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Sometime between 8am and 8.30am, a 12-year-old girl was walking along Marden Way in Petersfield when she noticed three men in a van.
They swore at her and threw litter at her, so she quickened her pace to get away from them.
One of the men then opened the door of the van and told her to get into the van.
The girl ignored the men and ran off.
Detectives have now released an e-fit of one of the men.
Detective Constable Iain Turner, from Alton CID, said: “Do you recognise this man? If so, please get in touch.
“This was obviously a very frightening situation for the girl concerned and we are keeping an open mind as to the nature of this incident.
“It may be that the men thought it would be amusing to try and frighten the girl and we urgently need to trace them so we can establish the exact nature of what happened
“The girl did the right thing by running away and raising the alarm, and I would like to remind people to ensure their children are aware of the stranger danger message.”
Anyone with any information should contact Det Con Turner at Alton CID on 101 or Crimestoppers anonymously on 0800 555 111.