KG-MO 2012 Problem 2

Given positive real numbers ${a_1},{a_2},...,{a_n}$ with ${a_1}+{a_2}+...+{a_n}= 1$ . Prove that $\left({\frac{1}{{a_1^2}}-1}\right)\left({\frac{1}{{a_2^2}}-1}\right)...\left({\frac{1}{{a_n^2}}-1}\right)\geqslant{({n^2}-1)^n}$ .