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 
def cal(n):
    ans = [0]*n
    arr = [(-n, 0)]
    heapq.heapify(arr)
    for i in range(n):
        (size, start) = heapq.heappop(arr)
        size = -size
        h = (size-1) // 2
        ans[start+h] = i+1
        if h > 0:
            heapq.heappush(arr, (-h, start))
        if size-h-1 > 0:
            heapq.heappush(arr, (-size+h+1, start+h+1))
        #print(ans, arr)
    
    return ans
def web():
    T = int(input())
    for t in range(1, T + 1):
        arr = [int(s) for s in input().split(" ")] 
        ans = cal(arr[0])
        for a in ans:
            print(a, end = ' ')
        print()
              
def file():
    x = open('p4_in.txt')
    T = int(x.readline())
    for t in range(1, T + 1):
        arr = [int(s) for s in x.readline().split(" ")] 
        ans = cal(arr[0])
        for a in ans:
            print(a, end = ' ')
        print()
#file()     
web()

'''
cd Desktop\Desktpop\coding contest\CodeJamQualify
python it_run.py python p4_runner.py 1 -- python p4.py
'''