Description

Bob enjoys playing computer games, especially strategy games. However, he often struggles to find quick ways to beat them. Now he has a problem.

He owns an ancient castle where the roads form a tree structure. He wants to place the minimum number of soldiers on the nodes of this tree so that these soldiers can watch over all the roads.

Note: When a soldier is placed on a node, all edges connected to that node can be observed.

Please write a program that, given a tree, helps Bob calculate the minimum number of soldiers he needs to place.

Input Format

The input data represents a tree, described as follows.

The first line contains a number $N$, representing the number of nodes in the tree.

The second to the $(N+1)$-th lines each describe a node's information, in the order of the node's index $i$, a numerical value $k$, where $k$ indicates that there are $k$ edges connected to node $i$, followed by $k$ numbers representing the indices of the connected nodes $r_1, r_2, \cdots, r_k$.

For a tree with $N$ nodes, the node indices range from $0$ to $N-1$, and each edge appears only once in the input file.

Output Format

The output contains only one number, which is the minimum number of soldiers required.

Sample 1

4
0 1 1
1 2 2 3
2 0
3 0

1

Data Range and Hint

For $100\%$ of the data, $0 < N \le 1500$.