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Question about Lightning / AMP

My understanding of AMP is that a transaction is split in pieces and routed through Multiple Paths. Can these pieces also route sequentially through the same channel? In this case it should be easy to route nearly any amount over an established route. Just divide the amount by the channel capacity and send x tansactions through the channel. Routing $100 through a $1 channel would require 100 transactions. Maybe I missed something. I couldn‘d find these details.
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