Let f(x) be a polynomial of degree 6 with leading coefficient 2009 . Suppose further, that f(1)=1...

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Let f(x) be a polynomial of degree 6 with leading coefficient 2009 . Suppose further, that f(1)=1, f(2)=3, f(3)=5, f(4)=7, f(5)=9, f^'(2)=2, then the sum of all the digits of f(6) is

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