Box of Chocolates

Chef just got a box of chocolates as his birthday gift. The box contains $N$ chocolates in a row (numbered $1$ through $N$), where $N$ is even. For each valid $i$, the $i$-th chocolate has a *sweetness value* $W_i$. Chef wants to eat all the chocolates in the first half of the box and leave all chocolates in the second half uneaten. Since he does not like chocolates that are too sweet, he will