Consider the polynomial \( P(x) \) with integer coefficients such that:
\[ P(1) = P(3) = P(5) = P(7) = a \]
and
\[ P(2) = P(4) = P(6) = P(8) = -a. \]
Determine the smallest possible value of \( a \). Let's think step by step and output the final answer within \boxed{}.
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