King's Quest

Once upon a time there lived a king who had $N$ sons. In his kingdom there were also $N$ beautiful girls, and the king knew, for each of his sons, which of those girls he liked. The sons were young and light-headed, so a single son could like several girls.

The king asked his wizard to pick, for each son, one girl that he likes so that the son could marry her — and the wizard did it. Each son was assigned a girl he likes, and of course each girl may marry only one son.

Looking at the list, the king said: “I like the list, but I am not fully satisfied. For each son I want to know every girl he could marry. Naturally, after he marries any one of them, it must still be possible to assign every other son a different girl he likes.”

Formally, for each son $i$ you must report all girls $g$ such that $i$ likes $g$ and there exists a perfect matching (each son paired with a distinct girl he likes) in which son $i$ is matched to girl $g$. Solve this problem to save the wizard's head.

The first line contains $N$ — the number of the king's sons ($1 \le N \le 2000$).

Each of the next $N$ lines describes the girls one son likes: first $K_i$ — the number of girls — followed by $K_i$ distinct integers between $1$ and $N$ denoting those girls. The sum of all $K_i$ does not exceed $200\,000$.

The last line contains the wizard's original list: $N$ distinct integers, where the $i$-th number is the girl that son $i$ marries in that list. The list is guaranteed to be valid, i.e. every son likes the girl assigned to him.

Output $N$ lines. For son $i$, first print $L_i$ — the number of distinct girls he likes and could marry so that every other son can still be matched to a girl he likes. Then, on the same line, print those girls' numbers in ascending order.

(The original statement allowed printing the girls in any order; to make the answer unique for automatic grading, print them in ascending order.)