Simulate satellite message propagation with timing

Design and implement the SatelliteNetwork to process a stream of N instructions:

• SatelliteConnected(SatelliteId): add a satellite; invoke ErrDuplicateSatellite(SatelliteId) if the satellite connects more than once.
• RelationshipEstablished(SatelliteId1, SatelliteId 2): add a bidirectional link; if either SatelliteId does not exist, skip the instruction and invoke ErrInvalidSatellite(the invalid id).
• MessageReceived(M, id1..idM): treat the listed M satellites as simultaneously notified at time t = 0. Propagation rules:
• A satellite forwards the message to each direct neighbor that has not yet been notified, one neighbor at a time, in increasing SatelliteId order; each send takes exactly 10 seconds.
• Different satellites may concurrently attempt to notify the same neighbor; each attempt still consumes 10 seconds, but as soon as any attempt completes, that neighbor is considered notified and no further attempts to it should proceed.
• A satellite never attempts to notify the satellite that notified it. Post-notification processing:
• After all of its direct neighbors have been notified, a satellite spends 30 seconds processing the message and then reports back to Earth. Reporting:
• Call OnSatelliteReportedBack(SatelliteId) at each satellite’s report completion time; if two reports complete at the same time, report the smaller SatelliteId first. Task: Provide data structures and an algorithm that consume the instruction stream online and trigger OnSatelliteReportedBack calls in the correct order for any input, handling duplicates/invalid references as specified. Explain your approach and analyze time and space complexity.