Erdős problem 867

Is it true that if $A=\{a_1<\cdots <a_t\}\subseteq \{1,\ldots,N\}$ has no solutions to $$a_i+a_{i+1}+\cdots+a_j\in A$$ then $$\lvert A\rvert \leq \frac{N}{2}+O(1)?$$