I am having trouble with the following question:

Let X be a single random variable having a Binomial distribution. You will use X to test H_0: p = 1/2 versus H_1: p does not equal 1/2. Find an expression for the Generalized Likelihood Ratio Test statistic and use this to show that the critical region of the likelihood ratio test can be written as xlnx +(n-x)ln(n-x) >= c for some constant c.

Any help would be great. Thanks.