Cluster Message Aggregation

You are given a tree of machines (nodes) where each node can only communicate with its direct parent and children through asynchronous messages. The tree is described by a parent array: for node i, parent[i] is its parent index (-1 for the root). Your task is to implement two independent aggregation operations that must run on this distributed cluster without global knowledge:

1. CountAggregation – every node must ultimately know the total number of machines in the tree.
2. TopologyAggregation – every node must ultimately know the exact string serialization of the entire tree topology. The serialization of a leaf is simply its id, while the serialization of an internal node is its id followed by its children’s serializations in order, wrapped in parentheses and comma-separated.

You may only add code inside the receiveMessage(message) handler that each node already exposes. The provided messaging primitives are:

• sendAsyncMessage(targetId, message) – non-blocking send to a single neighbor.
• Message types you can send/receive are: 'count', 'countResponse', 'topology', 'topologyResponse'.

When the algorithm finishes, the root must be able to print the total count and the topology string. The whole process must be initiated by the root sending initial messages to its children and must work for arbitrary tree shapes up to the given constraints.