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 PYTHON):

Solution:
import sys

__author__ = 'ratmir'

from collections import deque
from heapq import heappush, heappop

alphabet = "abcdefghijklmnopqrstuvwxyz"


def solve(n, a, graph):
    return 1


results = []


def execute():
    [t] = [int(x) for x in sys.stdin.readline().split()]
    for ti in range(0, t):
        [n] = [int(x1) for x1 in sys.stdin.readline().split()]
        h = []
        a = [0] * n
        heappush(h, (-n, 1, n))
        for ii in range(0, n):
            length, begin, end = heappop(h)
            if (end - begin + 1) % 2 == 1:
                to_ins = (begin + end) / 2
            else:
                to_ins = (begin + end - 1) / 2
            to_ins -= 1
            a[to_ins] = ii + 1
            to_ins += 1
            if to_ins >= begin:
                heappush(h, (-(to_ins - 1 - begin + 1), begin, to_ins - 1))
            if to_ins <= end:
                heappush(h, (-(end - 1 - to_ins + 1), to_ins + 1, end))
            #print a, h

        results.append(''.join('{} '.format(k) for k in a))

    print(''.join('{}\n'.format(k) for k in results))


execute()