Liverpool F.C and Manchester United F.C are having a football match in the stadium. At first, there are $$1000$$ more Liverpool fans than Manchester United fans in the stadium. $$30$$ minutes later, $$472$$ Liverpool fans, and $$4836$$ Manchester United fans enter the stadium. The number of Manchester United fans is $$3$$ times that of Liverpool fans. How many Liverpool fans are there at first? 
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