A shrink operation on an array $$$a$$$ of size $$$m$$$ is defined as follows:

Choose an index $$$i$$$ ($$$2 \le i \le m - 1$$$) such that $$$a_i \gt a_{i - 1}$$$ and $$$a_i \gt a_{i + 1}$$$.
Remove $$$a_i$$$ from the array.

Define the score of a permutation$$$^{\text{∗}}$$$ $$$p$$$ as the maximum number of times that you can perform the shrink operation on $$$p$$$.

Yousef has given you a single integer $$$n$$$. Construct a permutation $$$p$$$ of length $$$n$$$ with the maximum possible score. If there are multiple answers, you can output any of them.

$$$^{\text{∗}}$$$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

The first line of the input contains an integer $$$t$$$ ($$$1 \le t \le 10^3$$$) — the number of test cases.

Each test case contains an integer $$$n$$$ ($$$3 \le n \le 2 \cdot 10^5$$$) — the size of the permutation.

It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$2 \cdot 10^5$$$.

Output

For each test case, output any permutation $$$p_1, p_2, \dots, p_n$$$ that maximizes the number of shrink operations.

Note

In the first test case:

We choose $$$p = [1, 3, 2]$$$.
Choose index $$$2$$$, and remove $$$p_2$$$ from the array. The array becomes $$$p = [1, 2]$$$.

It can be shown that the maximum number of operations we can perform is $$$1$$$. Another valid answer is $$$p = [2, 3, 1]$$$.

In the second test case:

We choose $$$p = [2, 3, 6, 4, 5, 1]$$$.
Choose index $$$5$$$, and remove $$$p_5$$$ from the array. The array becomes $$$p = [2, 3, 6, 4, 1]$$$.
Choose index $$$3$$$, and remove $$$p_3$$$ from the array. The array becomes $$$p = [2, 3, 4, 1]$$$.
Choose index $$$3$$$, and remove $$$p_3$$$ from the array. The array becomes $$$p = [2, 3, 1]$$$.
Choose index $$$2$$$, and remove $$$p_2$$$ from the array. The array becomes $$$p = [2, 1]$$$.

The maximum number of operations we can perform is $$$4$$$. Any permutation with a score of $$$4$$$ is valid.

Shrink

Examples