Let the function \( f(x) = \frac{x}{3} + \frac{3}{x} + 3, \ x \neq 0 \) be strictly increasing in \( (-\infty, \alpha_{1}) \cup (\alpha_{2}, \infty) \) and strictly decreasing in \( (\alpha_{3}, \alpha_{4}) \cup (\alpha_{4}, \alpha_{5}) \). Then \( \displaystyle \sum_{i=1}^{5}\alpha_{i}^{2} \) is equal to:
