Race Map Labeling

The organizing committee of a motorcycle race labels the contest map. The map has $n$ places numbered $0$ through $n-1$. Every road is bidirectional and joins two different places.

Each place gets the label $0$ for regular or $1$ for service. If $d_i$ roads reach place $i$, then at most $\lfloor d_i / 2 \rfloor$ of its neighbors may carry the same label as place $i$. Several labelings usually satisfy that rule, so only the labeling produced by the following procedure counts as correct.

1. Give every place the label $0$.
2. While some place breaks the rule, take the smallest-numbered such place and flip its label: $0$ becomes $1$, and $1$ becomes $0$.
3. Repeat step 2 until no place breaks the rule.

Each flip raises the number of roads whose two ends carry different labels by at least $1$, so the procedure always stops after finitely many flips.

The first line contains the number of places $n$. ($1 \le n \le 1000$)

Each of the next $n$ lines describes one place, line $i$ describing place $i$. ($i = 0, 1, \dots, n-1$) A line has this form.

number_of_neighbors: neighbor1 neighbor2 ... neighborm

number_of_neighbors is the number of roads reaching place $i$, followed by the numbers of the neighboring places separated by spaces. The line 2: 1 2 means two neighbors, numbered $1$ and $2$.

No road joins a place to itself, and two places are joined by at most one road. If $b$ appears in the neighbor list of place $a$, then $a$ appears in the neighbor list of place $b$. The line of a place with no neighbor ends right after the colon.

Print $n$ on the first line. Then print $n$ lines, one per place starting from place $0$, each carrying the label the procedure produced. A line has this form.

label number_of_neighbors: neighbor1 neighbor2 ... neighborm

label is $0$ for a regular place and $1$ for a service place. Print the neighbor list in the order it was given in the input. Separate tokens with one space, and put the colon directly after number_of_neighbors. The line of a place with no neighbor ends right after the colon.