Circle Eating

There are $N$ candies (numbered $1$ through $N$) on a circular table. For each valid $i$, candies $i$ and $i+1$ are adjacent; candies $1$ and $N$ are also adjacent. You want to eat all these candies. Initially, your *happiness level* is $0$. For each valid $i$, when you eat the $i$-th candy, the happiness level increases by $a_i$. Note that $a_i$ may be negative and your happiness level may als