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 solve():
    n = int(input())
    small = n-1
    large = n
    indexes = [(0, True)] # i, is_large
    ans = [0 for i in range(n)]
    x = 1
    while large > 2:
        # print(small, large, ans, indexes)
        new_indexes = []
        large_indexes = []
        small_indexes = []
        for i, is_large in indexes:
            if is_large:
                large_indexes.append(i + (large - 1) // 2)
                if large % 2 == 0:
                    new_indexes.append((i, False))
                    new_indexes.append((i + (large-1) // 2 + 1, True))
                else:
                    new_indexes.append((i, True))
                    new_indexes.append((i + (large-1) // 2 + 1, True))
            elif small > 0:
                small_indexes.append(i + (small - 1) // 2)
                if small % 2 == 0:
                    new_indexes.append((i, False))
                    new_indexes.append((i + (small-1) // 2 + 1, True))
                else:
                    new_indexes.append((i, False))
                    new_indexes.append((i + (small-1) // 2 + 1, False))
        for i in large_indexes:
            ans[i] = x
            x += 1
        for i in small_indexes:
            ans[i] = x
            x += 1
        indexes = new_indexes
        small = (small + large - 2) // 4
        large = small + 1
    # print(small, large, ans, indexes)
    if large == 2:
        for i, is_large in indexes:
            if is_large:
                ans[i] = x
                x += 1
        for i, is_large in indexes:
            if is_large:
                ans[i+1] = x
            else:
                ans[i] = x
            x += 1
    elif large == 1:
        for i, is_large in indexes:
            if is_large:
                ans[i] = x
                x += 1
    print(" ".join(map(str, ans)))

if __name__ == '__main__':
    t = int(input())
    for tc in range(t):
        solve()