Rhyme

Description:

Input:

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

The first line of each test case contains a single integer $$$n$$$ ($$$1 \le n \le 10^5$$$) — the number of string pairs.

Next $$$n$$$ lines contains descriptions of pairs — one per line. The $$$i$$$-th line contains space-separated strings $$$s_i$$$ and $$$t_i$$$ and marker $$$r_i$$$. Strings are non-empty, consist of lowercase Latin letters and each have length at most $$$2 \cdot 10^5$$$. The marker $$$r_i$$$ equals to $$$1$$$ if strings have to rhyme, or $$$0$$$ if they must not rhyme.

It's guaranteed that for each test case there is at least one pair with $$$r_i$$$ equal to $$$1$$$ and that the total length of all strings over all test cases doesn't exceed $$$4 \cdot 10^5$$$.

Output:

For each test case, firstly print integer $$$m$$$ — the number of possible non-negative integer values of $$$k$$$ such that pairs that have to rhyme, rhyme and pairs that must not rhyme, don't rhyme. Next, print all these values of $$$k$$$ (without repetitions). You can print them in any order.

Sample Input:

3
1
kotlin heroes 1
2
join kotlin 1
episode eight 0
4
abc abcdef 0
xyz zzz 1
aaa bba 0
c d 0

Sample Output:

1
0
2
1 2
0

Note:

In the first test case, if $$$k$$$ is at least $$$1$$$ then kotlin and heroes don't rhyme.

In the second test case, for $$$k = 2$$$ join and kotlin rhyme, and episode and eight don't rhyme.