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$\large f(x)= x^{150} + x^{2} -7x + 1$

Let $x_{1}$, $x_{2}$, $x_{3}$$\ldots$ $x_{150}$ be the roots of the above equation. Define

$\large S = \huge \sum_{i=1}^{150}\dfrac{1}{(1+x_{i})^{2}}$

Find $|S|$.

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