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Turkish authorities have arrested a family of six who it was feared were travelling to Syria.
The alarm was raised on Thursday after parents Asif Malik, 31, and Sara Kiran, 29, left without mentioning travel plans to family members.
They were last seen boarding a ferry to France at the Port of Dover on Wednesday, April 8, at 12.30am.
Their disappearance was described as "entirely out of character" for the family, which also includes children, Zoha Malik, 7, Essa Malik, 4, Zakariya Malik, 2, and Yhaya Malik, 1.
Thames Valley Police say inquiries suggested the family travelled south through Europe, possibly by train.
It is believed they may have travelled through Budapest, Hungary, on or around Sunday, April 12.
"We are extremely concerned for the safety of this family, especially the four young children..." - Det Ch Con John Campbell
Officers have raised fears the family could be travelling to Syria based on concerns from relatives and information posted online by the Islamic State (ISIL).
Acting Deputy Chief Constable, John Campbell said: "We are extremely concerned for the safety of this family, especially the four young children.
"We are reaching out to Asif and Sara, in the hope that they hear our messages and we encourage them to make contact with us so we can return them safely to their families who are extremely worried about them.
“We would urge anyone with information about the family’s whereabouts to come forward and speak to police so the family can safely return to the UK.
“We would ask anyone who saw the family as they travelled to Dover, waiting at the port, on the ferry or when they arrived at Calais to contact the police.
"Any piece of information, no matter how small, could help the UK or European authorities to locate the family so that they can be safely returned home to their loved ones.
“We are concerned about anyone who has or is intending to travel to the part of Syria that is controlled by the terrorist group calling themselves Islamic State. It is an extremely dangerous place and not a place where young children should be taken.
“The choice of returning home from Syria is often taken away from those under the control of Islamic State, leaving families in the UK devastated and with very few options to secure their loved ones safe return.”
In a statement, family members say they are “distraught” and urge anyone else considering leaving in this manner to consider the impact on loved ones.
Anyone with information is asked to call Thames Valley Police on 101 quoting reference number 342 or from outside the UK by calling 0044 1865 841 148.