Ukrainian President Petro Poroshenko has said the entry of more than 100 Russian aid trucks into the country is a "flagrant violation of international law."
In a statement on his website, he added none of the trucks' cargo had been checked before being driven in.
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Motorists who cause death by speeding, street racing or while on a mobile phone are among those who could be handed tougher punishments.
Cubans have lined the streets since Thursday as the ashes of the Communist leader were driven on a 600-mile journey across the island.
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