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Leicester boss Claudio Ranieri has warned his leaders they must win the league because no-one remembers the runner-up.
The Foxes are seven points clear at the top of the Barclays Premier League and need just three wins from their last five games to claim the title.
They host West Ham on Sunday, 24 hours before nearest rivals Tottenham go to Stoke, before playing Swansea, Manchester United, Everton and Chelsea.
Previous shock footballing winners have included Denmark and Greece clinching the European Championship in 1992 and 2004 respectively w hile newly-promoted Nottingham Forest won the top flight in 1978.
And Ranieri insisted Leicester must win the title if they want to write their own names in history and be compared to previous victors.
He said: "We've made a good story, but to make something you will remember in 30 or 40 years we have to win.
"We don't achieve anything yet. We have to fight to achieve the Champions League.
"Football is very strange. If you weren't here in Leicester but somewhere else, maybe City or United, with seven points more, you would say 'it is finished'.
"At this moment you don't think this. Why? Because we are Leicester. We have to fight and we have to be focused and strong."
Leicester wrapped up a top-four spot with a 2-0 win over Sunderland last week to guarantee at least a Champions League play-off place.
They have won their last five games and are odds-on to win their first top-flight title but Ranieri does not feel they have qualified having not yet made the group stages.
"It is two matches and two matches is not the Champions League, I want to play six. I don't think there is the (Champions League) music," he said.
"I love the music. I think it will be a fantastic achievement. From the dream arrives the reality, but wait first."
Riyad Mahrez, Jamie Vardy and N'Golo Kante have also all been nominated for the PFA Player of the Year and Ranieri hopes at least one can win.
He said: "I am very proud because they deserve it. They are doing a fantastic performance in every match and I hope one of them can win. They are three sons for me. If one son wins I am very happy."
Ranieri has no fresh injury worries against the Hammers but does not expect Matty James to play this season with the midfielder having been out for almost a year with a knee injury.