CWMO 2016 Problem 6

Let $a_1,a_2,\ldots,a_n$ be non-negative real numbers , $S_k= \sum\limits_{i=1}^{k}a_i$ $(1\le k\le n)$ .Prove that $$\sum\limits_{i=1}^{n}\left(a_iS_i\sum\limits_{j=i}^{n}a^2_j\right)\le \sum\limits_{i=1}^{n}\left(a_iS_i\right)^2$$