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RAM raiders smashed their way into the Co-op store in Faversham early today.
They backed a Peugeot through the glass front doors at about 4.15am and stole £1,000 worth of cigarettes.
Police are examining CCTV footage. People who woke to the noise of the alarm reported seeing three people, including a woman.
The driver is described as tall and aged 25 to 30. There are no other descriptions.
A police spokeswoman said: "The crime scene is being preserved for our crime scene investigation unit to come down and dust for fingerprints.
"We would appeal for anyone who might have been offered cheap cigarettes to come forward and ring Crimestoppers on 0800 555111."