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A man suffered a cut to his chin during an altercation with another man.
The man was attacked with a sharp object, but police investigating the incident say it is not known what sort of object it was.
Officers are urging anyone who saw the incident, which happened on Chatham High Street shortly after 1pm on Friday, to contact them.
It happened outside a kebab shop near the junction with Medway Street.
The suspect is thought to have left the scene in a car.
Anyone who witnessed the incident or has any further information is urged to call the appeal line on 01634 792209, quoting reference 46/148848/19 or call Crimestoppers anonymously on 0800 555111.