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 PYTHON):

Solution:

import heapq

class Segment(object):
    def __init__(self, start, end):
        self.start = start
        self.end = end
    def __cmp__(self, other):
        l1 = self.end - self.start + 1
        l2 = other.end - other.start + 1
        if l1 != l2:
            return cmp(l2, l1)
        else:
            return cmp(self.start, other.start)
    def __str__(self):
        return "[{} {}]".format(self.start, self.end)

t = int(raw_input())
for _ in range(t):
    n = int(raw_input())
    q = []
    heapq.heappush(q, Segment(0, n - 1))
    res = [0 for _ in range(n)]
    iter = 1
    for _ in range(n):
        next = heapq.heappop(q)
        l = next.end - next.start + 1
        if l % 2 == 1:
            mid = (next.end + next.start) / 2
        else:
            mid = (next)
        sum = next.end + next.start
        mid = sum / 2 if l % 2 == 1 else (sum - 1) / 2
        res[mid] = iter
        # [next.start, mid - 1] [mid + 1, next.end]
        if next.start <= mid - 1:
            heapq.heappush(q, Segment(next.start, mid - 1))
        if mid + 1 <= next.end:
            heapq.heappush(q, Segment(mid + 1, next.end))
        iter += 1
    print(" ".join(map(str, res)))