CN-SMO 2013 Problem 8

$n\geq 3$ is a integer. $\alpha,\beta,\gamma \in (0,1)$ . For every $a_k,b_k,c_k\geq0(k=1,2,\dotsc,n)$ with $\sum\limits_{k=1}^n(k+\alpha)a_k\leq \alpha, \sum\limits_{k=1}^n(k+\beta)b_k\leq \beta, \sum\limits_{k=1}^n(k+\gamma)c_k\leq \gamma$ , we always have $\sum\limits_{k=1}^n(k+\lambda)a_kb_kc_k\leq \lambda$ . Find the minimum of $\lambda$