In this problem, we consider only polynomials with integer coeffients. Call two polynomials $p$ and $q$ [i]really close[/i] if $p(2k + 1) \equiv q(2k + 1)$ (mod $210$) for all $k \in Z^+$. Call a polynomial $p$ [i]partial credit[/i] if no polynomial of lesser degree is [i]really close[/i] to it. What is the maximum possible degree of [i]partial credit[/i]?


Let's think step by step and output the final answer within \boxed{}.
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