The map below represents a neighborhood. Each node represents a house, and the segments represent the paths between those houses. Alice's house is shown in red, and Bob's house is shown in green.

Alice is going to Bob's house to celebrate his birthday. For each house that she visits along the way, she will invite one person from that house. Additionally, Alice will not visit the same house (including her own house) or pass through the same path more than once.

What is the maximum even number of people Alice can invite?

Details and Assumptions:

  • Alice cannot turn while in the middle of a path represented by a black line segment, she can only turn while at one of the houses.

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