An airline company is planning to introduce a network of connections between the ten different airports of Sawubonia. The airports are ranked by priority from first to last (with no ties). We call such a network *feasible* if it satisfies the following conditions:

- All connections operate in both directions.
- If there is a direct connection between two airports $A$ and $B$, and $C$ has higher priority than $B$, then there must also be a direct connection between $A$ and $C$.

Some of the airports may not be served, and even the empty network (no connections at all) is allowed. How many feasible networks are there?

Let's think step by step and output the final answer within \boxed{}.
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