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:
def main():

    import sys, math
    #from bisect import bisect_left as bl, bisect_right as br, insort
    from heapq import heapify, heappush, heappop
    from collections import defaultdict as dd, deque, Counter
    #from itertools import permutations,combinations
    def data(): return sys.stdin.readline().strip()
    def mdata(): return list(map(int, data().split()))
    def out(*var, end="\n"): sys.stdout.write('\n'.join(map(str, var))+end)
    sys.setrecursionlimit(100000)
    INF = float('inf')
    mod = int(1e9)+7

    def recur(l,r,ans):
        global cnt
        if l>r:
            return
        if l==r:
            ans.append([1,l])
            return
        mid = (l + r) // 2
        ans.append([r - l + 1, mid])
        recur(l, mid - 1,ans)
        recur(mid + 1, r,ans)

    for t in range(int(data())):
        n=int(data())
        global cnt
        cnt=1
        ans=[]
        recur(0,n-1,ans)
        ans.sort(key=lambda x:x[1])
        ans.sort(key=lambda x:x[0],reverse=True)
        ans1=[0]*n
        for i in range(n):
            ans1[ans[i][1]]=i+1
        print(*ans1)




if __name__ == '__main__':
    main()