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 PYTHON3):

Solution:
import heapq


class Segment:
    def __init__(self, li, ri) -> None:
        self.size = ri - li + 1
        self.li = li
        self.ri = ri

    def __str__(self) -> str:
        return '(' + str(self.size) + ', ' + str(self.li) + ')'


def comparator(s, o):
    if o.size > s.size:
        return False
    if o.size < s.size:
        return True
    return s.li < o.li


setattr(Segment, "__lt__", comparator)

if __name__ == '__main__':
    for _ in range(int(input())):
        n = int(input())

        arr = [0 for _ in range(n)]

        segs = [Segment(1, n)]

        for i in range(1, n + 1):
            seg = heapq.heappop(segs)
            l = seg.size

            if l % 2:
                mp = ((seg.li + seg.ri) // 2)
            else:
                mp = ((seg.li + seg.ri - 1) // 2)

            arr[mp - 1] = i

            if seg.size > 1:
                if seg.li < mp:
                    heapq.heappush(segs, Segment(seg.li, mp - 1))
                if seg.ri > mp:
                    heapq.heappush(segs, Segment(mp + 1, seg.ri))

        print(*arr)