You are given an integer $$$n$$$. You need to construct a permutation$$$^{\text{∗}}$$$ $$$a_1, a_2, \ldots, a_n$$$ using integers from $$$1$$$ to $$$n$$$ such that the following condition is satisfied:

$$$$$$ a_1 \bmod a_2 \ge a_2 \bmod a_3 \geq \ldots \ge a_{n-1} \bmod a_{n}, $$$$$$ where $$$u$$$ mod $$$v$$$ denotes the remainder of dividing $$$u$$$ by $$$v$$$.

If multiple valid permutations exist, you may output any of them.

It can be shown that a valid permutation always exists for every $$$n \ge 2$$$.

$$$^{\text{∗}}$$$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

Each test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1 \le t \le 100$$$). The description of the test cases follows.

The first line of each test case contains a single integer $$$n$$$ ($$$2 \le n \le 100$$$).

Output

For each test case, output on a single line $$$n$$$ space-separated integers $$$a_1, a_2, \ldots a_n$$$.

If multiple valid permutations exist, you may output any of them.

Note

In the second test case, $$$2 \bmod 3 \ge 3 \bmod 1$$$, so the permutation $$$[2, 3, 1]$$$ is valid.

In the third test case, $$$2 \bmod 4 \ge 4 \bmod 3 \ge 3 \bmod 1$$$, so the permutation $$$[2, 4, 3, 1]$$$ is valid.

A Simple Sequence

Examples