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Let f(x) be a polynomial of degree 6 wit...

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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