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 deque
import heapq

def construct(nums, q):
    arr = []
    num = 1
    while q:
        left, right = q.popleft()

        if left <= right:
            if (left+right+1) % 2 == 0:
                mid = (left+right-1)//2

                q.append([mid+1, right])
                q.append([left, mid-1])

            else:
                mid = (left+right)//2
                q.append([left, mid-1])
                q.append([mid+1, right])

            arr.append([right-left, left, right, mid])

    # print(arr)

    sorted_arr = sorted(arr, key=lambda x: (-x[0], x[1], x[2]))

    num = 1

    for i in range(len(sorted_arr)):
        zeroes, left, right, mid = sorted_arr[i]

        nums[mid] = num
        num += 1

    # print(sorted_arr)
    




t = int(input())

while t:
    t -= 1


    n = int(input())

    nums = [0 for i in range(n)]

    q = deque()
    q.append([0, n-1])
    # print(arr)
    arr = []
    construct(nums, q)

    for i in range(len(nums)):
        print(nums[i], end=' ')

    print()