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:
# from collections import Counter
# arr=sorted([(n-int(x),i) for i,x in enumerate(input().split())])
# arr=[int(q)-1 for q in input().split()
# n=int(input())
# n,k=map(int,input().split())
# arr=list(map(int,input().split()))
# for i in range(m):
#for _ in range(int(input())):
#from queue import PriorityQueue
import heapq
def main(n):
    ans=[0]*n
    i=0
    j=n-1
    h=[(i-j-1,i,j)]
    heapq.heapify(h)
    cnt=1
    while h:
        len,x,y=heapq.heappop(h)
        len=-len
        mid=(x+y)//2
        ans[mid]=cnt
        if mid-x>0:
            heapq.heappush(h,(x-mid,x,mid-1))
        if y-mid>0:
            heapq.heappush(h,(mid-y,mid+1,y))

        cnt+=1
        
    print(*ans)







for _ in range(int(input())):
    n=int(input())
    main(n)