# Fraction of Fraction

$\large a + \frac{1}{b + \frac{1}{c + \frac{1}{d}}} = \dfrac{229}{99}$

If $$a, b, c$$ and $$d$$ are positive integers satisfying the equation above, find the value of $$a^{2} + b^{2} + c^{2} + d^{2}$$.

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