Skiers

On the southern slope of a mountain there are several ski tracks and a single ski lift. Every track runs from the top station of the lift down to the bottom station. Each morning a team of lift workers inspects the tracks: they ride the lift up together to the top station, and then each worker skis down to the bottom station along a track of their own choosing. Every worker skis down exactly once. Different workers' routes may share sections. Every route always leads downwards.

The ski area is a network of clearings joined by cuttings through the forest. Every clearing sits at a distinct height, and any two clearings are joined by at most one cutting. Skiing from the top to the bottom, a worker can pass through any clearing (though not necessarily all of them in a single run). Routes meet only at clearings; there are no tunnels or bridges.

A cutting is inspected when at least one worker skis along it. The workers want to inspect every cutting between the clearings using as few workers as possible.

Write a program that reads the map of ski tracks and computes the minimum number of workers whose routes together cover every cutting.

The first line contains one integer $n$, the number of clearings ($2 \le n \le 5000$). The clearings are numbered from $1$ to $n$: clearing $1$ is the top station of the lift and clearing $n$ is the bottom station.

Each of the next $n-1$ lines describes the downward cuttings leaving one clearing. Line $i+1$ (for $i$ from $1$ to $n-1$) describes clearing $i$: it begins with an integer $k$, the number of cuttings that lead down from clearing $i$, followed by the numbers of the $k$ clearings they lead to, listed from west to east in the order the cuttings are arranged.

Output a single integer: the minimum number of workers whose routes together inspect every cutting in the forest.