Matthew Woods, 19, from Chorley in Lancashire, has been jailed for 12 weeks after admitting making grossly offensive comments on his Facebook page about missing 5-year-old April Jones.
He made a number of derogatory and explicit posts about April and Madeline McCann.
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Police forces in Greater Manchester and Merseyside have reported a rise in the number of violent homophobic offences so far this year.
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The family of Lee Rigby say they want to meet the Prime Minister to seek answers about his death.