1882B · Sets and Union

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

Input Format: 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 $S_{i}$.

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

Note: In 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 $S = \varnothing$.