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.
For example for the tree:
the solution is one soldier ( at the node 1).

The input 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_identifier
_{1}node_identifier_{2}... node_identifier_{number_of_roads}or node_identifier:(0)

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