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:  Choose the maximum by length subarray (continuous subsegment) consisting only of zeros, among all such segments choose the leftmost one;  Let this segment be $[l; r]$. If $r-l+1$ is odd (not divisible by $2$) then assign (set) $a[\frac{l+r}{2}] := i$ (where $i$ is the number of the current action), otherwise (if $r-l+1$ is even) assign (set) $a[\frac{l+r-1}{2}] := i$. 

Consider the array $a$ of length $5$ (initially $a=[0, 0, 0, 0, 0]$). Then it changes as follows:  Firstly, we choose the segment $[1; 5]$ and assign $a[3] := 1$, so $a$ becomes $[0, 0, 1, 0, 0]$;  then we choose the segment $[1; 2]$ and assign $a[1] := 2$, so $a$ becomes $[2, 0, 1, 0, 0]$;  then we choose the segment $[4; 5]$ and assign $a[4] := 3$, so $a$ becomes $[2, 0, 1, 3, 0]$;  then we choose the segment $[2; 2]$ and assign $a[2] := 4$, so $a$ becomes $[2, 4, 1, 3, 0]$;  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 $t$ ($1 \le t \le 10^4$) — the number of test cases. Then $t$ test cases follow.

The only line of the test case contains one integer $n$ ($1 \le n \le 2 \cdot 10^5$) — the length of $a$.

It is guaranteed that the sum of $n$ over all test cases does not exceed $2 \cdot 10^5$ ($\sum n \le 2 \cdot 10^5$).


-----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

```python

USER_FILENAME = "<user_code>"
import sys, json, builtins
import math, heapq, bisect, itertools, functools, collections, statistics, fractions, decimal, operator, array, random, re, string, os, pathlib
try:
    import resource as _res
except Exception:
    _res = None
from collections import Counter, defaultdict, deque, OrderedDict
from functools import lru_cache, reduce
from itertools import accumulate, permutations, combinations, product
from math import gcd, ceil, floor, sqrt
from decimal import Decimal
try:
    from typing import *
except Exception:
    pass
try:
    sys.setrecursionlimit(1_000_000)
except Exception:
    pass
try:
    import site as _site
    try:
        _sys_sites = _site.getsitepackages() if hasattr(_site, "getsitepackages") else []
        for _p in _sys_sites:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
    try:
        _usp = _site.getusersitepackages()
        if isinstance(_usp, str):
            _usp = [_usp]
        for _p in _usp:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
except Exception:
    pass

ns = {"__name__": "__main__"}
for _k, _v in list(globals().items()):
    if not _k.startswith("_"):
        ns[_k] = _v
_CODE = 'import heapq\nfor _ in range(int(input())):\n    n=int(input())\n    a=[0]*n\n    que=[(-n,0,n-1)]\n    heapq.heapify(que)\n    i=1\n    while que:\n        len,l,r=heapq.heappop(que)\n        if len%2==1:\n            a[(l+r)//2]=i\n            if r!=l:\n                nl=(-(r-l)//2,l,(l+r)//2-1)\n                nr=(-(r-l)//2,(l+r)//2+1,r)\n                heapq.heappush(que,nl)\n                heapq.heappush(que,nr)\n        else:\n            a[(l+r-1)//2]=i\n            nl=(-(r-l-1)//2,l,(l+r-1)//2-1)\n            nr=(-(r-l+1)//2,(l+r-1)//2+1,r)\n            if r==l+1:\n                heapq.heappush(que,nr)\n            else:\n                heapq.heappush(que,nr)\n                heapq.heappush(que,nl)\n        i+=1\n    print(*a)'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 13439