A16183 | Sets and Union

You 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, $\{2, 4, 6\} \cup \{2, 3\} \cup \{3, 6, 7\} = \{2, 3, 4, 6, 7\}$ .

Each 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 $S_{i}$ .

For each test case, print a single integer — the maximum number of elements in an attainable $S$ such that $S \neq S_{1} \cup S_{2} \cup \ldots \cup S_{n}$ .