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A man reportedly sexually assaulted a woman inside a high street shop before exposing himself to a man and another woman.
Police have since arrested a 31-year-old man following the incidents in Sheerness.
It happened at about 9.30am on Monday.
The suspect is described as being black, in his early 30s and about 5ft 7ins tall with a medium build.
A man from Sydenham Hill, London, was arrested on the morning of the offences and has since been released on bail, pending further enquiries, until August 30.
Multiple witnesses have already provided a statement to officers. However, it is believed there are people with important information who are yet to make a formal report.
Anyone with information is asked to contact police on 01795 419119 quoting 46/138649/21, or call the independent charity Crimestoppers anonymously on 0800 555111 or complete the online form.