Kotlin Heroes: Episode 8 |
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Finished |

The following languages are only available languages for the problems from the contest

Kotlin Heroes: Episode 8:

- Kotlin 1.7.20
- Kotlin 1.9.21

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*special problem

implementation

*1800

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C. Rhyme

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputLet's say that two strings $$$s$$$ and $$$t$$$ rhyme if both strings have length at least $$$k$$$, and their last $$$k$$$ characters are equal. For example, if $$$k = 3$$$, the strings abcd and cebcd rhyme, the strings ab and ab don't rhyme, the strings aaaa and aaaaa rhyme, the strings abcd and abce don't rhyme.

You have $$$n$$$ pairs of strings $$$(s_i, t_i)$$$, and for each pair of strings you know, should they rhyme or should not.

Find all possible non-negative integer values for $$$k$$$ such that pairs that have to rhyme, rhyme and pairs that must not rhyme, don't rhyme.

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.

Example

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

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.

Codeforces (c) Copyright 2010-2024 Mike Mirzayanov

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