This life is like a TV show; we're swept along as the plotlines go.

— SHUN, TRAP

There are $$$n$$$ blogs. The $$$i$$$-th blog mentioned $$$l_i$$$ users in order as an array $$$a_i=[a_{i,1},a_{i,2},\ldots,a_{i,l_i}]$$$.

You are going to post all $$$n$$$ blogs. Let us maintain a sequence $$$Q$$$ that describes the list of users you have recently mentioned. You need to perform the following operation exactly $$$n$$$ times:

Choose an unposted blog $$$i$$$ ($$$1\le i\le n$$$), then post it. This will cause the following operations for each $$$1\le j\le l_i$$$ in order:
- If $$$a_{i,j}$$$ already exists in $$$Q$$$, then move $$$a_{i,j}$$$ to the beginning of $$$Q$$$.
- Otherwise, insert $$$a_{i,j}$$$ at the beginning of $$$Q$$$.

Find the lexicographically smallest$$$^{\text{∗}}$$$ $$$Q$$$ after all $$$n$$$ operations.

$$$^{\text{∗}}$$$An array $$$x$$$ is lexicographically smaller than an array $$$y$$$ if and only if one of the following holds:

$$$x$$$ is a prefix of $$$y$$$, but $$$x \ne y$$$; or
in the first position where $$$x$$$ and $$$y$$$ differ, the array $$$x$$$ has a smaller element than the corresponding element in $$$y$$$.

Input

Each test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1 \le t \le 1000$$$). The description of the test cases follows.

The first line contains a single integer $$$n$$$ ($$$1\le n\le 3000$$$) — the number of blogs.

Then $$$n$$$ lines follow, the $$$i$$$-th line starting with an integer $$$l_i$$$ ($$$1\le l_i\le 3000$$$), describing the number of users mentioned in the $$$i$$$-th blog, which is followed by $$$l_i$$$ integers $$$a_{i,1},a_{i,2},\ldots,a_{i,l_i}$$$ ($$$1\le a_{i,j}\le 10^6$$$) — the list of users mentioned in the $$$i$$$-th blog.

It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$3000$$$.

Denote $$$\sum\limits_{i=1}^n l_i$$$ as $$$L$$$. It is guaranteed that the sum of $$$L$$$ over all test cases does not exceed $$$3000$$$.

Output

Denote $$$m$$$ as the number of users mentioned in at least one blog. For each test case, output $$$m$$$ integers $$$Q_1,Q_2,\ldots,Q_m$$$ — the lexicographically smallest $$$Q$$$.

Note

In the first test case, you can post the blogs as follows:

Post the first blog, and $$$Q$$$ will become $$$[6,4,3,2,1]$$$.
Post the third blog, and $$$Q$$$ will become $$$[3,2,9,1,6,4]$$$.
Post the second blog, and $$$Q$$$ will become $$$[1,5,2,3,9,6,4]$$$.

There is another method to post blogs:

Post the third blog, and $$$Q$$$ will become $$$[3,2,9,1]$$$.
Post the first blog, and $$$Q$$$ will become $$$[6,4,3,2,1,9]$$$.
Post the second blog, and $$$Q$$$ will become $$$[1,5,2,6,4,3,9]$$$.

We can see that $$$[1,5,2,3,9,6,4]$$$ is lexicographically smaller than the other one. If we do not post the second blog at the end, the first element of the array will not be $$$1$$$, so $$$[1,5,2,3,9,6,4]$$$ is the lexicographically smallest array $$$Q$$$.

In the second test case, you can post the blogs as follows:

Post the first blog, and $$$Q$$$ will become $$$[6,1]$$$.
Post the second blog, and $$$Q$$$ will keep itself $$$[6,1]$$$.

In the third test case, you have to post the only blog, and $$$Q$$$ will become $$$[1,6]$$$.

Simons and Posting Blogs

Examples