If $$a,b,c$$ are distinct real numbers such that $$a+\frac{1}{b}=b+\frac{1}{c}=c+\frac{1}{a}$$, evaluate $$abc$$.

A

$$\pm\sqrt{2}$$

B

$$\sqrt{2}-1$$

C

$$\sqrt{3}$$

D

$$\pm1$$