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:
t=int(input())
import operator
for _ in range(t):
    n=int(input())
    if(n==1):
        print(1)
    elif(n==2):
        print(1,2)
    else:
        lis=[]
        for i in range(n):
            lis.append(0)
        stack=[]
        lis[(n-1)//2]=1
        if(n%2==1):
            stack.append((-((n-1)//2-1),0,(n-1)//2-1))
            stack.append((-(n-1-((n-1)//2+1)),(n-1)//2+1,n-1))
        else:
            stack.append((-(n-1-((n-1)//2+1)),(n-1)//2+1,n-1))
            stack.append((-((n-1)//2-1),0,(n-1)//2-1))
        next=2
        j=0
        k=2
        prev=stack[0][0]
        while j<k:
            if(stack[j][0]!=prev):
                stack.sort(key = lambda x: (x[0], x[1]))
                prev=stack[j][0]
            i=stack[j]
            if(i[2]-i[1]==0):
                lis[i[1]]=next
            else:
                if((i[2]-i[1]+1)%2==0):
                    lis[(i[2]+i[1])//2]=next
                    if(i[2]!=(i[2]+i[1])//2):
                        stack.append((-(i[2]-((i[2]+i[1])//2+1)),(i[2]+i[1])//2+1,i[2]))
                        k+=1
                    if(i[1]!=(i[2]+i[1])//2):
                        stack.append((-((i[2]+i[1])//2-1-i[1]),i[1],(i[2]+i[1])//2-1))
                        k+=1
                else:
                    lis[(i[2]+i[1])//2]=next
                    if(i[1]!=(i[2]+i[1])//2):
                        stack.append((-((i[2]+i[1])//2-1-i[1]),i[1],(i[2]+i[1])//2-1))
                        k+=1
                    if(i[2]!=(i[2]+i[1])//2):
                        stack.append((-(i[2]-((i[2]+i[1])//2+1)),(i[2]+i[1])//2+1,i[2]))
                        k+=1
            next+=1
            j+=1
            # print(lis,stack)
        for i in lis:
            print(i,end=" ")
        print()