Prove inequality $(a_1+a_2+...+a_n)(\frac1{a_1}+\frac1{a_2}+...+\frac1{a_n})\geq n^2$ when $a_1,a_2,...,a_n$ are positive numbers.

Question

Let's assume that $a_{1},a_{2},...,a_{n}$ are positive. How to prove this inequality:

$(a_{1}+a_{2}+...+a_{n})(\frac{1}{a_{1}}+\frac{1}{a_{2}}+...+\frac{1}{a_{n}})\geq n^{2}$

My effort: I don't know where to begin.