Counting surjective functions

Let \(I_7=\{1,2,3,4,5,6,7\}\). Let \(N\) be the number of surjective functions \(f:I_7\to I_7\) such that \(f(f(a))\neq a\) for all values of \(a\). What are the last three digits of \(N\)?

Details and assumptions

A function \(f:A \to B\) is surjective if for each \(b \in B\), there exists \(a\in A\) such that \(f(a)=b\).

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