BALKAN-SL 2014 A5

$\boxed{A5}$ Let $n\in{N},n>2$ ,and suppose $a_1,a_2,...,a_{2n}$ is a permutation of the numbers $1,2,...,2n$ such that $a_1<a_3<...<a_{2n-1}$ and $a_2>a_4>...>a_{2n}.$ Prove that $$(a_1-a_2)^2+(a_3-a_4)^2+...+(a_{2n-1}-a_{2n})^2>n^3$$