Strategic Game

Time Limit: 10 Seconds
Memory Limit: 32768 KB

Bob enjoys playing computer games, especially strategic games, but sometimes he
cannot find the solution fast enough and then he is very sad. Now he has the
following problem. He must defend a medieval city, the roads of which form a
tree. He has to put the minimum number of soldiers on the nodes so that they
can observe all the edges. Can you help him?

Your program should find the minimum number of soldiers that Bob has to put
for a given tree.

The input file contains several data sets in text format. Each data set represents
a tree with the following description:

the number of nodes

the description of each node in the following format

node_identifier:(number_of_roads) node_identifier1 node_identifier2 ... node_identifier

or

node_identifier:(0)

The node identifiers are integer numbers between 0 and n-1, for n nodes (0 <
n <= 1500). Every edge appears only once in the input data.

For example for the tree:

the solution is one soldier ( at the node 1).

The output should be printed on the standard output. For each given input data
set, print one integer number in a single line that gives the result (the minimum
number of soldiers). An example is given in the following table:

**Input**

4

0:(1) 1

1:(2) 2 3

2:(0)

3:(0)

5

3:(3) 1 4 2

1:(1) 0

2:(0)

0:(0)

4:(0)

**Output**

1

2

Source:

**Southeastern Europe 2000**
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