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:
from sys import stdin, stdout
from collections import deque, defaultdict
from heapq import heappush, heappop
import math as m

rl = lambda: stdin.readline()
rll = lambda: stdin.readline().split()
rli = lambda: map(int, stdin.readline().split())

INF, NINF = float('inf'), float('-inf')

def main():
	T = int(rl())
	for _ in range(T):
		n = int(rl())
		A = [0]*n
		H = []
		heappush(H, (-n, 0, n-1)) #((len, L), L, R)
		i = 1
		while H:
			_, L, R = heappop(H)
			x = R - L + 1
			mid = 0
			if x % 2 == 1:
				mid = (L + R)//2
			else:
				mid = (L + R - 1)//2
			A[mid] = i 
			#left half
			NL, NR = L, mid - 1
			NLEN = NR - NL + 1
			if NLEN > 0:
				heappush(H, (-NLEN, NL, NR))
			#right half
			ML, MR = mid + 1, R
			MLEN = MR - ML + 1
			if MLEN > 0:
				heappush(H, (-MLEN, ML, MR))
			i += 1
		print(" ".join(map(str, A)))
	stdout.close()

if __name__ == "__main__":
	main()