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Find the largest sum such that no two elements are touching
Inspired by this (off topic) post
Given an array of numbers, find the largest sum over a subset not containing two consecutive elements
[1,2,3,4] -> 6 // [_,2,_,4]
[1,2,3,4,5] -> 9 // [1,_,3,_,5]
[1,1,0,0,1,0,0,1] -> 3 ...