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 solve(k):

    stack = [(-k,0,k-1)]  # -length, start, end (both inclusive)
    heapq.heapify(stack) 

    res = ["x" for _ in range(k)]
    cnt = 0

    while stack:
        # print(res, stack)
        cnt += 1
        length, start, end = heapq.heappop(stack)
        length = -length  # fix sign
        if length%2 == 1:  # if segment is odd length
            mid_point = (start+end)//2
            res[mid_point] = cnt
            if not start == end:
                heapq.heappush(stack, (-(mid_point-start), start, mid_point-1))
                heapq.heappush(stack, (-(mid_point-start), mid_point+1, end))
        else:  # segment is of even length
            mid_point = (start+end-1)//2
            res[mid_point] = cnt
            if length == 2:  # one other left
                heapq.heappush(stack, (-1, end, end))
            else: 
                heapq.heappush(stack, (-(length//2 - 1), start, mid_point-1))
                heapq.heappush(stack, (-(length//2), mid_point+1, end))

        # if cnt > 5:
        #     break

    # print()
    # print()
    # print()
    return " ".join([str(x) for x in res])
                


strr = input()
for _ in range(int(strr)):
    k = int(input())
    print(solve(k))