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The function f:N→Nf:\mathbb{N}\to\mathbb{N}f:N→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.m2+f(n)∣mf(m)+n ∀ (m,n)∈N2. Let the sum of all possible values of f(2014)f(2014)f(2014) be NNN. Find the value of N mod 1000N\bmod{1000}Nmod1000.
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