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:
# https://codeforces.com/contest/1353/problem/D

import sys
import os
import heapq

try:
    path = "./file/input.txt"
    if os.path.exists(path):
        sys.stdin = open(path, 'r')
    # sys.stdout = open(r"./file/output.txt", 'w')
except:
    pass

class Node:
    def __init__(self, n, left, right):
        self.left = left
        self.right = right
        self.weight = n - right + left

    def __lt__(self, other):
        return self.weight < other.weight or (self.weight == other.weight and self.left < other.left)

t = int(input())

for _ in range(t):
    n = int(input())

    q = []
    result = [0] * (n + 1)
    heapq.heappush(q, Node(n, 1, n))

    index = 1
    while True:
        if len(q) == 0:
            break

        node = heapq.heappop(q)
        if node is None:
            break
        
        if node.left == node.right:
            result[node.left] = index
            index += 1
        else:
            middle = int((node.left + node.right) / 2)
            result[middle] = index
            index += 1

            if node.left != middle:
                heapq.heappush(q, Node(n, node.left, middle - 1))
            heapq.heappush(q, Node(n, middle + 1, node.right))

    print(" ".join(str(i) for i in result[1:]))