
  int n;
  cin >> n;
  priority_queue<data> q;
  q.push(data(1, n, n));
  int id = 1;
  vector<int> a(n + 1, 0);
  while (!q.empty()) {
    data t = q.top();
    q.pop();
    int l = t.l, r = t.r, len = t.len;
    if (len % 2 == 1) {
      int mid = (l + r) / 2;
      a[mid] = id++;
      if (len == 1) continue;
      q.push(data(l, mid - 1, mid - 1 - l + 1));
      q.push(data(mid + 1, r, r - mid - 1 + 1));
    } else {
      int mid = (l + r - 1) / 2;
      a[mid] = id++;
      if (len == 2) {
        q.push(data(mid + 1, r, r - mid - 1 + 1));
      } else {
        q.push(data(l, mid - 1, mid - 1 - l + 1));
        q.push(data(mid + 1, r, r - mid - 1 + 1));
      }
    }
  }
  for (int i = 1; i <= n; i++) cout << a[i] << " ";
  cout << "\n";
}
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  int t;
  cin >> t;
  for (int tc = 1; tc <= t; tc++) solve();
  return 0;
}