AUSTRIAN-POLISH 1982 Problem 9

Define $S_n=\sum_{j,k=1}^{n} \frac{1}{\sqrt{j^2+k^2}}$ . Find a positive constant $C$ such that the inequality $n\le S_n \le Cn$ holds for all $n \ge 3$ . (Note. The smaller $C$ , the better the solution.)