"...if you require a Visa to enter the Republic of Cyprus (the South) there will be a record of entry but not of exit ..."
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Funny story, 40 years ago, as an 18 year old student, I flew to Paris to attend college. After I got off the plane and got my bag, and walking around a bit dazed, I asked someone where I needed to go. They pointed me to an exit and suddenly I was out of the airport, no customs, no passport check. Later, returning from a train trip to the Netherlands, my passport was stamped in France (this is before the open borders of the EU). So when I left France for the US a year later, the passport control officer wanted to know how I had entered Europe from the US on a train. I told him the story and he stamped me out.