B. Sets and Uniontime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputYou have n sets of integers S_{1}, S_{2}, \ldots, S_{n}. We call a set S attainable, if it is possible to choose some (possibly, none) of the sets S_{1}, S_{2}, \ldots, S_{n} so that S is equal to their union^{\dagger}. If you choose none of S_{1}, S_{2}, \ldots, S_{n}, their union is an empty set.Find the maximum number of elements in an attainable S such that S \neq S_{1} \cup S_{2} \cup \ldots \cup S_{n}.^{\dagger} The union of sets A_1, A_2, \ldots, A_k is defined as the set of elements present in at least one of these sets. It is denoted by A_1 \cup A_2 \cup \ldots \cup A_k. For example, \{2, 4, 6\} \cup \{2, 3\} \cup \{3, 6, 7\} = \{2, 3, 4, 6, 7\}.InputEach 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 (1 \le n \le 50).The following n lines describe the sets S_1, S_2, \ldots, S_n. The i-th of these lines contains an integer k_{i} (1 \le k_{i} \le 50) — the number of elements in S_{i}, followed by k_{i} integers s_{i, 1}, s_{i, 2}, \ldots, s_{i, k_{i}} (1 \le s_{i, 1} < s_{i, 2} < \ldots < s_{i, k_{i}} \le 50) — the elements of S_{i}.OutputFor each test case, print a single integer — the maximum number of elements in an attainable S such that S \neq S_{1} \cup S_{2} \cup \ldots \cup S_{n}.ExampleInput
433 1 2 32 4 52 3 444 1 2 3 43 2 5 63 3 5 63 4 5 651 13 3 6 101 92 1 33 5 8 912 4 28Output
4
5
6
0
NoteIn the first test case, S = S_{1} \cup S_{3} = \{1, 2, 3, 4\} is the largest attainable set not equal to S_1 \cup S_2 \cup S_3 = \{1, 2, 3, 4, 5\}.In the second test case, we can pick S = S_{2} \cup S_{3} \cup S_{4} = \{2, 3, 4, 5, 6\}.In the third test case, we can pick S = S_{2} \cup S_{5} = S_{2} \cup S_{3} \cup S_{5} = \{3, 5, 6, 8, 9, 10\}.In the fourth test case, the only attainable set is S = \varnothing.
433 1 2 32 4 52 3 444 1 2 3 43 2 5 63 3 5 63 4 5 651 13 3 6 101 92 1 33 5 8 912 4 28
4 5 6 0 
['bitmasks', 'brute force', 'constructive algorithms', 'greedy', '*1300']