Erdős problem 34

For any permutation $\pi\in S_n$ of $\{1,\ldots,n\}$ let $S(\pi)$ count the number of distinct consecutive sums, that is, sums of the shape $\sum_{u\leq i\leq v}\pi(i)$. Is it true that $$S(\pi) = o(n^2)$$ for all $\pi\in S_n$?