$\mathbf{5 5}$ Set $A=\{0,1,2, \cdots, 9\}, B_{1}, B_{2}, \cdots, B_{k}$ are a family of non-empty subsets of $A$, and when $i \neq$ $j$, $B_{i} \cap B_{j}$ has at most two elements. Find the maximum value of $k$.