Let $$\left[\cdot\right]$$ denote the greatest integer function, and let f (x) = $$\min \left\{\sqrt{2x},x^{2}\right\}$$. Let S = $$\left\{x \in (-2,2): \text{the function,} g(x)= |x|\left[x^{2}\right]\text{is discontinuous at x} \right\}.$$ Then $$\sum_{x\in S}f(x)$$ equals

A

$$2-\sqrt{2}$$

B

$$1-\sqrt{2}$$

C

$$2\sqrt{6}-3\sqrt{2}$$

D

$$\sqrt{6}-2\sqrt{2}$$