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I don't know if it's just me, but the test cases for later problems are getting more annoying associated with minor issues of handling large numbers.
Anyway, I've got an solution for this problem. To arrive at the answer skipping the unneccessary intermediate steps, generate a list of all 's at the beginning (and this is where Python fails on the server without modulo, but not on my machine). It can be achieved easily if you observe the cases for odd and even separately.
After that, to get to the answer is just a matter of accumulating those 's. You are just one step away when you have the highest element of the answer.