Let $f(x) = x^{2}(1-x)^{2}$. What is the value of the sum
\begin{align*}
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)?
\end{align*}

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