CMO 2009 Problem 4

Given an integer $n > 3.$ Let $a_{1},a_{2},\cdots,a_{n}$ be real numbers satisfying $min |a_{i} - a_{j}| = 1, 1\le i\le j\le n.$ Find the minimum value of $\sum_{k = 1}^n|a_{k}|^3.$