Let $f(x) = x^{2}(1-x)^{2}$. Find the value of the sum
\[f \left(\frac{1}{2019} \right)-f  \left(\frac{2}{2019} \right)+f \left(\frac{3}{2019} \right)-f \left(\frac{4}{2019} \right)+\cdots + f \left(\frac{2017}{2019} \right) - f \left(\frac{2018}{2019} \right).\]

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