[probabilistic method] Say a subset S of the non-negative integers is a pairwise cover if every positive integer i can be expressed as the sum of two integers in S. Define the density of S to be the function f where f(n) = |S intersect {1,2,...,n}|. Prove the existence of a pairwise cover whose density is o(n). Hint: Generate a random S as follows: for each i independently, put i in S with some probability p(i). Show that with positive probability S is a pairwise cover with density o(n).