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:
'''     ░░█ ▄▀█ █   █▀ █░█ █▀█ █▀▀ █▀▀   █▀█ ▄▀█ █▀▄▀█  
        █▄█ █▀█ █   ▄█ █▀█ █▀▄ ██▄ ██▄   █▀▄ █▀█ █░▀░█     '''


# [temp1.py] => [29-07-2020 @ 08:58:22] 
# Author & Template by : Udit "luctivud" Gupta
# https://www.linkedin.com/in/udit-gupta-1b7863135/


import math;   from collections import *
import sys;    from functools import reduce
import time;   from itertools import groupby

# sys.setrecursionlimit(10**6)

def input()         : return sys.stdin.readline()
def get_ints()      : return map(int, input().strip().split())
def get_list()      : return list(get_ints())
def get_string()    : return list(input().strip().split())
def printxsp(*args) : return print(*args, end="")
def printsp(*args)  : return print(*args, end=" ")


DIRECTIONS = [(+0, +1), (+0, -1), (+1, +0), (+1, -1)] 
NEIGHBOURS = [(-1, -1), (-1, +0), (-1, +1), (+0, -1),\
              (+1, +1), (+1, +0), (+1, -1), (+0, +1)]


CAPS_ALPHABETS = {chr(i+ord('A')) : i for i in range(26)}
SMOL_ALPHABETS = {chr(i+ord('a')) : i for i in range(26)}
INF = float('inf')


# Custom input output is now piped through terminal commands.


S34t = time.time()
for _testcases_ in range(int(input())): 
    n = int(input())
    li = [(1, n)]
    i = 0
    while i < len(li):
        l, r = li[i]
        # print(l, r)
        if l != r:
            if (r-l+1) & 1:
                m = (l+r)//2
            else:
                m = (l+r-1)//2
            if m-1 >= l:
                li.append((l, m-1))
            if m+1<=r:
                li.append((m+1, r))
        i += 1
    # print(li)
    assert len(li) == n
    li = sorted(li, key = lambda x : ((x[0]-x[1]), x[0]))
    # print(li)
    ans = [0] * (n+1)
    for i in range(n):
        l, r = li[i]
        if (r-l+1) & 1:
                m = (l+r)//2
        else:
            m = (l+r-1)//2
        ans[m] = i+1
    print(*ans[1:])


S34p = time.time()
# print("Time Elapsed: {}".format(float(S34p-S34t)))