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:
tests = int(input())
for i in range(tests):
    n = int(input())
    answer = [1] * n
    line = [[1, n, 1]]
    result = []
    while n > 1:
        n = n // 2
        stack = []
        for j in range(len(line)):
            left = line[j][0]
            right = line[j][1]
            if right == left:
                stack.append([left, right, 0])
            elif (right + left) % 2 == 0:
                if (right + left) // 2 - left == n:
                    stack.append([left, (left + right) // 2 - 1, 1])
                    stack.append([(left + right) // 2 + 1, right, 1])
                else:
                    stack.append([left, (left + right) // 2 - 1, 0])
                    stack.append([(left + right) // 2 + 1, right, 0])
            else:
                stack.append([left, (left + right) // 2 - 1, 0])
                stack.append([(left + right) // 2 + 1, right, 1])

            if line[j][2] == 1:
                result.append((right + left) // 2)

        for j in range(len(line)):
            if line[j][2] == 0:
                left = line[j][0]
                right = line[j][1]
                if left != right:
                    result.append((right + left) // 2)

        if n == 1:
            for j in range(len(stack)):
                if stack[j][0] == stack[j][1]:
                    result.append(stack[j][0])

        line = stack

    for j in range(len(result)):
        answer[result[j] - 1] = j + 1

    for j in range(len(answer)):
        print(answer[j], end=' ')
    print()