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:
#!/usr/bin/env python3
# vim: set fileencoding=utf-8

# pylint: disable=unused-import, invalid-name, missing-docstring, bad-continuation, too-few-public-methods


"""Module docstring
"""

import heapq
import sys
from typing import List


def solve(nb: int) -> List[int]:
    result = [0] * nb
    intervals = [(-nb, 0)]
    for i in range(nb):
        # LOG.debug((intervals))
        zeros, idx = heapq.heappop(intervals)
        zeros *= -1
        z_idx = idx + (zeros - 1) // 2
        result[z_idx] = i + 1
        # LOG.debug((result))
        zeros -= 1
        h = zeros // 2
        heapq.heappush(intervals, (-h, idx))
        heapq.heappush(intervals, (h - zeros, z_idx + 1))
    return result


def do_job():
    "Do the work"
    # first line is number of test cases
    T = int(input())
    for _testcase in range(T):
        n = int(input())
        result = solve(n)
        print(*result)


if __name__ == "__main__":
    do_job()