Let $$a$$, $$b$$, $$c$$ be the lengths of the sides of a triangle $$ABC$$. Let $$\alpha$$, $$\beta$$, $$\gamma$$ be positive integers and $$p = \beta a + \gamma b + \alpha c$$, $$q = \gamma a + \alpha b + \beta c$$ and $$r = \alpha a + \beta b + \gamma c$$. Then $$p$$, $$q$$, $$r$$ are lengths of the sides of a triangle

A

only if $$\alpha$$, $$\beta$$, $$\gamma$$ are all distinct

B

only if $$\alpha + \beta > \gamma$$, $$\beta + \gamma > \alpha$$, $$\gamma + \alpha > \beta$$

C

only if $$\alpha > \beta > \gamma$$

D

only if $$\alpha > a$$, $$\beta > b$$, $$\gamma > c$$

E

for all values of $$\alpha$$, $$\beta$$, $$\gamma$$