For each subset T of U=\{1,2,3, \ldots, 18\}, let s(T) be the sum of the elements of T, with s(\varnothing) defined to be 0 . If T is chosen at random among all subsets of U, the probability that s(T) is divisible by 3 is \frac{m}{n}, where m and n are relatively prime positive integers. Find m.