Consider the quadratic equation $$(c-5)x^2 - 2cx + (c-4) = 0$$, $$c \neq 5$$. Let $$S$$ be the set of all integral values of $$c$$ for which one root of the equation lies in the interval $$(0, 2)$$ and its other root lies in the interval $$(2, 3)$$. Then the number of elements in $$S$$ is:

A

11

B

12

C

18

D

10