C. Rhymetime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard 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.InputEach 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.OutputFor 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.ExampleInput
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
NoteIn 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.
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

1 0 2 1 2 0 
['*special problem', 'implementation', '*1800']