China Southeastern Mathematical Olympiad

Let $n\ge 3$ be integer. Suppose that $\alpha ,\beta ,\gamma \in (0,1)$ and $a_k,b_k,c_k\ge 0$ $(k=1,2,\dots ,n)$ satisfy ${\sum }_{k=1}^n(k+\alpha )a_k\le \alpha$, ${\sum }_{k=1}^n(k+\beta )b_k\le \beta$ and ${\sum }_{k=1}^n(k+\gamma )c_k\le \gamma$. Find the minimum of $\lambda$ such that ${\sum }_{k=1}^n(k+\lambda )a_k{b}_k{c}_k\le \lambda$.