You are given a positive integer $$$n$$$.

Find a permutation$$$^\dagger$$$ $$$p$$$ of length $$$n$$$ such that there do not exist two distinct indices $$$i$$$ and $$$j$$$ ($$$1 \leq i, j \lt n$$$; $$$i \neq j$$$) such that $$$p_i$$$ divides $$$p_j$$$ and $$$p_{i+1}$$$ divides $$$p_{j+1}$$$.

Refer to the Notes section for some examples.

Under the constraints of this problem, it can be proven that at least one $$$p$$$ exists.

$$$^\dagger$$$ A permutation of length $$$n$$$ is an array consisting of $$$n$$$ distinct integers from $$$1$$$ to $$$n$$$ in arbitrary order. For example, $$$[2,3,1,5,4]$$$ is a permutation, but $$$[1,2,2]$$$ is not a permutation ($$$2$$$ appears twice in the array), and $$$[1,3,4]$$$ is also not a permutation ($$$n=3$$$ but there is $$$4$$$ in the array).

Input

Each test contains multiple test cases. The first line contains a single integer $$$t$$$ ($$$1 \leq t \leq 10^3$$$) — the number of test cases. The description of the test cases follows.

The first line of each test case contains a single integer $$$n$$$ ($$$3 \leq n \leq 10^5$$$) — the length of the permutation $$$p$$$.

It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$10^5$$$.

Output

For each test case, output $$$p_1, p_2, \ldots, p_n$$$.

If there are multiple solutions, you may output any one of them.

Note

In the first test case, $$$p=[4,1,2,3]$$$ is a valid permutation. However, the permutation $$$p=[1,2,3,4]$$$ is not a valid permutation as we can choose $$$i=1$$$ and $$$j=3$$$. Then $$$p_1=1$$$ divides $$$p_3=3$$$ and $$$p_2=2$$$ divides $$$p_4=4$$$. Note that the permutation $$$p=[3, 4, 2, 1]$$$ is also not a valid permutation as we can choose $$$i=3$$$ and $$$j=2$$$. Then $$$p_3=2$$$ divides $$$p_2=4$$$ and $$$p_4=1$$$ divides $$$p_3=2$$$.

In the second test case, $$$p=[1,2,3]$$$ is a valid permutation. In fact, all $$$6$$$ permutations of length $$$3$$$ are valid.

Permutation Printing

Examples