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Turkmenistan is a rather safe place. Violent crimes are almost non-existent, but petty crime rate have increased. For this reason, visitors are pre-warned and told to be very careful, especially when out on the streets.
Another thing to be aware of in going to Turkmenistan is their dishes. Most of them are cooked with coconut oil and not everyone is used to this. Thus, before eating any Turkmen food, check if one's stomach is ready to digest that kind of oil. Unlike other oils this county has to offer, coco oil is the widely used. Perhaps due to its price that it doesn't make such a name in the world.