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The function f:NNf:\mathbb{N}\to\mathbb{N} satisfies: m2+f(n)mf(m)+n    (m,n)N2.m^2+f(n)\mid mf(m)+n ~~~\forall ~(m,n)\in\mathbb{N}^2. Let the sum of all possible values of f(2014)f(2014) be NN. Find the value of Nmod1000N\bmod{1000}.

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