Find the largest integer n, where 2009^n divides (2008^(2009^2010) + 2010^(2009 ^2008))

So, the only observation I've made is that you can rewrite this in the form:

(x-1)^(x^(x+1)) + (x+1)^(x^(x-1))

I also know that I have to use the binomial theorem, but I'm not exactly sure how that relates to finding the largest n possible...

Help?