P2999 [USACO10NOV] Chocolate Milk S

Farmer John's milk production and shipping system is an intricate one! He uses milking machines for his many cows to harvest the milk that then flows into pipes. Each of these pipes connects a milking machine to a joint, where it might be joined by exactly one more pipe (the milk flowing through both pipes merges). The milk then flows through additional pipes (which all start and end at joints) until it reaches the long central pipe connecting to the distribution room. The milk then goes through a reverse process of splitting at various joints until it is flows into milk tanks that are picked up and taken to market. Farmer John notices that there is at most one way for milk to travel from one joint to any other joint. Furthermore, since Farmer John is an efficient man by nature, he has made sure that milk will flow through each and every pipe; in other words, no pipe is unneeded. If we think of a milking machine, joint, or milk tank as a node, there are N (2 9 ``` Visual inspection shows that the chocolate inserter can be installed at either joint 6 or 7, as all milk flows through those joints.

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