The russians had a pretty cool solution for problems like this on their Mig29 backfire bombers.
Now russian military airports are messy (and I mean like chunk and rusting aircraft rotting away on runways, oil, animals, etc. The russian reasoning behind that is: In war you can not always expect to have a perfectly clean airport.
So the Mig29 had air intakes opening towards the top for take offs and landings. The main air intakes are closed up for that time. Once the plane has gained hight, they open the vents. There is still a small risk, but that gets smaller the higher the plane flies.
I am not sure how applicable that would be for conventional planes though, since their air intakes are much larger (for fuel efficiency reasons).
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