Let the domain of the function $$f(x)=\log_{3}\log_{5}\log_{7}(9x-x^{2}-13)$$ be the interval (m, n). Let the hyperbola $$\f\frac{x^{2}}{a^{2}}-\f\frac{y^{2}}{b^{2}}=1$$ have eccentricity $$\f\frac{n}{3}$$ and the length of the latus rectum $$\f\frac{8m}{3}$$. Then $$b^{2}-a^{2}$$ is equal to:

A

11

B

7

C

5

D

9