Simplify $$\frac{1}{2 + 2p} + \frac{1}{2 + 2q} + \frac{1}{2 + 2r}$$, where $$p = \frac{x}{y + z}$$, if $$q = \frac{y}{z + x}$$ and $$r = \frac{z}{x + y}$$.

A

1

B

x + y + z

C

2

D

$$\frac{1}{2}$$