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Women are walking in pairs after a series of attacks on women in the Gillingham area - which police say could be linked.
Worrying incidents at Riverside Country Park and the Woodlands Road area have been reportedv in recent weeks.
Police are appealing for anyone with information to contact them, and are keeping an open mind as to whether the attacks could be connected.
The first happened in the country park in Lower Rainham Road at 9am on August 12 when a woman was sexually assaulted as she walked along the riverbank.
She was inappropriately touched by a white man wearing a grey tracksuit, who was said to be aged 20 to 30, 5ft 8in and of normal build.
The next came when a woman in her 50s was walking near Motney Hill Road at about 8.30am on October 9.
She heard someone running behind her and as she stepped to one side, a man grabbed her. She fell to the ground, and the man left.
Police released an e-fit of the suspect, who was described as white, aged between 40 and 50, of medium build, 5ft 9in, with stubble and wearing a grey hoodie.
The small car park on Motney Hill Road is listed on a swinging website as a good spot for "daytime fun".
Two incidents were then reported around Woodlands Road on October 16.
At 8.52am police received a report from a woman who said a man was acting suspiciously.
Officers then received a call from another woman between 9.20am and 9.45am, who told them she had been approached by a man who was running.
He stopped and inappropriately touched her before running away.
The same day, at about 4.45pm, officers received a report of an assault at Riverside Country Park when a woman says she was hit and pushed by an unknown man.
One woman, who walks her dog in the area but didn't want to be named, said at the time: "I heard there were two attacks in the alleyway alongside Woodlands cemetery.
"We're all walking in pairs now around Riverside Country Park.
A spokesman for police in Medway, added: "Detectives are not ruling out the possibility that the incidents recently reported to have happened in Gillingham and Riverside Country Park are linked and would encourage anyone with information to contact police."
Anyone who can help is asked to call officers on 101.
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