Given a list of integers, write a function that returns the largest sum of non-adjacent numbers. The "largest sum of non-adjacent numbers" is the sum of any subset of non-contiguous elements.
Examples:
>>> coding_problem_09([2, 4, 6, 8])
12
>>> coding_problem_09([5, 1, 1, 5])
10
>>> coding_problem_09([1, 2, 3, 4, 5, 6])
12
>>> coding_problem_09([-8, 4, -3, 2, 3, 4])
10
>>> coding_problem_09([2, 4, 6, 2, 5])
13