RO-TST 2014 Problem 12

Determine the smallest real constant $c$ such that $$\sum_{k=1}^{n}\left ( \frac{1}{k}\sum_{j=1}^{k}x_j \right )^2\leq c\sum_{k=1}^{n}x_k^2$$ for all positive integers $n$ and all positive real numbers $x_1,\cdots ,x_n$ .