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
import math
from heapq import heappush
from heapq import heappop
'''
h = []
heappush(h, (5, 'write code'))
heappush(h, (2, 'wre code'))
x = heappop(h)
print(x)
'''
n = int(input())

for i in range(n):
    m = int(input())
    h = []
    arr = [0 for x in range(m)]
    heappush(h, (-m, 0))
    for j in range(m):
        el = heappop(h)
        #print(el)
       
        l = el[0] * (-1)
        l = math.ceil(l)
        l1 = math.floor((l - 0.001) / 2) 
        l2 = el[1]
        pos = l1 + l2
        
        arr[pos] = j + 1
        a = -(l1 - (l2/1000000000.0))
        b = l2
        #print(a,b)
        if a<-0.5:
            heappush(h, (a, b))
        
        a = -(l - l1 - 1 - ((l2 + 1 + l1) / 1000000000.0))
        b = l2 + 1 + l1
        #print(a,b, 'b')
        if a<-0.5:
            heappush(h, (a, b))
        
    arr = [str(x) for x in arr]
    print(' '.join(arr))