# Symmetric Expressions Often Have Obvious Solutions. This One Doesn't.

Algebra Level 5

What is the maximum possible value of the expression $\sum^{200}_{i=1}|a_i-2a_{i+1}|,$ where $$a_1, a_2, \ldots, a_{201}$$ are real numbers such that $$1\leq a_i\leq 4$$ for $$i=1$$ to 201?

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