Bosses

A company of $n$ employees is due for a restructuring. The new hierarchy is a rooted tree, and every node is the boss of its children.

Each employee has a list of employees they accept as their boss. Every employee must also be assigned a salary. A salary is a positive integer, and the salary of each boss must be larger than the sum of the salaries of their immediate subordinates.

Structure the company so that all of the above conditions hold and the sum of all salaries is as small as possible.

The first input line contains an integer $n$: the number of employees. The employees are numbered $1$, $2$, $\dots$, $n$.

After this, the input contains $n$ lines that describe the preferences of the employees. The $i$th such line contains an integer $k_i$, followed by a list of $k_i$ integers. The list consists of all employees that the $i$th employee accepts as their boss.

Here $1 \le n \le 300$ and the sum of all $k_i$ is at most $5\,000$. The numbers on one line are distinct and never include $i$ itself.

Print the lowest total salary among all valid restructurings on one line. You can assume that at least one solution exists.